## Transfer Orbits

### Direct Flight Minimum Energy Orbits

The Minimum Energy Orbits to travel to Jupiter and Neptune are shown in the diagram below.

Energy and Velocity Changes for Orbit Transitions

Transistion | Velocity Change km/s | Energy Change MJ/kg |

Earth orbit to Jupiter Transfer Orbit | 8.7 | 297 |

Jupiter Transfer orbit to Jupiter orbit | 5.6 | 57.8 |

Earth orbit to Neptune Transfer Orbit | 11.5 | 409 |

Transfer orbit to Neptune orbit | 4.1 | 13.8 |

Earth Orbit to Jupiter Orbit | - | 355 |

Earth orbit to Neptune Orbit | - | 423 |

### Orbits using Gravitational Assist from Jupiter

**Parameters of Orbit #1** to Jupiter
- a = 3.50 AU
- P = 6.548 yrs
- e = 0.714
- E = -126.7 MJ/kg
- v
_{peri} = 39.0 km/s
- t
_{Transit}= 1.674 yrs
- Angle from Perihelion = θ = 160°

**Parameters of Orbit #2** from Jupiter to Neptune

Selection via Minimum Semi-major axis to reach Neptune.

Use Conservation of Energy and Angular Momentum to determine, e.
- a = 18.0 AU
- e = 0.776 (from Tisserand Relation)
- E = -24.6 MJ/kg
- P = 76.368 yrs
- r
_{peri} = 4.025
- t
_{Transit}= 25.37 yrs
- v(at Neptune) = 3.14 km/s

Some **Parameters of the Jupiter Flyby**
- v
_{ingress} = 10.25 km/s
- v
_{egress} = 16.46 km/s
- ΔE = -24.6 - (126.7) = 102.1 MJ/kg
- t
_{flyby} = 0.37 yrs

Transition | Velocity Change (km/s) | Energy MJ/kg |

Earth Orbit to Orbit #1 | 9.2 | 316.5 |

Orbit #2 to Neptune Orbit | 2.30 | 9.9 |

Total Energy | - | 326 |

Jupiter Flyby | 6.2 | 83 |

So the use of Jupiter's Gravitational Assist saves (423 - 326) = 97 MJ/kg. Another
benefit is a reduction of the velocity change needed at Neptunes orbit with there is
less fuel available. |

Created by L.Bogan - June 07, 2005