Dual Component burns

[garyw]

I've got a TX in orbit and the time has come to bring them home. My path tracks south of the base and I've had the idea that I can use a dual component burn (not sure if that is the correct phrase so please correct me if I'm wrong).

The idea is to perform a burn that is part plane change to help push the entry path closer to the base and part deorbit burn.

What I'm after is if there are any equations (with explanations!) on this sort of burn? How can I tell how much delta-v is going into the plane change and how much into the deorbit burn?

Thanks.

 

[Urwumpe]

Well, if you can live with some small loss in accuracy, just imagine that the burn will take place instantly.

Now, the plane change and the deorbit can be imagined as such: The new orbit afterwards, has a different plane and a lower periapsis. So, you will have a single burn. But you can still split it two components, just ignore Earth and claim that you can fly through it and return back to the place of the first burn - the result would be the same.

So, you will have the delta-velocity vector for the plane change burn, and the delta velocity vector of the periapsis change, both added together (vector addition!) result in the final burn. If you calculate both components burns in the same coordinate system (ideally LVLH), you can use orbit HUD for pointing - and done.

You will have some small errors because control, gravity and steering losses apply, and these are not possible to be split into two.