Add Kepler astro-bench v0.1 (pool + held-out + verifier-as-reward)
Browse files- README.md +92 -0
- heldout.jsonl +44 -0
- pool.jsonl +120 -0
- units.py +144 -0
- verifier.py +129 -0
README.md
ADDED
|
@@ -0,0 +1,92 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
---
|
| 2 |
+
license: apache-2.0
|
| 3 |
+
task_categories:
|
| 4 |
+
- text-generation
|
| 5 |
+
- question-answering
|
| 6 |
+
language:
|
| 7 |
+
- en
|
| 8 |
+
tags:
|
| 9 |
+
- astrodynamics
|
| 10 |
+
- astrophysics
|
| 11 |
+
- reasoning
|
| 12 |
+
- numeric-reasoning
|
| 13 |
+
- verifier
|
| 14 |
+
- rlvr
|
| 15 |
+
- spark-tested
|
| 16 |
+
pretty_name: Kepler astro-bench v0.1
|
| 17 |
+
size_categories:
|
| 18 |
+
- n<1K
|
| 19 |
+
configs:
|
| 20 |
+
- config_name: pool
|
| 21 |
+
data_files: pool.jsonl
|
| 22 |
+
- config_name: heldout
|
| 23 |
+
data_files: heldout.jsonl
|
| 24 |
+
---
|
| 25 |
+
# Kepler astro-bench v0.1
|
| 26 |
+
|
| 27 |
+
The benchmark behind **[Orionfold/Kepler-GGUF](https://huggingface.co/Orionfold/Kepler-GGUF)** —
|
| 28 |
+
a verifier-checked set of astrodynamics and quantitative-astrophysics word problems, each with a
|
| 29 |
+
single numeric gold answer and a **programmatic verifier that doubles as a reinforcement-learning
|
| 30 |
+
reward**.
|
| 31 |
+
|
| 32 |
+
## What's here
|
| 33 |
+
|
| 34 |
+
| File | Rows | Purpose |
|
| 35 |
+
|---|---:|---|
|
| 36 |
+
| `pool.jsonl` | 120 | Training / selection pool — 16 formula families (9 orbital, 7 astrophysics), 3 difficulty tiers. |
|
| 37 |
+
| `heldout.jsonl` | 44 | External curveball held-out — different seeds + hand-curated edge cases, **disjoint** from the pool. The number on the model card is measured here. |
|
| 38 |
+
| `verifier.py` | — | `astro_numeric_match(...)` — the scorer. |
|
| 39 |
+
| `units.py` | — | SI-unit parsing/normalization used by the verifier. |
|
| 40 |
+
|
| 41 |
+
## Row schema
|
| 42 |
+
|
| 43 |
+
```json
|
| 44 |
+
{
|
| 45 |
+
"task_id": "astro-orb-leo_period-0000",
|
| 46 |
+
"topic": "orbital_mechanics",
|
| 47 |
+
"subtopic": "leo_period",
|
| 48 |
+
"tier": 2,
|
| 49 |
+
"prompt": "A satellite orbits at altitude h = 1,030 km ... Give your final answer as \\boxed{value unit}.",
|
| 50 |
+
"answer": "105.6 min",
|
| 51 |
+
"gold_value_si": 6336.46,
|
| 52 |
+
"gold_unit": "s",
|
| 53 |
+
"rel_tol": 0.02,
|
| 54 |
+
"hand_curated": false,
|
| 55 |
+
"params": {"h_km": 1030}
|
| 56 |
+
}
|
| 57 |
+
```
|
| 58 |
+
|
| 59 |
+
All physical constants are given **in the prompt** — the task tests reasoning, not memorization.
|
| 60 |
+
The expected answer is a single `\boxed{value unit}`.
|
| 61 |
+
|
| 62 |
+
## The verifier *is* the reward
|
| 63 |
+
|
| 64 |
+
`astro_numeric_match` extracts the `\boxed{}` answer, normalizes units to SI, and checks the value
|
| 65 |
+
against the gold within a per-row relative tolerance (default ±2%). It returns a binary score, so it
|
| 66 |
+
plugs directly into an RLVR loop as the reward — the same scorer used to build Kepler's SFT corpus,
|
| 67 |
+
to gate the SFT checkpoint, and to run the head-to-head comparison.
|
| 68 |
+
|
| 69 |
+
```python
|
| 70 |
+
from verifier import astro_numeric_match # needs units.py alongside
|
| 71 |
+
|
| 72 |
+
reward = astro_numeric_match(
|
| 73 |
+
completion=model_output, # the model's full text, containing \boxed{...}
|
| 74 |
+
expected="105.6 min", # the row's "answer" field
|
| 75 |
+
rel_tolerance=0.02, # the row's "rel_tol" field
|
| 76 |
+
) # -> 1.0 if correct within tolerance, else 0.0
|
| 77 |
+
```
|
| 78 |
+
|
| 79 |
+
## Known coverage gaps
|
| 80 |
+
|
| 81 |
+
Honest about its weak spots: the families `hohmann_transfer` (two-burn transfers) and
|
| 82 |
+
`altitude_from_period` (inverse Kepler) are the hardest rows and where models — including Kepler —
|
| 83 |
+
most often miss. Treat them as the frontier of this benchmark.
|
| 84 |
+
|
| 85 |
+
## Methods
|
| 86 |
+
|
| 87 |
+
Full construction + measurement protocol:
|
| 88 |
+
[The Gate Before the GPU — Deciding SFT vs RL vs RLVR Before You Spend the Run](https://ainative.business/field-notes/the-gate-before-the-gpu/).
|
| 89 |
+
|
| 90 |
+
---
|
| 91 |
+
|
| 92 |
+
Published by **Orionfold LLC** · [orionfold.com](https://orionfold.com) · Methods at [ainative.business/field-notes](https://ainative.business/field-notes/).
