Transfer Orbits - Simple Help Requested

[Commander Zoom]

The math in most of the entries on Hohmann orbits makes my eyes glaze over. I\'m looking for some simple rules of thumb as to where in an orbit to apply acceleration, and in what direction, to most efficiently expand, contract, and/or 'aim' the apoapsis.

Example:

To shift the apokee counter/clockwise, apply thrust about X degrees ahead/behind/at perikee, in/opposite/at a Y degree angle from the direction of orbit.

To circularize an orbit, ...

I can eyeball this stuff, now that we have an orbital map, but I\'d appreciate a starting point.

[Ivan Ivanovich]

To raise/lower apogee, burn at perigee. And vice versa. Burning before apogee raises/lowers the apogee rather than the perigee and pushes it away from your craft. Burning after apogee raises/lowers it too, but pushes it in the other direction. And of course, if you burn enough at apogee, it becomes perigee, when raising the orbit. And vice versa, of course.

[Commander Zoom]

Got the first two, and the last, of course. But could you be more specific about the middle part? Burning in mid-orbit to shift its axis - where along the orbit is best? At what angle?

EDIT: Incidentally, you didn\'t actually specify in which direction to burn for the first part either - I know what you mean only from my own experience - so for the benefit of anyone else who may be reading:

To increase apokee, burn at perikee, in the direction of orbit (green circle).

To decrease apokee, burn at perikee, in the opposite direction (green circle with X).

[Ivan Ivanovich]

Because it should be obvious what direction to burn to raise/lower the orbit... c\'mon, it\'s not rocket science to know that your orbit decreases if you get slower.

When you\'re not exactly at apogee/perigee, you push the apogee/perigee away from you if you initiate a burn. So if you\'re about to reach apogee and thrust to increase speed, the apogee moves away from you, 'ahead' of you. Likewise, if you\'re past apogee and increase speed, you push the apogee away from you, 'behind' you. The effect only becomes really noticeable, though, if you have similar apogee/perigee heights, because obviously to shift a highly elliptical orbit halfway across a planet requires a DAMN LOT of fuel.

But try it for yourself. Get into an orbit. Any orbit. Then get to apogee and increase speed a little to lift perigee up to apogee level. And then play with it. If you\'re right between apogee and perigee, you should be able to raise/lower your total orbit with a burn (though, of course, you\'ll have to expend as much fuel as you would have to if burning at perigee to raise apogee, then up at perigee to get the apogee up, so don\'t expect to see a lot of change for a little thrust!).

[Commander Zoom]

Okay, fair enough...

Let\'s say I\'m in a circular parking orbit around Kearth/Kerbin, with the Mun at 12 o\'clock (N), and I want to 'aim' my apoapsis at 10 o\'clock (NW). What\'s the best point, roughly, to start thrusting to expand it in that direction? What if I already have an eccentric orbit, and I want to shift its major axis clockwise or counter-clockwise?

[Ivan Ivanovich]

By default, the best point to apply thrust to push your apogee in any direction is to do it 180 degrees opposite that point. It\'s basically an extrapolation from the fact that you push the apogee upwards by thrusting at perigee. Pretty much independent of the orbit you\'re in. You could of course first 'move' perigee and apogee, but the energy you\'d have to expend stays the same.

[Commander Zoom]

Got it. Thanks.