Archive-name: space/constants Last-modified: $Date: 93/04/01 14:39:04 $  CONSTANTS AND EQUATIONS FOR CALCULATIONS      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.)      NUMBERS  	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).      EQUATIONS  	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  	    Vc	 = sqrt(M * G / r) 	    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 	    g	= 9.80665 m / s^2  	    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  	    d@12km (40000 ft) = d0*.18 	    d@9 km (30000 ft) = d0*.27 	    d@6 km (20000 ft) = d0*.43 	    d@3 km (10000 ft) = d0*.65  		    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.      CONSTANTS  	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?