|
heldout.jsonl
ADDED
|
@@ -0,0 +1,44 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
{"task_id": "astro-ap-parallax_distance-10000", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.230 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "4.348 pc", "gold_value_si": 1.3415989484782608e+17, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.23}}
|
| 2 |
+
{"task_id": "astro-orb-specific_orbital_energy-10001", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 18,500 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-10.77 MJ/kg", "gold_value_si": -10772972.972972972, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 18500}}
|
| 3 |
+
{"task_id": "astro-orb-kepler_third_law-10002", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 29,700 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "14.15 hr", "gold_value_si": 50938.46987104555, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 29700}}
|
| 4 |
+
{"task_id": "astro-orb-leo_period-10003", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,760 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "121.6 min", "gold_value_si": 7296.711289508915, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1760}}
|
| 5 |
+
{"task_id": "astro-orb-circular_velocity-10004", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 34,100 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.419 km/s", "gold_value_si": 3418.939829847449, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 34100}}
|
| 6 |
+
{"task_id": "astro-orb-altitude_from_period-10005", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 14.5 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "2.382e+04 km", "gold_value_si": 23817360.059145853, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 14.5}}
|
| 7 |
+
{"task_id": "astro-orb-leo_period-10006", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,910 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "125 min", "gold_value_si": 7499.553336214183, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1910}}
|
| 8 |
+
{"task_id": "astro-orb-altitude_from_period-10007", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 5.2 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "8867 km", "gold_value_si": 8867062.439897366, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 5.2}}
|
| 9 |
+
{"task_id": "astro-orb-hohmann_transfer-10008", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 10,800 km and r₂ = 33,400 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2433 m/s", "gold_value_si": 2432.9760908005046, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 10800, "r2_km": 33400}}
|
| 10 |
+
{"task_id": "astro-orb-leo_period-10009", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,480 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "115.4 min", "gold_value_si": 6923.069432141767, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1480}}
|
| 11 |
+
{"task_id": "astro-orb-circular_velocity-10010", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 17,800 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.732 km/s", "gold_value_si": 4732.151564242875, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 17800}}
|
| 12 |
+
{"task_id": "astro-orb-kepler_third_law-10011", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 23,200 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "9.769 hr", "gold_value_si": 35167.637852603686, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 23200}}
|
| 13 |
+
{"task_id": "astro-orb-escape_velocity-10012", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 16,300 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.993 km/s", "gold_value_si": 6993.423729484915, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 16300}}
|
| 14 |
+
{"task_id": "astro-ap-distance_modulus-10013", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 13.5 and absolute magnitude M = 1.5. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "2512 pc", "gold_value_si": 7.750871648983145e+19, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 13.5, "M": 1.5}}
|
| 15 |
+
{"task_id": "astro-ap-hubble_law-10014", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 5,500 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "78.57 Mpc", "gold_value_si": 2.424460956892857e+24, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 5500}}
|
| 16 |
+
{"task_id": "astro-orb-vis_viva-10015", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 34,600 km. At an instant its distance from Earth's center is r = 51,600 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "1.982 km/s", "gold_value_si": 1982.266679644276, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 34600, "r_km": 51600.0}}
|
| 17 |
+
{"task_id": "astro-orb-hohmann_transfer-10016", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 11,300 km and r₂ = 30,500 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2192 m/s", "gold_value_si": 2192.4246072596065, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 11300, "r2_km": 30500}}
|
| 18 |
+
{"task_id": "astro-orb-circular_velocity-10017", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 28,600 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.733 km/s", "gold_value_si": 3733.237594510017, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 28600}}
|
| 19 |
+
{"task_id": "astro-ap-schwarzschild_radius-10018", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 4.85e+06 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "1.433e+07 km", "gold_value_si": 14326148964.775715, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 4850000.0}}
|
| 20 |
+
{"task_id": "astro-ap-hubble_law-10019", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 11,800 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "168.6 Mpc", "gold_value_si": 5.201570780242857e+24, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 11800}}
|
| 21 |
+
{"task_id": "astro-orb-vis_viva-10020", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 19,000 km. At an instant its distance from Earth's center is r = 14,000 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "5.997 km/s", "gold_value_si": 5996.991727060834, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 19000, "r_km": 14000.0}}
|
| 22 |
+
{"task_id": "astro-ap-parallax_distance-10021", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.671 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "1.49 pc", "gold_value_si": 4.598625307749627e+16, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.671}}
|
| 23 |
+
{"task_id": "astro-orb-hohmann_transfer-10022", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 11,600 km and r₂ = 28,300 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2011 m/s", "gold_value_si": 2011.0014314091009, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 11600, "r2_km": 28300}}
|
| 24 |
+
{"task_id": "astro-orb-escape_velocity-10023", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 14,500 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.415 km/s", "gold_value_si": 7414.803459622351, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 14500}}
|
| 25 |
+
{"task_id": "astro-orb-synodic_period-10024", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 547.5 days and T₂ = 1,971.0 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "758.1 days", "gold_value_si": 65497846.15384615, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 547.5, "T2_d": 1971.0000000000002}}
|
| 26 |
+
{"task_id": "astro-ap-wien_law-10025", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 26,700 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "108.5 nm", "gold_value_si": 1.0853932584269663e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 26700}}
|
| 27 |
+
{"task_id": "astro-orb-synodic_period-10026", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 419.7 days and T₂ = 1,186.2 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "649.6 days", "gold_value_si": 56126571.42857141, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 419.74999999999994, "T2_d": 1186.25}}
|
| 28 |
+
{"task_id": "astro-ap-wien_law-10027", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 15,600 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "185.8 nm", "gold_value_si": 1.8576923076923076e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 15600}}
|
| 29 |
+
{"task_id": "astro-orb-vis_viva-10028", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 9,600 km. At an instant its distance from Earth's center is r = 7,700 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.875 km/s", "gold_value_si": 7874.746611741498, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 9600, "r_km": 7700.0}}
|
| 30 |
+
{"task_id": "astro-orb-altitude_from_period-10029", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 18.8 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "2.952e+04 km", "gold_value_si": 29523900.397143885, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 18.8}}
|
| 31 |
+
{"task_id": "astro-orb-kepler_third_law-10030", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 25,700 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "11.39 hr", "gold_value_si": 41002.5537098919, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 25700}}
|
| 32 |
+
{"task_id": "astro-ap-transit_radius-10031", "topic": "astrophysics", "subtopic": "transit_radius", "tier": 2, "prompt": "An exoplanet transit has fractional depth ΔF/F = 0.012140. The host star radius is R_★ = 2.3 R_⊙ (R_⊙ = 6.957×10^8 m, R_⊕ = 6.371×10^6 m). Using ΔF/F = (R_p/R_★)², compute the planet radius in Earth radii (R_⊕). Give your final answer as \\boxed{value unit}.", "answer": "27.67 R_earth", "gold_value_si": 176302789.0502416, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"depth": 0.01214, "r_star_rsun": 2.3}}
|
| 33 |
+
{"task_id": "astro-orb-specific_orbital_energy-10032", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 25,600 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-7.785 MJ/kg", "gold_value_si": -7785156.25, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 25600}}
|
| 34 |
+
{"task_id": "astro-orb-circular_velocity-10033", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 13,000 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "5.537 km/s", "gold_value_si": 5537.286200074767, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 13000}}
|
| 35 |
+
{"task_id": "astro-orb-vis_viva-10034", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 9,900 km. At an instant its distance from Earth's center is r = 8,850 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.058 km/s", "gold_value_si": 7058.0783349699, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 9900, "r_km": 8850.0}}
