Efficiency when in an eccentric orbit

[jarmund]

Greetings fellow kerbonauts.

I'd love some input on my logic regarding eccentric orbital efficiency.

Let's presume Val is orbiting Gilly and wants to go to...

Kerbin: Burn at Gillys PE around Eve, because higher orbital speed thus Mr Oberth helping out more.

Eve: Burn at Gillys AP around Eve, because it's better to lower the PE further than lowering you AP all the way.

 

Is my logic sound? Any flaws? Any other useful commentaries?

[bewing]

Hmmm. I don't think Gilly is a good example here. You might want to use one of the moons of Jool, instead.

The problem with Gilly is that it has no gravity, and no Oberth of its own. So you should never do any burns from Gilly, except to go to a Pe around Eve -- because in doing so, you gain lots of Oberth. Yes, it's best to do it when Gilly is at its Ap.

If you have a moon with lots of gravity, and therefore lots of Oberth, and lots of orbital velocity too -- then if you are going interplanetary, you want to burn when you are at your Pe around the moon, and the moon is at its Pe around its host planet -- because that gives you maximum Oberth. Provided that the window is there, of course.

 

[Snark]

I would say to the OP that yes, your logic is sound.

However, in the case of "I want to go to Kerbin from Gilly", there's a third option you haven't considered:  Wait until Gilly is at its Ap around Eve, do a burn to escape retrograde from Gilly to drop your Pe down to very low Eve orbit (same as if you were going to Eve rather than Kerbin) ... and then do your main Kerbin ejection burn when you're at your Eve Pe.  This will give you a huge Oberth boost and save a lot of dV.

Of course, it'll make navigation, launch window planning, etc. more of a pain, so it'll likely be pretty inconvenient.  If you're not fortunate in terms of how the planets are lining up, you may need to do it in stages that are widely separated in time (e.g. do the Gilly-escape burn to get in a very elliptical Eve orbit; then wait weeks or months until your Eve Pe is pointing in the solar-prograde direction to do your Eve-escape burn; then maybe need to wait a few years doing multiple solar orbits until you get Kerbin to line up with your ship when you're at Ap).

But in terms of "how can I get from Gilly to Kerbin with the absolute minimum possible dV", that'll be your best bet.

[OhioBob]

Since the gravity of Gilly is so small, we can almost ignore it.  Therefore, the answer to your first question comes down to, from orbit can we most efficiently depart Eve for a transfer to Kerbin?  The answer to that is the gate orbit.

The hyperbolic excess velocity, v_∞, for a transfer from Eve to Kerbin (if done at an optimum launch window) varies from about 700 to 1000 m/s.  This means that the gate orbit varies from about 16 to 33 km.  Since Gilly's periapsis is about 14 km and its apoapsis is about 49 km, ejecting from periapsis is clearly better than ejecting from apoapsis.

Note that the gate orbit is assumed circular.  Therefore, ejecting from Gilly at any point is its orbit other than the apsides will introduce some radial velocity, which will undoubtedly mess with our efficiency.

Furthermore, note that we must depart Eve when the ejection angle is correct.  We can't just declare that we're going to eject at periapsis because periapsis may not be anywhere close to the correct ejection angle.  The situation is rarely as simple as we often want to make it.  It is very unlikely that all the variables will converge at just the right place to allow for the ideal ejection.

 

Edited July 2, 2016 by OhioBob