Orbital Physics and Numbers

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

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 = Energy_gravity/m = - G M/r = - k/r²
[ k = MG ]
a = semi-major axis
Total Orbital Energy = E_total = - 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 Body	k
Earth	398 649 km³/s 0.002647 AU (km/s)²
Sun	887.21 AU (km/s)²
Jupiter	0.8474 AU (km/s)²

Energy (per mass) of circular orbits

Orbit	Distance	Energy (km/s)²	Orbit Speed (km/s)
Low Earth Orbit	7000 km	- 28.5	7.55
Earth's orbit	1.00 AU	- 443.6	29.8
Jupiter's orbit	5.20 AU	- 85.3	13.06
Low Jupiter Orbit	80 000 km	- 792	126
Neptune's orbit	30.0 AU	- 14.8	5.44

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 * V_orbit = 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