Burn Order

[Burninate]

Optimizing for minimum fuel expenditure:

You are in a 4AU x 6AU eccentric orbit, inclined 10 degrees off from the ecliptic plane. The plane conjunction is very close to periapsis and apoapsis. You want to make an encounter with an atmosphere-possessing object in a 10AU circular orbit on the ecliptic. You have the forecasting power and patience to have this be a high-velocity encounter (to wait for the orbits to line up and do an aerocapture/impact, rather than trying to circularize), but not to hit a bullet with a bullet and do it off-plane.

Do you raise apoapsis first, or correct inclination first, or do some phased process, or does it not matter? How would one determine this? How about for other plane conjunctions, N degrees off from the periapsis and apoapsis?

First piece of the puzzle I know from very basic orbital mechanics is that inclination is better corrected at apoapsis than periapsis. More than that, I havn't determined.

Bonuspoints: How about for other initial inclinations M?

Double Bonuspoints: How about for other initial periapses P and apoapses A and target circular orbit radii R in a fully generalized solution?

Edited November 18, 2013 by Burninate

[Kulebron]

I'd match the planes in apoapsis. Reason why:

Raise apoapsis and let planet's gravity do part of the work (if aerobraking is possible, then better).

If you circularize your orbit to almost match that of the planet, what will be different is the encounter speed. (You move very slowly on a very eccentric orbit, while on a circural orbit you move ~ as fast as the planet). But no matter the encounter speed, you'll still fall on the planet, and flyby speed will be not much different.

Edited November 18, 2013 by Kulebron

[Burninate]

The question was intended to be: If you have to raise apoapsis substantially (but keep periapsis low), *and* do an inclination change, which to do first? And secondarily, how does that answer decay as plane ascending/descending points move away from the apo/periapses?

[el_coyoto]

The question was intended to be: If you have to raise apoapsis substantially (but keep periapsis low), *and* do an inclination change, which to do first? And secondarily, how does that answer decay as plane ascending/descending points move away from the apo/periapses?

Plane changes are cheaper when done away from the center of the system.

So, you should prefer the method that leaves you with an AN/DN node the farthest possible from Kerbol...