| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |
| {"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}} | |