To change orbital inclination (like from East-West to Polar North-South) is it better to do that at the Apoapsis or Periapsis?

[jpinard]

My periapsis is at 75k and my apoapsis is at 90k and I'm low on fuel but need to change my East/West orbit to a North/South polar orbit.  Will it be more efficient to do this at the high or low point of my orbit?  Thanks!

[Guest]

What I just recently found out myself is! That it should generally take less DV changing your inclination at your orbit’s highest point (that being where you are travelling the slowest!) 

if you are trying to attempt a 90 degree change it might even be worth it to raise your apogee and then doing the inclination change at the higher altitude and bring the apogee back down after. Just quicksave before you try it... I don’t want Kerbal blood on my conscience XD

[Guest]

The best way to change your inclination is to do it farther away from the planet and to change your height do it closer

[ajburges]

How low is low fuel? The ratio of Ap to Pe is low enough that 90° inclination change will be expressive.

In general the best cost for inclination change angle of u is v/sin(u/2); the vector difference between current and desired velocity vectors. For 90° changes, that is v*u^.5!

For more than about 30° changes it becomes better to boost Ap to create a lower velocity for the inclination change. Also consider that reasonable normal components during large pro/retrograde (and radial, but that's less commonly used as a burn vector) burns enjoy sub linear dV costs.

[Zhetaan]

1 hour ago, jpinard said:

My periapsis is at 75k and my apoapsis is at 90k and I'm low on fuel but need to change my East/West orbit to a North/South polar orbit.  Will it be more efficient to do this at the high or low point of my orbit?  Thanks!

Apoapsis.  To build on @Dale Christopher's excellent answer, inclination changes are changes in direction, but because velocity is the combination of speed and direction, it is easiest to change direction when you also have low speed.  That happens at the apoapsis.

The mathematics behind that are somewhat complicated, but the end result is easy to see.

If you are in orbit of Kerbin on a 75 km x 90 km ellipse, then it is best to increase your apoapsis while you are at 75 km as far as you can, change inclination once you are at the raised apoapsis, and then reduce your orbit to circular once you've made the change.

In your orbit, should you decide to change inclination at 90 km, the orbital speed is 2,250 m/s.  A ninety-degree inclination change to an equivalent polar orbit will require a burn of 3,182 m/s.  Your orbital speed at 75 km is 2,300 m/s and the same inclination change will require a 3,253 m/s burn.

However, if you decide to raise your apoapsis first and then perform the inclination change, then it looks a bit differently.  A burn to raise your apoapsis to Minmus's orbit (47,000 km) from 75 km costs 912 m/s.  Once at that higher apoapsis, the burn to change your inclination costs 65 m/s, and a burn to return to your previous orbit costs another 912 m/s, for a total of 1,889 m/s.

Edited July 2, 2019 by Zhetaan

[jpinard]

1 hour ago, ajburges said:

How low is low fuel? The ratio of Ap to Pe is low enough that 90° inclination change will be expressive.

In general the best cost for inclination change angle of u is v/sin(u/2); the vector difference between current and desired velocity vectors. For 90° changes, that is v*u^.5!

For more than about 30° changes it becomes better to boost Ap to create a lower velocity for the inclination change. Also consider that reasonable normal components during large pro/retrograde (and radial, but that's less commonly used as a burn vector) burns enjoy sub linear dV costs.

 

Well I found out I couldn't make it.  Bummer.  Looks like I have to launch into polar orbit with this rocket setup I guess.

 

Thanks for all the info all!

[Guest]

I actually had to do something similar to this recently (getting sat into a polar orbit of Kerbin from a 80km equatorial orbit) 

I raised the apogee to 76 million kms I believe and the DV for a full 90 degree inclination change was only 40ms @_@!

(using aerobraking to bring that back down took a while........... but it was a super cheap way of reaching that orbit. under 1k ms i think!)

Edited July 7, 2019 by Guest