Hohmann Transfer Orbits

or, how do we put a satellite in geosynchronous orbit?

The space shuttle travels in a Low Earth Orbit at a height of about h=400 km. A geosynchronous communications satellite needs to be at an altitude of h=35,000 km.

Do we go straight up? No, takes too much energy.

We use a Hohmann transfer orbit

What is the semimajor axis of the transfer orbit?

So we can then calculate how much energy to add (ie how much we need to increase v) to get to the higher orbit.

Interplanetary Travel

Use the same principle, except this time between planet orbits.

But: timing is crucial -- Launch Windows are important.
(that is, you want to make sure the planet is there when you are!)

Example: Let's go to Mars!

What is the semi-major axis of the Earth-Mars transfer orbit?
And how long does it take to get there? What is the period of the transfer orbit?
So how long does it take to get there?

Does it matter which direction you go?