|
| 36 |
+
{"task_id": "astro-orb-leo_period-10035", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,280 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "111 min", "gold_value_si": 6660.219219787364, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1280}}
|
| 37 |
+
{"task_id": "astro-orb-kepler_third_law-10036", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 41,200 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "23.12 hr", "gold_value_si": 83225.62115977312, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 41200}}
|
| 38 |
+
{"task_id": "astro-orb-escape_velocity-10037", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 15,600 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.149 km/s", "gold_value_si": 7148.605745357909, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 15600}}
|
| 39 |
+
{"task_id": "astro-ap-schwarzschild_radius-10038", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 83 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "245.2 km", "gold_value_si": 245169.14723224417, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 83.0}}
|
| 40 |
+
{"task_id": "astro-ap-distance_modulus-10039", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 14.5 and absolute magnitude M = 2.0. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "3162 pc", "gold_value_si": 9.757769282459845e+19, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 14.5, "M": 2.0}}
|
| 41 |
+
{"task_id": "astro-orb-leo_period_hours-20000", "topic": "orbital_mechanics", "subtopic": "leo_period_hours", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,480 km (R = 6.371×10^6 m, μ = 3.986×10^14 m³/s²). Report the orbital period in HOURS. Give your final answer as \\boxed{value unit}.", "answer": "1.923 hr", "gold_value_si": 6923.069432141767, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": true, "params": {"h_km": 1480}}
|
| 42 |
+
{"task_id": "astro-orb-mars_circular_velocity-20001", "topic": "orbital_mechanics", "subtopic": "mars_circular_velocity", "tier": 1, "prompt": "A probe is in a circular orbit of radius r = 10,800 km about Mars (μ_Mars = 4.283×10^13 m³/s²). Compute the circular speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "1.991 km/s", "gold_value_si": 1991.4167672139201, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": true, "params": {"r_km": 10800}}
|
| 43 |
+
{"task_id": "astro-ap-schwarzschild_meters-20002", "topic": "astrophysics", "subtopic": "schwarzschild_meters", "tier": 2, "prompt": "A black hole of mass M = 15 M_⊙ (M_⊙ = 1.989×10^30 kg, G = 6.674×10^-11 m³ kg⁻¹ s⁻², c = 2.998×10^8 m/s). Compute the Schwarzschild radius r_s = 2GM/c² in METERS. Give your final answer as \\boxed{value unit}.", "answer": "4.431e+04 m", "gold_value_si": 44307.67721064654, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": true, "params": {"m_solar": 15}}
|
| 44 |
+
{"task_id": "astro-ap-hubble_in_pc-20003", "topic": "astrophysics", "subtopic": "hubble_in_pc", "tier": 2, "prompt": "A nearby galaxy recedes at v = 4,900 km/s (H₀ = 70 km/s/Mpc). Give its distance in PARSECS (not Mpc). Give your final answer as \\boxed{value unit}.", "answer": "7e+07 pc", "gold_value_si": 2.15997430705e+24, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": true, "params": {"v_kms": 4900}}
|
pool.jsonl
ADDED
|
@@ -0,0 +1,120 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
{"task_id": "astro-orb-leo_period-0000", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,030 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "105.6 min", "gold_value_si": 6336.461894323604, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1030}}
|
| 2 |
+
{"task_id": "astro-orb-hohmann_transfer-0001", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 9,300 km and r₂ = 22,600 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2239 m/s", "gold_value_si": 2238.9992266463796, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 9300, "r2_km": 22600}}
|
| 3 |
+
{"task_id": "astro-orb-kepler_third_law-0002", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 18,900 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "7.183 hr", "gold_value_si": 25858.535648485115, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 18900}}
|
| 4 |
+
{"task_id": "astro-orb-kepler_third_law-0003", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 44,300 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "25.78 hr", "gold_value_si": 92793.34075359785, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 44300}}
|
| 5 |
+
{"task_id": "astro-orb-escape_velocity-0004", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 13,600 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.656 km/s", "gold_value_si": 7656.21623642015, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 13600}}
|
| 6 |
+
{"task_id": "astro-orb-leo_period-0005", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 390 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "92.21 min", "gold_value_si": 5532.579014289351, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 390}}
|
| 7 |
+
{"task_id": "astro-orb-synodic_period-0006", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 547.5 days and T₂ = 1,843.2 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "778.8 days", "gold_value_si": 67291605.63380282, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 547.5, "T2_d": 1843.25}}
|
| 8 |
+
{"task_id": "astro-orb-leo_period-0007", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 480 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "94.06 min", "gold_value_si": 5643.417394649844, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 480}}
|
| 9 |
+
{"task_id": "astro-orb-escape_velocity-0008", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 12,300 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "8.051 km/s", "gold_value_si": 8050.6526524301935, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 12300}}
|
| 10 |
+
{"task_id": "astro-orb-kepler_third_law-0009", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 39,300 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "21.54 hr", "gold_value_si": 77535.40268036372, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 39300}}
|
| 11 |
+
{"task_id": "astro-ap-distance_modulus-0010", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 20.0 and absolute magnitude M = -2.0. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "2.512e+05 pc", "gold_value_si": 7.750871648983153e+21, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 20.0, "M": -2.0}}
|
| 12 |
+
{"task_id": "astro-orb-hohmann_transfer-0011", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 10,800 km and r₂ = 27,100 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2130 m/s", "gold_value_si": 2129.7530577325983, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 10800, "r2_km": 27100}}
|
| 13 |
+
{"task_id": "astro-orb-hohmann_transfer-0012", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 8,600 km and r₂ = 34,200 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "3048 m/s", "gold_value_si": 3048.2174718669976, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 8600, "r2_km": 34200}}
|
| 14 |
+
{"task_id": "astro-ap-hubble_law-0013", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 26,900 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "384.3 Mpc", "gold_value_si": 1.1857818134621429e+25, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 26900}}
|
| 15 |
+
{"task_id": "astro-orb-kepler_third_law-0014", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 29,900 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "14.29 hr", "gold_value_si": 51453.86511212905, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 29900}}
|
| 16 |
+
{"task_id": "astro-orb-specific_orbital_energy-0015", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 13,300 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-14.98 MJ/kg", "gold_value_si": -14984962.406015038, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 13300}}
|
| 17 |
+
{"task_id": "astro-ap-transit_radius-0016", "topic": "astrophysics", "subtopic": "transit_radius", "tier": 2, "prompt": "An exoplanet transit has fractional depth ΔF/F = 0.018740. The host star radius is R_★ = 1.8 R_⊙ (R_⊙ = 6.957×10^8 m, R_⊕ = 6.371×10^6 m). Using ΔF/F = (R_p/R_★)², compute the planet radius in Earth radii (R_⊕). Give your final answer as \\boxed{value unit}.", "answer": "26.91 R_earth", "gold_value_si": 171427030.29692838, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"depth": 0.01874, "r_star_rsun": 1.8}}
|
| 18 |
+
{"task_id": "astro-orb-altitude_from_period-0017", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 9.9 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.704e+04 km", "gold_value_si": 17036281.75473459, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 9.9}}
|
| 19 |
+
{"task_id": "astro-ap-distance_modulus-0018", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 13.5 and absolute magnitude M = 1.0. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "3162 pc", "gold_value_si": 9.757769282459845e+19, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 13.5, "M": 1.0}}
|
| 20 |
+
{"task_id": "astro-orb-vis_viva-0019", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 9,400 km. At an instant its distance from Earth's center is r = 9,700 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.307 km/s", "gold_value_si": 6307.242796274798, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 9400, "r_km": 9700.0}}
|
| 21 |
+
{"task_id": "astro-orb-hohmann_transfer-0020", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 7,700 km and r₂ = 31,700 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "3261 m/s", "gold_value_si": 3261.027119290647, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 7700, "r2_km": 31700}}
|
| 22 |
+
{"task_id": "astro-orb-escape_velocity-0021", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 17,700 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.711 km/s", "gold_value_si": 6711.151020696738, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 17700}}
|
| 23 |
+
{"task_id": "astro-orb-vis_viva-0022", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 39,100 km. At an instant its distance from Earth's center is r = 43,850 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "2.826 km/s", "gold_value_si": 2825.9133450240824, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 39100, "r_km": 43850.0}}
|
| 24 |
+
