Optimal burn to lower your periapsis

[Kasuha]

Of course, optimal burn to lower your periapsis is done at apoapsis. But here I thought what to do if I don't have the apoapsis within the SOI or if I just don't want to wait till my ship gets there.

To my surprise, the optimum burn came out as combination of radial and retrograde burns which lowered the periapsis and kept the apoapsis distance constant.

Unfortunately I don't know how to find such burn without a lot of fiddling with node controls.

Apoapsis burn - 157 m/s

Arbitrary point burn, pure retrograde - 303 m/s

Arbitrary point burn, pure radial - 362 m/s

Arbitrary point burn, optimal - 256 m/s

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[rhoark]

It's the direction tangent to the new apoapsis.

[Sirrobert]

This is how I always adjust my periaps of an encounter before the actual encounter. A few m/s while far away enough make a huge difference if the end result is 300 days away

[SkyRender]

There are some interesting circumstances where it makes more sense to fire in a direction besides retrograde to lower your periapsis. Indeed, sometimes firing towards the planet actually IS the most efficient way to get down there... but it usually isn't.

[Kasuha]

Okay I was wrong, the maneuver does not keep the apoapsis height. I tried it again for much lower point on the orbit and optimal burn has much lower apoapsis there.

Now it looks like the apoapsis has to stay on the original orbit.

Edit: yes, I tried again in the original place and I got it down to 234 m/s burn. What's in the image in the first post is not optimal burn from that position.

Edited October 25, 2013 by Kasuha

[AmpsterMan]

The reason a radial burn in that case is.optimal is because Radial burns can be used to change both Argument of Periapsis (ie. Move the Pe, Ap nodes along your orbit) and a retrograde burn is used to decrease Semi Major Axis (ie. Lower your orbit)

As to how to find where to optimal point is I don't know. I kinda just finally had a light bulb moment and understood what the 6 orbital elements are; I'm still trying to grasp how it is that the orbits are affected.

That said, I suspect the optimal way to do it has to be < 90° radial+ from retrograde. This is because a radial + burn brings Apoapsis closer to you and a retro lowers Periapsis.