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Formulae for Orbital Mechanics
These are misc equations for use in orbital calculations. If there are any
errors or questions, please leave me a message. ---Bill Bard, 75366,2557
Misc Satellite Orbit Equations
------------------------------
Mf = M * (exp(DVa / (g * Isp) ) - 1),
Mf = M * (exp(DVa / Ispg ) - 1),
Ispg = Isp * g,
where Mf = Mass of fuel lost during the burn (ie fuel mass burned)
M = Initial total mass
DVa = Change in velocity (delta-v) in m/s
Isp = specific impulse in seconds
Ispg = specific impulse in m/s
g = 9.81 m/s^2
Velocity of satellites in elliptical orbit
-----------------------------------------
V1 = (mu * ( (2 / r1) - (1 / a) ) )^(1/2),
V1 = V2 * r2 / r1,
r1 = altitude1 + re,
r2 = altitude2 + re,
where V1 = Velocity of a satellite at point 1 in m/s
r1 = distance of the satellite from the earth's center in meters
at point 1
altitude1 = the altitude of the satellite above the earth at
point 1
V2 = Velocity of a satellite at point 2 in m/s
r2 = distance of the satellite from the earth's center in meters
at point 2
altitude2 = the altitude of the satellite above the earth at
point 2
a = semimajor axis of the orbit in meters
mu = 3.986008 x 10^14 m^3/s^2
re = 6378.15 Km = radius of the earth
Velocity of satellites in circular orbit
----------------------------------------
Vcircle = (mu / r)^(1/2),
r = altitude + re,
where Vcircle = Velocity of a satellite in a circular orbit at
rcircle in m/s
r = distance of a satellite in circular orbit from the
earth's center in meters
altitude = the altitude of the satellite above the earth
mu = 3.986008 x 10^14 m^3/s^2
re = 6378.15 Km = radius of the earth
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