{"task_id": "astro-ap-wien_law-0023", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 15,000 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "193.2 nm", "gold_value_si": 1.932e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 15000}}
|
| 25 |
+
{"task_id": "astro-orb-vis_viva-0024", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 33,300 km. At an instant its distance from Earth's center is r = 37,150 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.08 km/s", "gold_value_si": 3080.4188403388075, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 33300, "r_km": 37150.0}}
|
| 26 |
+
{"task_id": "astro-ap-distance_modulus-0025", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 6.0 and absolute magnitude M = 0.5. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "125.9 pc", "gold_value_si": 3.8846379199539185e+18, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 6.0, "M": 0.5}}
|
| 27 |
+
{"task_id": "astro-orb-circular_velocity-0026", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 27,600 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.8 km/s", "gold_value_si": 3800.2669623997795, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 27600}}
|
| 28 |
+
{"task_id": "astro-orb-vis_viva-0027", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 37,500 km. At an instant its distance from Earth's center is r = 64,650 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "1.304 km/s", "gold_value_si": 1304.4845013970655, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 37500, "r_km": 64650.0}}
|
| 29 |
+
{"task_id": "astro-orb-kepler_third_law-0028", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 27,300 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "12.47 hr", "gold_value_si": 44890.57742434611, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 27300}}
|
| 30 |
+
{"task_id": "astro-ap-wien_law-0029", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 18,900 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "153.3 nm", "gold_value_si": 1.5333333333333333e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 18900}}
|
| 31 |
+
{"task_id": "astro-orb-escape_velocity-0030", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 8,600 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "9.628 km/s", "gold_value_si": 9627.963150043972, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 8600}}
|
| 32 |
+
{"task_id": "astro-orb-circular_velocity-0031", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 21,400 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.316 km/s", "gold_value_si": 4315.804470118991, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 21400}}
|
| 33 |
+
{"task_id": "astro-ap-transit_radius-0032", "topic": "astrophysics", "subtopic": "transit_radius", "tier": 2, "prompt": "An exoplanet transit has fractional depth ΔF/F = 0.016690. The host star radius is R_★ = 0.5 R_⊙ (R_⊙ = 6.957×10^8 m, R_⊕ = 6.371×10^6 m). Using ΔF/F = (R_p/R_★)², compute the planet radius in Earth radii (R_⊕). Give your final answer as \\boxed{value unit}.", "answer": "7.054 R_earth", "gold_value_si": 44938665.974025086, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"depth": 0.01669, "r_star_rsun": 0.5}}
|
| 34 |
+
{"task_id": "astro-orb-vis_viva-0033", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 10,500 km. At an instant its distance from Earth's center is r = 9,950 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.493 km/s", "gold_value_si": 6492.97299033121, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 10500, "r_km": 9950.0}}
|
| 35 |
+
{"task_id": "astro-orb-circular_velocity-0034", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 16,700 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.886 km/s", "gold_value_si": 4885.515681384503, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 16700}}
|
| 36 |
+
{"task_id": "astro-orb-specific_orbital_energy-0035", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 43,100 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-4.624 MJ/kg", "gold_value_si": -4624129.930394432, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 43100}}
|
| 37 |
+
{"task_id": "astro-ap-parallax_distance-0036", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.715 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "1.399 pc", "gold_value_si": 4.315632981118882e+16, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.715}}
|
| 38 |
+
{"task_id": "astro-ap-transit_radius-0037", "topic": "astrophysics", "subtopic": "transit_radius", "tier": 2, "prompt": "An exoplanet transit has fractional depth ΔF/F = 0.016250. The host star radius is R_★ = 2.1 R_⊙ (R_⊙ = 6.957×10^8 m, R_⊕ = 6.371×10^6 m). Using ΔF/F = (R_p/R_★)², compute the planet radius in Earth radii (R_⊕). Give your final answer as \\boxed{value unit}.", "answer": "29.23 R_earth", "gold_value_si": 186237863.46934128, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"depth": 0.01625, "r_star_rsun": 2.1}}
|
| 39 |
+
{"task_id": "astro-orb-specific_orbital_energy-0038", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 44,800 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-4.449 MJ/kg", "gold_value_si": -4448660.714285715, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 44800}}
|
| 40 |
+
{"task_id": "astro-orb-leo_period-0039", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,970 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "126.4 min", "gold_value_si": 7581.207838503933, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1970}}
|
| 41 |
+
{"task_id": "astro-orb-leo_period-0040", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,690 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "120 min", "gold_value_si": 7202.688002077256, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1690}}
|
| 42 |
+
{"task_id": "astro-ap-parallax_distance-0041", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.669 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "1.495 pc", "gold_value_si": 4.6123730665171896e+16, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.669}}
|
| 43 |
+
{"task_id": "astro-orb-synodic_period-0042", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 511.0 days and T₂ = 1,277.5 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "851.7 days", "gold_value_si": 73583999.99999999, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 510.99999999999994, "T2_d": 1277.5}}
|
| 44 |
+
{"task_id": "astro-ap-hubble_law-0043", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 23,900 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "341.4 Mpc", "gold_value_si": 1.0535384885407142e+25, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 23900}}
|
| 45 |
+
{"task_id": "astro-orb-kepler_third_law-0044", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 19,500 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "7.528 hr", "gold_value_si": 27099.616076718576, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 19500}}
|
| 46 |
+
{"task_id": "astro-orb-altitude_from_period-0045", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 18 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "2.85e+04 km", "gold_value_si": 28498243.32472083, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 18.0}}
|
| 47 |
+
{"task_id": "astro-orb-circular_velocity-0046", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 21,900 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.266 km/s", "gold_value_si": 4266.252833812025, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 21900}}
|
| 48 |
+
{"task_id": "astro-orb-leo_period-0047", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 650 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "97.58 min", "gold_value_si": 5854.767868623821, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 650}}
|
| 49 |
+
{"task_id": "astro-orb-kepler_third_law-0048", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 24,100 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "10.34 hr", "gold_value_si": 37233.7505671123, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 24100}}
|
| 50 |
+
{"task_id": "astro-orb-synodic_period-0049", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 511.0 days and T₂ = 2,007.5 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "685.5 days", "gold_value_si": 59226146.34146341, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 510.99999999999994, "T2_d": 2007.5}}
|
| 51 |
+
{"task_id": "astro-ap-stefan_boltzmann-0050", "topic": "astrophysics", "subtopic": "stefan_boltzmann", "tier": 3, "prompt": "A star has radius R = 15.7 R_⊙ (R_⊙ = 6.957×10^8 m) and surface temperature T = 6,100 K. With σ = 5.670×10^-8 W m⁻² K⁻⁴, compute its luminosity L = 4πR²σT⁴ in watts. Give your final answer as \\boxed{value unit}.", "answer": "1.177e+29 W", "gold_value_si": 1.176943390948736e+29, "gold_unit": "W", "rel_tol": 0.02, "hand_curated": false, "params": {"r_rsun": 15.7, "T_K": 6100}}
|
| 52 |
+
{"task_id": "astro-ap-parallax_distance-0051", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.796 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "1.256 pc", "gold_value_si": 3.876479373743718e+16, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.796}}
|
| 53 |
+
{"task_id": "astro-orb-altitude_from_period-0052", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 8.7 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.51e+04 km", "gold_value_si": 15104355.153582223, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 8.7}}
|
| 54 |
+
{"task_id": "astro-orb-synodic_period-0053", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 511.0 days and T₂ = 1,916.2 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "696.8 days", "gold_value_si": 60205090.90909089, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 510.99999999999994, "T2_d": 1916.25}}
|
| 55 |
+
{"task_id": "astro-ap-wien_law-0054", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 15,200 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "190.7 nm", "gold_value_si": 1.906578947368421e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 15200}}
|
| 56 |
+
{"task_id": "astro-orb-hohmann_transfer-0055", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 8,700 km and r₂ = 27,000 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2716 m/s", "gold_value_si": 2715.839868374189, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 8700, "r2_km": 27000}}
|
| 57 |
+
{"task_id": "astro-orb-vis_viva-0056", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 15,800 km. At an instant its distance from Earth's center is r = 20,800 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.619 km/s", "gold_value_si": 3619.2644246666, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 15800, "r_km": 20800.0}}
