Orbital Physics and Numbers


Two Body Central Force Orbits
(one object, mass = M, is much more massive than the other with mass = m)

Shape of orbits diagram

Orbital Energies

Energy = Gravitational + Kinetic


Kinetic Energy/mass = 1/2 v2
G = gravitational constant = 6.67x10-11 N m2/kg2 (J/kg.m/kg)
Gravitation Potential at m = Energygravity/m = - G M/r = - k/r2
[ k = MG ]
a = semi-major axis
Total Orbital Energy = Etotal = - k/2a

Rocket Fuels Specific Energy
Most Rocket Fuels Combinations limited to 4 MJ/kg
Hydrogen/Oxygen = 10 MJ/kg
Fuel Value of Gasoline = 44 MJ/kg

The Value of k for Various Central Bodies:

Central Bodyk
Earth398 649 km3/s
0.002647 AU (km/s)2
Sun887.21 AU (km/s)2
Jupiter0.8474 AU (km/s)2

Energy (per mass) of circular orbits

OrbitDistanceEnergy (km/s)2Orbit Speed (km/s)
Low Earth Orbit7000 km- 28.57.55
Earth's orbit1.00 AU- 443.629.8
Jupiter's orbit5.20 AU- 85.313.06
Low Jupiter Orbit80 000 km- 792126
Neptune's orbit30.0 AU- 14.85.44


Escaping the Earth's Gravity

Low Earth Orbit

Created by L.Bogan - June 07, 2005