Background:
Transfer Orbits

Tour Home

To move from one planet to another, you need to change your orbit. For example, to move from the Earth to Jupiter, you need to plot an orbit which takes you from 1 AU from the Sun (the Earth's orbital distance) to 5.2 AU from the Sun (Jupiter's orbital distance). There are many such orbits that will do that, but the simplest orbit -- and the one which would require the least amount of energy -- is called a Hohmann transfer orbit.

Think of yourself on the Earth (or really, in orbit around the Earth). Because you are moving with the Earth, you are essentially in a circular orbit around the Sun, moving at with a certain orbital speed (29.5 km/s, in fact). If you boosted your speed a little, you would no longer be on a circular orbit, but you would start moving outwards from the Sun on an elliptical orbit. Eventually you would reach aphelion (the furthest point from the Sun on the orbit) and start to fall back inwards. A Hohmann transfer orbit is the orbit where aphelion occurs just at Jupiter's distance from the Sun -- in other words, you added just enough energy to your orbit at the Earth to get out to Jupiter.

So a Hohmann transfer orbit has a perihelion distance equal to your original distance from the Sun, and an aphelion distance equal to where you want to go:



Oh, there's one more complication: You want Jupiter to actually be there when you get out to its orbit. In other words, you have to time your launch just right so that you and Jupiter meet up at the right time! How do you do this? Once you calculate your orbit, you should be able to figure out how long it takes to go from the Earth to Jupiter (using Kepler's Third Law). Then, knowing how long it takes for Jupiter to make one full orbit, you can calculate how far along its orbit Jupiter will travel while the probe is on its way. If Jupiter will travel 1/4 of its orbit, you want to launch when Jupiter is 1/4 of an orbit (ie, 90 degrees) away from the rendezvous point. (More accurately, the numbers are 23% of the orbit, and so you need to launch when Jupiter is 83 degrees away from the rendezvous point.)