## 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

TransistionVelocity Change
km/s
Energy Change
MJ/kg
Earth orbit to Jupiter Transfer Orbit8.7297
Jupiter Transfer orbit to Jupiter orbit5.657.8
Earth orbit to Neptune Transfer Orbit11.5409
Transfer orbit to Neptune orbit4.113.8
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
• vperi = 39.0 km/s
• tTransit= 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
• rperi = 4.025
• tTransit= 25.37 yrs
• v(at Neptune) = 3.14 km/s
Some Parameters of the Jupiter Flyby
• vingress = 10.25 km/s
• vegress = 16.46 km/s
• ΔE = -24.6 - (126.7) = 102.1 MJ/kg
• tflyby = 0.37 yrs
TransitionVelocity Change (km/s)Energy MJ/kg
Earth Orbit to Orbit #19.2316.5
Orbit #2 to Neptune Orbit2.309.9
Total Energy-326
Jupiter Flyby6.283

 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