|
| 58 |
+
{"task_id": "astro-ap-schwarzschild_radius-0057", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 4.53e+06 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "1.338e+07 km", "gold_value_si": 13380918517.615255, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 4530000.0}}
|
| 59 |
+
{"task_id": "astro-ap-hubble_law-0058", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 1,300 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "18.57 Mpc", "gold_value_si": 5.730544079928572e+23, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 1300}}
|
| 60 |
+
{"task_id": "astro-orb-circular_velocity-0059", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 24,400 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.042 km/s", "gold_value_si": 4041.7898972819567, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 24400}}
|
| 61 |
+
{"task_id": "astro-orb-circular_velocity-0060", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 17,000 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.842 km/s", "gold_value_si": 4842.216313169974, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 17000}}
|
| 62 |
+
{"task_id": "astro-orb-circular_velocity-0061", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 7,300 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.389 km/s", "gold_value_si": 7389.366666097129, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 7300}}
|
| 63 |
+
{"task_id": "astro-orb-vis_viva-0062", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 26,000 km. At an instant its distance from Earth's center is r = 40,000 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "2.145 km/s", "gold_value_si": 2144.581723607372, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 26000, "r_km": 40000.0}}
|
| 64 |
+
{"task_id": "astro-ap-hubble_law-0063", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 9,800 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "140 Mpc", "gold_value_si": 4.3199486140999997e+24, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 9800}}
|
| 65 |
+
{"task_id": "astro-orb-leo_period-0064", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,660 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "119.4 min", "gold_value_si": 7162.51690558725, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1660}}
|
| 66 |
+
{"task_id": "astro-orb-hohmann_transfer-0065", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 11,100 km and r₂ = 24,600 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "1893 m/s", "gold_value_si": 1893.433702184107, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 11100, "r2_km": 24600}}
|
| 67 |
+
{"task_id": "astro-ap-hubble_law-0066", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 27,400 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "391.4 Mpc", "gold_value_si": 1.2078223676157143e+25, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 27400}}
|
| 68 |
+
{"task_id": "astro-orb-hohmann_transfer-0067", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 8,400 km and r₂ = 21,400 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2442 m/s", "gold_value_si": 2442.251755077507, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 8400, "r2_km": 21400}}
|
| 69 |
+
{"task_id": "astro-ap-hubble_law-0068", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 6,500 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "92.86 Mpc", "gold_value_si": 2.865272039964286e+24, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 6500}}
|
| 70 |
+
{"task_id": "astro-orb-leo_period-0069", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,550 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "116.9 min", "gold_value_si": 7015.865281277513, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1550}}
|
| 71 |
+
{"task_id": "astro-orb-hohmann_transfer-0070", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 10,100 km and r₂ = 38,500 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "2769 m/s", "gold_value_si": 2768.5121376781085, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 10100, "r2_km": 38500}}
|
| 72 |
+
{"task_id": "astro-orb-kepler_third_law-0071", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 42,800 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "24.48 hr", "gold_value_si": 88120.4841738047, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 42800}}
|
| 73 |
+
{"task_id": "astro-ap-hubble_law-0072", "topic": "astrophysics", "subtopic": "hubble_law", "tier": 1, "prompt": "A galaxy recedes at v = 7,200 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \\boxed{value unit}.", "answer": "102.9 Mpc", "gold_value_si": 3.1738397981142856e+24, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"v_kms": 7200}}
|
| 74 |
+
{"task_id": "astro-orb-vis_viva-0073", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 29,500 km. At an instant its distance from Earth's center is r = 44,850 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "2.065 km/s", "gold_value_si": 2064.6889592527073, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 29500, "r_km": 44850.0}}
|
| 75 |
+
{"task_id": "astro-orb-altitude_from_period-0074", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 6.5 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.131e+04 km", "gold_value_si": 11311205.116730478, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 6.5}}
|
| 76 |
+
{"task_id": "astro-ap-distance_modulus-0075", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 0.5 and absolute magnitude M = -5.5. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "158.5 pc", "gold_value_si": 4.890469393049225e+18, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 0.5, "M": -5.5}}
|
| 77 |
+
{"task_id": "astro-orb-circular_velocity-0076", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 35,800 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.337 km/s", "gold_value_si": 3336.776620076703, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 35800}}
|
| 78 |
+
{"task_id": "astro-orb-specific_orbital_energy-0077", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 27,800 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-7.169 MJ/kg", "gold_value_si": -7169064.748201439, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 27800}}
|
| 79 |
+
{"task_id": "astro-ap-parallax_distance-0078", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.402 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "2.488 pc", "gold_value_si": 7.675814879353234e+16, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.402}}
|
| 80 |
+
{"task_id": "astro-orb-altitude_from_period-0079", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 5.9 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.021e+04 km", "gold_value_si": 10205602.65616799, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 5.9}}
|
| 81 |
+
{"task_id": "astro-orb-circular_velocity-0080", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 29,400 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.682 km/s", "gold_value_si": 3682.094937566344, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 29400}}
|
| 82 |
+
{"task_id": "astro-ap-schwarzschild_radius-0081", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 93 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "274.7 km", "gold_value_si": 274707.5987060085, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 93.0}}
|
| 83 |
+
{"task_id": "astro-orb-kepler_third_law-0082", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 20,000 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "7.819 hr", "gold_value_si": 28148.562085893667, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 20000}}
|
| 84 |
+
{"task_id": "astro-orb-synodic_period-0083", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 419.7 days and T₂ = 1,752.0 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "552 days", "gold_value_si": 47692799.99999999, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 419.74999999999994, "T2_d": 1752.0}}
|
| 85 |
+
{"task_id": "astro-ap-schwarzschild_radius-0084", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 57 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "168.4 km", "gold_value_si": 168369.17340045684, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 57.0}}
|
| 86 |
+
{"task_id": "astro-ap-wien_law-0085", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 25,800 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "112.3 nm", "gold_value_si": 1.1232558139534884e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 25800}}
|
| 87 |
+
{"task_id": "astro-orb-altitude_from_period-0086", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 8.3 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.444e+04 km", "gold_value_si": 14440956.7471942, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 8.3}}
|
| 88 |
+
{"task_id": "astro-orb-altitude_from_period-0087", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 11 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.874e+04 km", "gold_value_si": 18739535.618521426, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 11.0}}
|
| 89 |
+
{"task_id": "astro-orb-escape_velocity-0088", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 8,500 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "9.684 km/s", "gold_value_si": 9684.432626339947, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 8500}}
|
| 90 |
+
{"task_id": "astro-ap-wien_law-0089", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 15,300 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "189.4 nm", "gold_value_si": 1.8941176470588234e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 15300}}
|
| 91 |
+
{"task_id": "astro-ap-parallax_distance-0090", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.265 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "3.774 pc", "gold_value_si": 1.1644066345283018e+17, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.265}}
|
| 92 |
+
{"task_id": "astro-orb-escape_velocity-0091", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 18,700 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.529 km/s", "gold_value_si": 6529.243144712927, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 18700}}
|
| 93 |
+
{"task_id": "astro-orb-vis_viva-0092", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 14,000 km. At an instant its distance from Earth's center is r = 20,300 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "3.286 km/s", "gold_value_si": 3286.26039582419, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 14000, "r_km": 20300.0}}
