Encounter before or after Apoapsis

[Alshain]

I was working on a Duna transfer and realized I found an encounter after passing my apoapsis. I usually encounter before it, and it made me wonder if there is a benefit to attempting to find an encounter on the return? I know in an elliptical orbit, the apoapsis is the point at which you are traveling the slowest. Would it be better to try and encounter after apoapsis to make the capture burn cheaper?

I hope this is making sense, I'm having trouble describing it. (If there are names to describe the two halves of the orbit, I would love to know what they are)

EDIT: OK, what I'm saying is which of the following would be more efficient on the capture burn? (I used the Mun as a quick example, but the same applies to Duna, etc.)

Edited April 16, 2015 by Alshain

[Deutherius]

I think that for atmospheric bodies it doesn't matter, as you'll be aerobraking anyways (and the planet's atmosphere will essentially grab you to go as fast as the celestial body does).

For bodies without atmosphere, it will be largely dependent on a few factors - how elliptical your orbit is, how much is your Ap overshooting the target body's orbit and how massive is the target body.

- More eccentric orbit will need more dV to circularize (related mainly to departure and target bodies - Moho -> Eeloo will take more to circularize than Duna -> Eeloo)

- The more you overshoot the target orbit with your Ap, the more velocity you will have to redirect (essentially burn radial out instead of prograde) at the encounter, which will take more dV, but

- The more massive the target is, the more gravity it has and is able to help you via a gravity assist (you just have to pick the right direction at which to arrive, behind or before the body to either accelerate or brake)

Best case scenario, the way I see it, would be to position your Ap as close to the target orbit as possible, and let its atmo and/or gravity help.

Please note that I may or may not have no idea what I'm talking about It just kinda makes sense to me - it's more efficient to circularize at Ap than it is before/after Ap when doing a Hohmann transfer, so the same principle should apply here as well (it's still a Hohmann, just with a celestial body at the end)... Right?

EDIT: As to the two presented pictures, I think the second one would be more efficient, but both would be suboptimal. Best result here (as for ease of circularization) would be the classic free return "loop" around the Mun - that should mean arriving slightly ahead of the Mun with Ap slightly above the Mun's orbit.

Edited April 16, 2015 by Deutherius

[Alshain]

Well, aerobraking with atmospheric bodies is going to become more difficult with re-entry heat. You won't be able to dip down to 12km around Duna to capture without burning something up, unless you have a heat shield. If I understand correctly, the key element is your speed, the faster you are traveling, the more you will have to burn to capture. We aren't circularizing till we get there, so eccentricity of your orbit around the sun shouldn't matter, just how fast you are passing by Duna. So, I guess the question is, which method would produce a slower fly-by, or will it even make a difference?

[Deutherius]

Eccentricity of your orbit will make a difference, it is however something you will have little control over, as it is (in a simple Hohmann transfer) determined by your origin and destination. If you start on Moho and go for Duna (and place Ap at Duna's orbit), you orbit will be much more eccentric than if you start on Kerbin, your velocity at Ap will be slower, and therefore Duna will be moving faster relative to you, demanding a harder circularization burn and/or more intense aerobraking.

If you overshoot the Ap, you might be moving faster relative to Duna at randezvous, but in a different direction - the difference in Kerbol-relative speeds might be better for circularization, but the difference in velocities might not.

That's where the gravity sling comes in along with the atmo to help.

I'll be the first one to admit that I have not studied orbital mechanics in depth, though, so I'm just stating what feels intuitive to me based on what little I know from playing KSP... It's entirely possible I got it wrong. If you want to be sure, it shouldn't be too hard to fire up a sandbox save, turn on infinite fuel and test it

[A_name]

I would think that you shouldn't place your Ap beyond the target orbit for two reasons. (1) You are using Dv on your transfer burn in order to raise the Ap beyond the target orbit when you could get a cheaper encounter by burning to a lower orbit which uses less Dv, if you time your transfer correctly, of course. (2) As you already mentioned, at the top of an elliptical orbit is when your are moving slowest, relative to the sun in this case, yes, but since Duna's orbital velocity around the sun is more or less constant, any additional orbital velocity you bring with you by timing the encounter on the way down from Ap is velocity you will need to cancel out by burning and thus using Dv.

[OhioBob]

Would it be better to try and encounter after apoapsis to make the capture burn cheaper?

Sometimes yes, sometimes no. What you want is the encounter that has the smallest relative velocity between the spacecraft and the planet/moon. One way to do this is to make the angle formed by the crossing of the orbits as small as possible. Generally, if the planet/moon is in the part of its orbit where it has passed periapsis and is approaching apoapsis, then you want to encounter the planet/moon before your spacecraft reaches apoapsis (called a Type I transfer). If the planet/moon is in the part of its orbit where it has passed apoapsis and is approaching periapsis, then you want to encounter the planet/moon after your spacecraft has passed apoapsis (called a Type II transfer). The reason for this is that if both are approaching apoapsis, then both have a positive flight path angle. And if both have past apoapsis and are approaching periapsis, then both have a negative flight path angle. By keeping the flight path angles both positive or both negative you reduce the relative angle and, therefore, the relative velocity. If the target planet/moon has a perfectly circular orbit (such as Mun), then it makes little difference whether you use a type I or type II transfer, the magnitude of the relative velocity will be the same, it will just have different direction. Of course a type I trajectory always has a shorter travel time than a type II.

Edited April 16, 2015 by OhioBob

[Yakky]

In your Mun examples (and in general when at least one of the orbits has low eccentricity), the closing speed of a post-apoapsis encounter is approximately equal to the closing speed of a comparable pre-apoapsis encounter, due to the conservation of energy and the symmetry of the situation. This is not the case if both you and the celestial body you're approaching have highly elliptical orbits with different arguments of periapsis. But fortunately, in those cases it's pretty obvious by inspection where the best (lowest relative velocity) intercept is going to be: you generally just want to look for the smallest closing angle (as others have said).

The main benefit to a post-apoapsis encounter in my experience is that it can give you much greater flexibility in creating an encounter window. You can essentially dial in whatever "hang time" you like by boosting or lowering your apoapsis varying amounts above the target body so that you'll run into it on the way back down from your apoapsis. This can be nice when you don't want to wait years for a better interplanetary transfer window to come around. You can play with that in your Mun example by exploring how much flexibility you get to move your encounter window around when you allow yourself to play with the height of your apoapsis and then do a post-apoapsis encounter.

Edited April 16, 2015 by Yakky

[Warzouz]

Relative speed shoud be nearly the same. But on an eliptic orbit, the speed is slow, so you'll have to wait a long time.

On my Eeloo mikssion, I had an encounter after Apo. It was more than 1 year after crossing the orbit before Apo, even if it seems very near.