Orbital Physics and Numbers

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

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
• 1 AU = 149.6 million km (1 km = 1000 m)
• 1 yr = 31.6 million seconds
• (km/s)2 = MegaJoule/kg (energy/mass)

 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

• Sphere of Influence of the Earth = 0.0100 AU = 1.5 million km
= 3.9 * Moon orbit radius
• Escape Velocity of the Earth = √2 * Vorbit = 10.7 km/s
• Energy into Earth Orbit = 33.9 MJ/kg
• Energy from Orbit to escape Earth's Gravity = 28.5 MJ/kg
• Energy of 62.4 MJ/kg will put the spacecraft outside the Earth's Sphere of Influence with zero velocity w.r.t. the Earth

Created by L.Bogan - June 07, 2005