|
| 94 |
+
{"task_id": "astro-orb-specific_orbital_energy-0093", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 36,200 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-5.506 MJ/kg", "gold_value_si": -5505524.861878453, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 36200}}
|
| 95 |
+
{"task_id": "astro-orb-escape_velocity-0094", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 15,700 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "7.126 km/s", "gold_value_si": 7125.803117101557, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 15700}}
|
| 96 |
+
{"task_id": "astro-ap-schwarzschild_radius-0095", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 74 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "218.6 km", "gold_value_si": 218584.54090585627, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 74.0}}
|
| 97 |
+
{"task_id": "astro-orb-escape_velocity-0096", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 19,000 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.477 km/s", "gold_value_si": 6477.491392263065, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 19000}}
|
| 98 |
+
{"task_id": "astro-orb-altitude_from_period-0097", "topic": "orbital_mechanics", "subtopic": "altitude_from_period", "tier": 3, "prompt": "An Earth satellite has an orbital period of T = 6 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \\boxed{value unit}.", "answer": "1.039e+04 km", "gold_value_si": 10392383.734007698, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_hr": 6.0}}
|
| 99 |
+
{"task_id": "astro-orb-synodic_period-0098", "topic": "orbital_mechanics", "subtopic": "synodic_period", "tier": 2, "prompt": "Two planets orbit the Sun with sidereal periods T₁ = 492.8 days and T₂ = 1,149.8 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \\boxed{value unit}.", "answer": "862.3 days", "gold_value_si": 74503800.0, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"T1_d": 492.75000000000006, "T2_d": 1149.75}}
|
| 100 |
+
{"task_id": "astro-orb-leo_period-0099", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,590 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "117.8 min", "gold_value_si": 7069.076101664404, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1590}}
|
| 101 |
+
{"task_id": "astro-orb-kepler_third_law-0100", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 14,700 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "4.927 hr", "gold_value_si": 17737.288228123318, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 14700}}
|
| 102 |
+
{"task_id": "astro-orb-hohmann_transfer-0101", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 11,200 km and r₂ = 20,200 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "1491 m/s", "gold_value_si": 1491.3975843734502, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 11200, "r2_km": 20200}}
|
| 103 |
+
{"task_id": "astro-orb-hohmann_transfer-0102", "topic": "orbital_mechanics", "subtopic": "hohmann_transfer", "tier": 3, "prompt": "Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 9,300 km and r₂ = 41,800 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \\boxed{value unit}.", "answer": "3052 m/s", "gold_value_si": 3051.9403635308618, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r1_km": 9300, "r2_km": 41800}}
|
| 104 |
+
{"task_id": "astro-orb-circular_velocity-0103", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 24,000 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.075 km/s", "gold_value_si": 4075.3322972897968, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 24000}}
|
| 105 |
+
{"task_id": "astro-orb-circular_velocity-0104", "topic": "orbital_mechanics", "subtopic": "circular_velocity", "tier": 1, "prompt": "A satellite is in a circular Earth orbit of radius r = 20,800 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.378 km/s", "gold_value_si": 4377.609112113773, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 20800}}
|
| 106 |
+
{"task_id": "astro-orb-specific_orbital_energy-0105", "topic": "orbital_mechanics", "subtopic": "specific_orbital_energy", "tier": 1, "prompt": "For an Earth orbit with semi-major axis a = 38,700 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \\boxed{value unit}.", "answer": "-5.15 MJ/kg", "gold_value_si": -5149870.801033592, "gold_unit": "J/kg", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 38700}}
|
| 107 |
+
{"task_id": "astro-orb-escape_velocity-0106", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 16,400 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "6.972 km/s", "gold_value_si": 6972.069714049119, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 16400}}
|
| 108 |
+
{"task_id": "astro-ap-distance_modulus-0107", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 17.5 and absolute magnitude M = -4.0. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "1.995e+05 pc", "gold_value_si": 6.156736194511261e+21, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 17.5, "M": -4.0}}
|
| 109 |
+
{"task_id": "astro-ap-transit_radius-0108", "topic": "astrophysics", "subtopic": "transit_radius", "tier": 2, "prompt": "An exoplanet transit has fractional depth ΔF/F = 0.021390. The host star radius is R_★ = 1.5 R_⊙ (R_⊙ = 6.957×10^8 m, R_⊕ = 6.371×10^6 m). Using ΔF/F = (R_p/R_★)², compute the planet radius in Earth radii (R_⊕). Give your final answer as \\boxed{value unit}.", "answer": "23.96 R_earth", "gold_value_si": 152622532.1748889, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"depth": 0.02139, "r_star_rsun": 1.5}}
|
| 110 |
+
{"task_id": "astro-ap-schwarzschild_radius-0109", "topic": "astrophysics", "subtopic": "schwarzschild_radius", "tier": 2, "prompt": "A black hole has mass M = 31 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \\boxed{value unit}.", "answer": "91.57 km", "gold_value_si": 91569.19956866952, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m_solar": 31.0}}
|
| 111 |
+
{"task_id": "astro-ap-wien_law-0110", "topic": "astrophysics", "subtopic": "wien_law", "tier": 1, "prompt": "A star has surface temperature T = 28,900 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \\boxed{value unit}.", "answer": "100.3 nm", "gold_value_si": 1.0027681660899655e-07, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"T_K": 28900}}
|
| 112 |
+
{"task_id": "astro-ap-parallax_distance-0111", "topic": "astrophysics", "subtopic": "parallax_distance", "tier": 1, "prompt": "A star has a measured parallax of p = 0.770 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \\boxed{value unit}.", "answer": "1.299 pc", "gold_value_si": 4.007373482467533e+16, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"p_arcsec": 0.77}}
|
| 113 |
+
{"task_id": "astro-orb-leo_period-0112", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 1,720 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "120.7 min", "gold_value_si": 7242.9339191195095, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 1720}}
|
| 114 |
+
{"task_id": "astro-orb-vis_viva-0113", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 26,600 km. At an instant its distance from Earth's center is r = 24,300 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "4.222 km/s", "gold_value_si": 4221.566291807448, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 26600, "r_km": 24300.0}}
|
| 115 |
+
{"task_id": "astro-ap-distance_modulus-0114", "topic": "astrophysics", "subtopic": "distance_modulus", "tier": 2, "prompt": "A star has apparent magnitude m = 10.5 and absolute magnitude M = 0.0. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \\boxed{value unit}.", "answer": "1259 pc", "gold_value_si": 3.884637919953918e+19, "gold_unit": "m", "rel_tol": 0.02, "hand_curated": false, "params": {"m": 10.5, "M": 0.0}}
|
| 116 |
+
{"task_id": "astro-orb-kepler_third_law-0115", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 15,200 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "5.181 hr", "gold_value_si": 18649.904105835427, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 15200}}
|
| 117 |
+
{"task_id": "astro-orb-vis_viva-0116", "topic": "orbital_mechanics", "subtopic": "vis_viva", "tier": 2, "prompt": "A spacecraft is on an Earth orbit with semi-major axis a = 20,400 km. At an instant its distance from Earth's center is r = 15,900 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \\boxed{value unit}.", "answer": "5.532 km/s", "gold_value_si": 5531.649762376474, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 20400, "r_km": 15900.0}}
|
| 118 |
+
{"task_id": "astro-orb-kepler_third_law-0117", "topic": "orbital_mechanics", "subtopic": "kepler_third_law", "tier": 1, "prompt": "A satellite is in an Earth orbit with semi-major axis a = 14,800 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \\boxed{value unit}.", "answer": "4.977 hr", "gold_value_si": 17918.58842781769, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"a_km": 14800}}
|
| 119 |
+
{"task_id": "astro-orb-escape_velocity-0118", "topic": "orbital_mechanics", "subtopic": "escape_velocity", "tier": 1, "prompt": "From a distance r = 11,800 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \\boxed{value unit}.", "answer": "8.219 km/s", "gold_value_si": 8219.44779373276, "gold_unit": "m/s", "rel_tol": 0.02, "hand_curated": false, "params": {"r_km": 11800}}
|
| 120 |
+
{"task_id": "astro-orb-leo_period-0119", "topic": "orbital_mechanics", "subtopic": "leo_period", "tier": 2, "prompt": "A satellite orbits at altitude h = 350 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \\boxed{value unit}.", "answer": "91.39 min", "gold_value_si": 5483.553238373392, "gold_unit": "s", "rel_tol": 0.02, "hand_curated": false, "params": {"h_km": 350}}
|
units.py
ADDED
|
@@ -0,0 +1,144 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Copyright 2026 Manav Sehgal
|
| 2 |
+
# SPDX-License-Identifier: Apache-2.0
|
| 3 |
+
"""units.py — minimal SI unit-normalization for the astrodynamics bench verifier.
|
| 4 |
+
|
| 5 |
+
Stdlib only (no ``pint`` dependency — matches the fieldkit no-extra-deps
|
| 6 |
+
discipline). The verifier compares a model's answer to gold by converting both
|
| 7 |
+
to SI within the same *dimension*; a dimension mismatch (gold is a period in
|
| 8 |
+
seconds, the model answered a speed in km/s) is a hard miss.
|
| 9 |
+
|
| 10 |
+
Public surface:
|
| 11 |
+
parse_quantity(text) -> (value: float, unit_norm: str) | None (first qty)
|
| 12 |
+
parse_last_quantity(text) -> (value, unit_norm) | None (last qty)
|
| 13 |
+
to_si(value, unit) -> (si_value: float, dimension: str)
|
| 14 |
+
same_dimension(u1, u2) -> bool
|
| 15 |
+
"""
