| Archive-name: space/constants |
| Last-modified: $Date: 93/04/01 14:39:04 $ |
| This list was originally compiled by Dale Greer. Additions would be |
| appreciated. |
| Numbers in parentheses are approximations that will serve for most |
| blue-skying purposes. |
| Unix systems provide the 'units' program, useful in converting |
| between different systems (metric/English, etc.) |
| 7726 m/s (8000) -- Earth orbital velocity at 300 km altitude |
| 3075 m/s (3000) -- Earth orbital velocity at 35786 km (geosync) |
| 6371 km (6400) -- Mean radius of Earth |
| 6378 km (6400) -- Equatorial radius of Earth |
| 1738 km (1700) -- Mean radius of Moon |
| 5.974e24 kg (6e24) -- Mass of Earth |
| 7.348e22 kg (7e22) -- Mass of Moon |
| 1.989e30 kg (2e30) -- Mass of Sun |
| 3.986e14 m^3/s^2 (4e14) -- Gravitational constant times mass of Earth |
| 4.903e12 m^3/s^2 (5e12) -- Gravitational constant times mass of Moon |
| 1.327e20 m^3/s^2 (13e19) -- Gravitational constant times mass of Sun |
| 384401 km ( 4e5) -- Mean Earth-Moon distance |
| 1.496e11 m (15e10) -- Mean Earth-Sun distance (Astronomical Unit) |
| 1 megaton (MT) TNT = about 4.2e15 J or the energy equivalent of |
| about .05 kg (50 gm) of matter. Ref: J.R Williams, "The Energy Level |
| of Things", Air Force Special Weapons Center (ARDC), Kirtland Air |
| Force Base, New Mexico, 1963. Also see "The Effects of Nuclear |
| Weapons", compiled by S. Glasstone and P.J. Dolan, published by the |
| US Department of Defense (obtain from the GPO). |
| Where d is distance, v is velocity, a is acceleration, t is time. |
| Additional more specialized equations are available from: |
| ames.arc.nasa.gov:pub/SPACE/FAQ/MoreEquations |
| For constant acceleration |
| d = d0 + vt + .5at^2 |
| v = v0 + at |
| v^2 = 2ad |
| Acceleration on a cylinder (space colony, etc.) of radius r and |
| rotation period t: |
| a = 4 pi**2 r / t^2 |
| For circular Keplerian orbits where: |
| Vc = velocity of a circular orbit |
| Vesc = escape velocity |
| M = Total mass of orbiting and orbited bodies |
| G = Gravitational constant (defined below) |
| u = G * M (can be measured much more accurately than G or M) |
| K = -G * M / 2 / a |
| r = radius of orbit (measured from center of mass of system) |
| V = orbital velocity |
| P = orbital period |
| a = semimajor axis of orbit |
| Vesc = sqrt(2 * M * G / r) = sqrt(2) * Vc |
| V^2 = u/a |
| P = 2 pi/(Sqrt(u/a^3)) |
| K = 1/2 V**2 - G * M / r (conservation of energy) |
| The period of an eccentric orbit is the same as the period |
| of a circular orbit with the same semi-major axis. |
| Change in velocity required for a plane change of angle phi in a |
| circular orbit: |
| delta V = 2 sqrt(GM/r) sin (phi/2) |
| Energy to put mass m into a circular orbit (ignores rotational |
| velocity, which reduces the energy a bit). |
| GMm (1/Re - 1/2Rcirc) |
| Re = radius of the earth |
| Rcirc = radius of the circular orbit. |
| Classical rocket equation, where |
| dv = change in velocity |
| Isp = specific impulse of engine |
| Ve = exhaust velocity |
| x = reaction mass |
| m1 = rocket mass excluding reaction mass |
| Ve = Isp * g |
| dv = Ve * ln((m1 + x) / m1) |
| = Ve * ln((final mass) / (initial mass)) |
| Relativistic rocket equation (constant acceleration) |
| t (unaccelerated) = c/a * sinh(a*t/c) |
| d = c**2/a * (cosh(a*t/c) - 1) |
| v = c * tanh(a*t/c) |
| Relativistic rocket with exhaust velocity Ve and mass ratio MR: |
| at/c = Ve/c * ln(MR), or |
| t (unaccelerated) = c/a * sinh(Ve/c * ln(MR)) |
| d = c**2/a * (cosh(Ve/C * ln(MR)) - 1) |
| v = c * tanh(Ve/C * ln(MR)) |
| Converting from parallax to distance: |
| d (in parsecs) = 1 / p (in arc seconds) |
| d (in astronomical units) = 206265 / p |
| Miscellaneous |
| f=ma -- Force is mass times acceleration |
| w=fd -- Work (energy) is force times distance |
| Atmospheric density varies as exp(-mgz/kT) where z is altitude, m is |
| molecular weight in kg of air, g is local acceleration of gravity, T |
| is temperature, k is Bolztmann's constant. On Earth up to 100 km, |
| d = d0*exp(-z*1.42e-4) |
| where d is density, d0 is density at 0km, is approximately true, so |
| Atmospheric scale height Dry lapse rate |
| (in km at emission level) (K/km) |
| Earth 7.5 9.8 |
| Mars 11 4.4 |
| Venus 4.9 10.5 |
| Titan 18 1.3 |
| Jupiter 19 2.0 |
| Saturn 37 0.7 |
| Uranus 24 0.7 |
| Neptune 21 0.8 |
| Triton 8 1 |
| Titius-Bode Law for approximating planetary distances: |
| R(n) = 0.4 + 0.3 * 2^N Astronomical Units (N = -infinity for |
| Mercury, 0 for Venus, 1 for Earth, etc.) |
| This fits fairly well except for Neptune. |
| 6.62618e-34 J-s (7e-34) -- Planck's Constant "h" |
| 1.054589e-34 J-s (1e-34) -- Planck's Constant / (2 * PI), "h bar" |
| 1.3807e-23 J/K (1.4e-23) - Boltzmann's Constant "k" |
| 5.6697e-8 W/m^2/K (6e-8) -- Stephan-Boltzmann Constant "sigma" |
| 6.673e-11 N m^2/kg^2 (7e-11) -- Newton's Gravitational Constant "G" |
| 0.0029 m K (3e-3) -- Wien's Constant "sigma(W)" |
| 3.827e26 W (4e26) -- Luminosity of Sun |
| 1370 W / m^2 (1400) -- Solar Constant (intensity at 1 AU) |
| 6.96e8 m (7e8) -- radius of Sun |
| 1738 km (2e3) -- radius of Moon |
| 299792458 m/s (3e8) -- speed of light in vacuum "c" |
| 9.46053e15 m (1e16) -- light year |
| 206264.806 AU (2e5) -- \ |
| 3.2616 light years (3) -- --> parsec |
| 3.0856e16 m (3e16) -- / |
| Black Hole radius (also called Schwarzschild Radius): |
| 2GM/c^2, where G is Newton's Grav Constant, M is mass of BH, |
| c is speed of light |
| Things to add (somebody look them up!) |
| Basic rocketry numbers & equations |
| Aerodynamical stuff |
| Energy to put a pound into orbit or accelerate to interstellar |
| velocities. |
| Non-circular cases? |
| NEXT: FAQ #7/15 - Astronomical Mnemonics |
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