It seems like you\'re getting a ton of help! My last two cents: Remember it takes two burns to go from one circular orbit to another. http://en.wikipedia.org/wiki/Hohmann_transfer_orbit I attached a picture: To go from high to low, you need to retrograde burns. The first at A, will turn your circular orbit into the red ellipse. (Stop the burn when your Pe is where you want it.) The second burn at B (your new Pe), is ALSO retrograde! Do this burn until your Ap comes down to the same height as your Pe (the definition of a circular orbit.) If you flip Ap and Pe, and replace retrograde with prograde, you have the recipe for a low to high Hoffman transfer. P.S. You don\'t need to start with a circular orbit to do this, either. As Bill said: To reduce your Pe, burn retro at Ap. To increase your Ap, burn pro at Pe. Once I memorized this, everything else fell into place.