Two Body Central Force Orbits

(one object, mass = M, is much more massive than the other with mass = m)

G = gravitational constant = 6.67x10

Gravitation Potential at m =

[ k = MG ]

- 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 EnergyMost Rocket Fuels Combinations limited to 4 MJ/kg Hydrogen/Oxygen = 10 MJ/kg Fuel Value of Gasoline = 44 MJ/kg |

Central Body | k |
---|---|

Earth | 398 649 km^{3}/s0.002647 AU (km/s) ^{2} |

Sun | 887.21 AU (km/s)^{2} |

Jupiter | 0.8474 AU (km/s)^{2} |

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 |

- 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