|
| 16 |
+
|
| 17 |
+
from __future__ import annotations
|
| 18 |
+
|
| 19 |
+
import re
|
| 20 |
+
|
| 21 |
+
# unit token (lowercased) -> (dimension, factor-to-SI)
|
| 22 |
+
# One canonical SI unit per dimension; factor converts the token TO that SI unit.
|
| 23 |
+
_UNITS: dict[str, tuple[str, float]] = {
|
| 24 |
+
# time -> seconds
|
| 25 |
+
"s": ("time", 1.0), "sec": ("time", 1.0), "second": ("time", 1.0), "seconds": ("time", 1.0),
|
| 26 |
+
"min": ("time", 60.0), "mins": ("time", 60.0), "minute": ("time", 60.0), "minutes": ("time", 60.0),
|
| 27 |
+
"h": ("time", 3600.0), "hr": ("time", 3600.0), "hrs": ("time", 3600.0),
|
| 28 |
+
"hour": ("time", 3600.0), "hours": ("time", 3600.0),
|
| 29 |
+
"day": ("time", 86400.0), "days": ("time", 86400.0),
|
| 30 |
+
"yr": ("time", 3.15576e7), "year": ("time", 3.15576e7), "years": ("time", 3.15576e7),
|
| 31 |
+
# length -> meters
|
| 32 |
+
"m": ("length", 1.0), "meter": ("length", 1.0), "meters": ("length", 1.0), "metre": ("length", 1.0),
|
| 33 |
+
"km": ("length", 1e3), "cm": ("length", 1e-2), "mm": ("length", 1e-3),
|
| 34 |
+
"nm": ("length", 1e-9), "angstrom": ("length", 1e-10),
|
| 35 |
+
"au": ("length", 1.495978707e11),
|
| 36 |
+
"pc": ("length", 3.0856775815e16), "kpc": ("length", 3.0856775815e19),
|
| 37 |
+
"mpc": ("length", 3.0856775815e22), "ly": ("length", 9.4607e15),
|
| 38 |
+
"r_earth": ("length", 6.371e6), "rearth": ("length", 6.371e6),
|
| 39 |
+
"r_sun": ("length", 6.957e8), "rsun": ("length", 6.957e8),
|
| 40 |
+
# speed -> m/s
|
| 41 |
+
"m/s": ("speed", 1.0), "km/s": ("speed", 1e3), "km/h": ("speed", 1000.0 / 3600.0),
|
| 42 |
+
# energy -> joules
|
| 43 |
+
"j": ("energy", 1.0), "kj": ("energy", 1e3), "mj": ("energy", 1e6), "gj": ("energy", 1e9),
|
| 44 |
+
# power / luminosity -> watts
|
| 45 |
+
"w": ("power", 1.0), "kw": ("power", 1e3), "mw": ("power", 1e6),
|
| 46 |
+
"watt": ("power", 1.0), "watts": ("power", 1.0),
|
| 47 |
+
"l_sun": ("power", 3.828e26), "lsun": ("power", 3.828e26),
|
| 48 |
+
# specific energy -> J/kg
|
| 49 |
+
"j/kg": ("specific_energy", 1.0), "kj/kg": ("specific_energy", 1e3), "mj/kg": ("specific_energy", 1e6),
|
| 50 |
+
# mass -> kg
|
| 51 |
+
"kg": ("mass", 1.0), "m_sun": ("mass", 1.989e30), "msun": ("mass", 1.989e30),
|
| 52 |
+
"m_earth": ("mass", 5.972e24),
|
| 53 |
+
# angle -> arcsec
|
| 54 |
+
"arcsec": ("angle", 1.0), '"': ("angle", 1.0), "as": ("angle", 1.0),
|
| 55 |
+
# dimensionless (bare ratio)
|
| 56 |
+
"": ("dimensionless", 1.0),
|
| 57 |
+
}
|
| 58 |
+
|
| 59 |
+
# number: optional sign, digits/commas, optional decimal, optional exponent.
|
| 60 |
+
_NUM = r"[-+]?\d[\d,]*(?:\.\d+)?(?:[eE][-+]?\d+)?"
|
| 61 |
+
# a unit token: letters/percent/slash/underscore, or a literal double-quote (arcsec).
|
| 62 |
+
_UNIT = r'(?:[A-Za-z_]+(?:/[A-Za-z_]+)?|")'
|
| 63 |
+
_QTY_RE = re.compile(rf"({_NUM})\s*({_UNIT})?")
|
| 64 |
+
|
| 65 |
+
|
| 66 |
+
def _clean_latex(text: str) -> str:
|
| 67 |
+
"""Normalize LaTeX/scientific notation into a plain ``1.23e4 unit`` form."""
|
| 68 |
+
t = text
|
| 69 |
+
t = t.replace("$", " ").replace("\\,", " ").replace("~", " ").replace("\\;", " ")
|
| 70 |
+
t = re.sub(r"\\text\s*\{([^}]*)\}", r" \1 ", t)
|
| 71 |
+
t = re.sub(r"\\mathrm\s*\{([^}]*)\}", r" \1 ", t)
|
| 72 |
+
t = t.replace("\\times", "x").replace("·", "x").replace("⋅", "x").replace("×", "x")
|
| 73 |
+
t = t.replace("\\cdot", "x").replace("∗", "x").replace("*", "x")
|
| 74 |
+
t = t.replace("^{", "^").replace("}", " ")
|
| 75 |
+
# collapse "1.2 x 10^3" / "1.2 x10 3" -> "1.2e3"
|
| 76 |
+
t = re.sub(r"(\d(?:\.\d+)?)\s*x\s*10\s*\^?\s*([-+]?\d+)", r"\1e\2", t)
|
| 77 |
+
# superscript exponent without base mantissa already handled; tidy spaces
|
| 78 |
+
t = re.sub(r"\s+", " ", t)
|
| 79 |
+
return t
|
| 80 |
+
|
| 81 |
+
|
| 82 |
+
def _norm_unit(raw: str | None) -> str | None:
|
| 83 |
+
if raw is None:
|
| 84 |
+
return ""
|
| 85 |
+
u = raw.strip().lower().rstrip(".")
|
| 86 |
+
# strip a trailing plural 's' only if that lands on a known unit and the
|
| 87 |
+
# original didn't (guards "meters" handled above, but catches "joules").
|
| 88 |
+
if u in _UNITS:
|
| 89 |
+
return u
|
| 90 |
+
if u.endswith("s") and u[:-1] in _UNITS:
|
| 91 |
+
return u[:-1]
|
| 92 |
+
return None # unknown unit token
|
| 93 |
+
|
| 94 |
+
|
| 95 |
+
def _parse_one(text: str, *, last: bool) -> tuple[float, str] | None:
|
| 96 |
+
t = _clean_latex(text)
|
| 97 |
+
matches = list(_QTY_RE.finditer(t))
|
| 98 |
+
if not matches:
|
| 99 |
+
return None
|
| 100 |
+
order = reversed(matches) if last else matches
|
| 101 |
+
for mobj in order:
|
| 102 |
+
raw_num = mobj.group(1).replace(",", "")
|
| 103 |
+
try:
|
| 104 |
+
val = float(raw_num)
|
| 105 |
+
except ValueError:
|
| 106 |
+
continue
|
| 107 |
+
unit = _norm_unit(mobj.group(2))
|
| 108 |
+
if unit is None:
|
| 109 |
+
# number had a trailing token that isn't a unit we know — treat as
|
| 110 |
+
# unitless (the model wrote e.g. "5.3 (approx)"); keep scanning only
|
| 111 |
+
# if there might be a better-tagged quantity, else accept unitless.
|
| 112 |
+
unit = ""
|
| 113 |
+
return (val, unit)
|
| 114 |
+
return None
|
| 115 |
+
|
| 116 |
+
|
| 117 |
+
def parse_quantity(text: str) -> tuple[float, str] | None:
|
| 118 |
+
"""First ``(value, normalized_unit)`` in `text`, or ``None``."""
|
| 119 |
+
return _parse_one(text, last=False)
|
| 120 |
+
|
| 121 |
+
|
| 122 |
+
def parse_last_quantity(text: str) -> tuple[float, str] | None:
|
| 123 |
+
"""Last ``(value, normalized_unit)`` in `text`, or ``None``."""
|
| 124 |
+
return _parse_one(text, last=True)
|
| 125 |
+
|
| 126 |
+
|
| 127 |
+
def to_si(value: float, unit: str) -> tuple[float, str]:
|
| 128 |
+
"""Convert ``(value, unit)`` to ``(si_value, dimension)``.
|
| 129 |
+
|
| 130 |
+
Raises ``KeyError`` for an unknown unit (callers pass only normalized units).
|
| 131 |
+
"""
|
| 132 |
+
dim, factor = _UNITS[unit]
|
| 133 |
+
return value * factor, dim
|
| 134 |
+
|
| 135 |
+
|
| 136 |
+
def same_dimension(unit_a: str, unit_b: str) -> bool:
|
| 137 |
+
"""True if both units exist and share a dimension."""
|
| 138 |
+
if unit_a not in _UNITS or unit_b not in _UNITS:
|
| 139 |
+
return False
|
| 140 |
+
return _UNITS[unit_a][0] == _UNITS[unit_b][0]
|
| 141 |
+
|
| 142 |
+
|
| 143 |
+
def is_known_unit(unit: str) -> bool:
|
| 144 |
+
return unit in _UNITS
|
verifier.py
ADDED
|
@@ -0,0 +1,129 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Copyright 2026 Manav Sehgal
|
| 2 |
+
# SPDX-License-Identifier: Apache-2.0
|
| 3 |
+
"""verifier.py — the numeric reward for the astrodynamics RLVR vertical.
|
| 4 |
+
|
| 5 |
+
This IS the reward (RV-2: the eval harness *is* the reward model, no learned RM).
|
| 6 |
+
It conforms to the `fieldkit.eval` verifier signature
|
| 7 |
+
``(predicted, expected, *, rel_tolerance) -> float`` so it drops straight into
|
| 8 |
+
``fieldkit.reward.RewardAdapter`` — the adapter's kwarg introspection forwards
|
| 9 |
+
``rel_tolerance`` and nothing else::
|
| 10 |
+
|
| 11 |
+
from fieldkit.reward import RewardAdapter
|
| 12 |
+
adapter = RewardAdapter(astro_numeric_match, scorer_kwargs={"rel_tolerance": 0.02})
|
| 13 |
+
reward = adapter.score(Rollout(prediction=rollout_text, expected=row["answer"]))
|
| 14 |
+
|
| 15 |
+
Kept LOCAL (not promoted to ``fieldkit.eval``) until a second vertical reuses a
|
| 16 |
+
unit-aware numeric scorer — per `feedback_keep_scorer_local_until_reuse`.
|
| 17 |
+
|
| 18 |
+
Grading policy (decided 2026-06-04, see `_IDEAS/astrodynamics-rlvr-vertical.md`):
|
| 19 |
+
* **binary** — 1.0 / 0.0, no partial credit (partial credit invites Goodhart).
|
| 20 |
+
* **relative tolerance** default ±2% (answers span orders of magnitude;
|
| 21 |
+
absolute tolerance breaks across scales).
|
| 22 |
+
* **unit-normalized** — convert both sides to SI; a dimension mismatch fails.
|
| 23 |
+
* a **bare number** (no unit) is graded against gold *in gold's unit* (the
|
| 24 |
+
common convention — the model answered in the expected unit).
|
| 25 |
+
* answer is read from a ``\\boxed{...}`` sentinel, then a "final answer:" line,
|
| 26 |
+
then the last quantity in the text (most lenient fallback).
|
| 27 |
+
"""
|
| 28 |
+
|
| 29 |
+
from __future__ import annotations
|
| 30 |
+
|
| 31 |
+
import re
|
| 32 |
+
|
| 33 |
+
from units import parse_last_quantity, parse_quantity, same_dimension, to_si
|
| 34 |
+
|
| 35 |
+
_BOXED_OPEN = "\\boxed{"
|
| 36 |
+
|
| 37 |
+
|
| 38 |
+
def extract_boxed(text: str) -> str | None:
|
| 39 |
+
"""Return the inner text of the LAST ``\\boxed{...}`` (brace-matched), or None."""
|
| 40 |
+
idx = text.rfind(_BOXED_OPEN)
|
| 41 |
+
if idx == -1:
|
| 42 |
+
return None
|
| 43 |
+
start = idx + len(_BOXED_OPEN)
|
| 44 |
+
depth = 1
|
| 45 |
+
i = start
|
| 46 |
+
while i < len(text) and depth > 0:
|
| 47 |
+
ch = text[i]
|
| 48 |
+
if ch == "{":
|
| 49 |
+
depth += 1
|
| 50 |
+
elif ch == "}":
|
| 51 |
+
depth -= 1
|
| 52 |
+
i += 1
|
| 53 |
+
if depth != 0:
|
| 54 |
+
return text[start:] # unterminated — take the tail
|
| 55 |
+
return text[start : i - 1]
|
| 56 |
+
|
| 57 |
+
|
| 58 |
+
_FINAL_RE = re.compile(r"final\s+answer\s*[:=]?\s*(.+)", re.IGNORECASE)
|
| 59 |
+
|
| 60 |
+
|
| 61 |
+
def extract_answer(predicted: str) -> str | None:
|
| 62 |
+
"""Pull the answer substring from a model generation.
|
| 63 |
+
|
| 64 |
+
Priority: ``\\boxed{}`` → a "final answer:" line → the whole text (the caller
|
| 65 |
+
then parses the *last* quantity from it).
|
| 66 |
+
"""
|
| 67 |
+
boxed = extract_boxed(predicted)
|
| 68 |
+
if boxed is not None and boxed.strip():
|
| 69 |
+
return boxed
|
| 70 |
+
m = None
|
| 71 |
+
for m in _FINAL_RE.finditer(predicted): # take the last "final answer" hit
|
| 72 |
+
pass
|
| 73 |
+
if m is not None:
|
| 74 |
+
return m.group(1)
|
| 75 |
+
return None # signal: fall back to last-quantity scan over the whole text
|
| 76 |
+
|
| 77 |
+
|
| 78 |
+
def astro_numeric_match(
|
| 79 |
+
predicted: str,
|
| 80 |
+
expected: str,
|
| 81 |
+
*,
|
| 82 |
+
rel_tolerance: float = 0.02,
|
| 83 |
+
) -> float:
|
| 84 |
+
"""1.0 if `predicted`'s answer matches `expected` within `rel_tolerance`, else 0.0.
|
| 85 |
+
|
| 86 |
+
`expected` is the bench row's canonical ``"<value> <unit>"`` gold string.
|
| 87 |
+
"""
|
| 88 |
+
gold = parse_quantity(expected)
|
| 89 |
+
if gold is None:
|
| 90 |
+
return 0.0
|
| 91 |
+
gold_val, gold_unit = gold
|
| 92 |
+
try:
|
| 93 |
+
gold_si, gold_dim = to_si(gold_val, gold_unit)
|
| 94 |
+
except KeyError:
|
| 95 |
+
return 0.0
|
| 96 |
+
|
| 97 |
+
answer_text = extract_answer(predicted)
|
| 98 |
+
if answer_text is not None:
|
| 99 |
+
pred = parse_quantity(answer_text)
|
| 100 |
+
else:
|
| 101 |
+
pred = parse_last_quantity(predicted)
|
| 102 |
+
if pred is None:
|
| 103 |
+
return 0.0
|
| 104 |
+
pred_val, pred_unit = pred
|
| 105 |
+
|
| 106 |
+
if pred_unit == "":
|
| 107 |
+
# bare number — assume the model answered in gold's unit.
|
| 108 |
+
pred_si = pred_val * (gold_si / gold_val if gold_val != 0 else 1.0)
|
| 109 |
+
else:
|
| 110 |
+
if not same_dimension(pred_unit, gold_unit):
|
| 111 |
+
return 0.0
|
| 112 |
+
pred_si, _ = to_si(pred_val, pred_unit)
|
| 113 |
+
|
| 114 |
+
if gold_si == 0.0:
|
| 115 |
+
return 1.0 if abs(pred_si) <= rel_tolerance else 0.0
|
| 116 |
+
return 1.0 if abs(pred_si - gold_si) <= rel_tolerance * abs(gold_si) else 0.0
|
| 117 |
+
|
| 118 |
+
|
| 119 |
+
# Convenience for non-reward callers (debugging / dataset self-check).
|
| 120 |
+
def explain(predicted: str, expected: str, *, rel_tolerance: float = 0.02) -> dict:
|
| 121 |
+
gold = parse_quantity(expected)
|
| 122 |
+
ans = extract_answer(predicted)
|
| 123 |
+
pred = parse_quantity(ans) if ans is not None else parse_last_quantity(predicted)
|
| 124 |
+
return {
|
| 125 |
+
"gold": gold,
|
| 126 |
+
"extracted": ans,
|
| 127 |
+
"pred": pred,
|
| 128 |
+
"score": astro_numeric_match(predicted, expected, rel_tolerance=rel_tolerance),
|
| 129 |
+
}
|