Venus Stranded Challenge - Physics:

[RSWingman]

It starts you in a high orbit around Venus with a limited amount of fuel (not enough for a conventional escape) back to Earth. I downloaded a replay which reveals that the trick is to perform a retrograde burn, placing your PE at around 100K alt, then to finish up with a prograde burn, extending your AP to reach Earth. But I'm at a loss to understand the physics of why this works.

Isn't the DV required to lower your PE to say 100K the same as would be required to raise it FROM 100K to the original height? Does this have something to do with the fact that the beginning orbit is circular? Is it presumable that in that orbit, there is a total sum of energy equaling that required to put you there, and then circlize as well?

So you're spending enough DV to de-circlize, then adding enough at PE to finish an escape to Earth? And this is somehow less than would be required for just a direct burn from high orbit. Something still isn't adding up. Trying to understand the lesson in this.

My other question would be - How do you plan such a maneuver with TransX? It must involve performing the setup maneuver before Escape.

 

[Shadow Addict]

Burns made closer to a planet give more energy than when done further from the planet. http://en.wikipedia.org/wiki/Oberth_effect

 

[Linguofreak]

Isn't the DV required to lower your PE to say 100K the same as would be required to raise it FROM 100K to the original height?

Yes, but you aren't lowering your PE and then raising it again. You're lowering your PE and then raising your AP.

 

[RSWingman]

Yes, but you aren't lowering your PE and then raising it again. You're lowering your PE and then raising your AP.

Right. That was more a failure in verbalization on my part. Though I'm sure semantics are important in these matters, I'm failing to see if there's an epiphany to be found in this distinction. Lowering one side & raising the other is what I was trying to express. I was attempting to compare the hypothetical expenditure of DV between raising a LVO Ap and lowering a HVO Pe. The same? I'm not sure.

But once I posted and got it out it occurred to me, that (in simplest terms) the key must have to do with the Pe velocity to which the maneuver will be adding. Perhaps the Oberth effect is a more involved way of explaining this? I'm gonna have to experiment some to reach a complete understanding.

I still can't figure out how this maneuver could be planned with TransX. It would seem, I need to Encounter Venus, and then Sling-direct to Earth. But I'm beginning with Venus as the Major body.

 

[agentgonzo]

TransX won't be able to plan this manoeuvre in one go as there will two separate manoeuvre events at Venus and TransX can't handle more than one per stage.

You can do the following though. Plan the Eject burn to get from Venus to Earth as normal (as if you had more fuel) with the manoeuvre date in a few orbit's time. Ignore the burn data, but burn retrograde manually at the opposite side of the planet to your planned manoeuvre to lower your PeA.

Turn Manoeuvre off and on again in TransX to reset the current stage, then replan the eject burn from Venus to Earth at Apoapsis (this will be a different time as your orbital period has changed).

Burn.

Profit

 

[Linguofreak]

Right. That was more a failure in verbalization on my part. Though I'm sure semantics are important in these matters, I'm failing to see if there's an epiphany to be found in this distinction. Lowering one side & raising the other is what I was trying to express. I was attempting to compare the hypothetical expenditure of DV between raising a LVO Ap and lowering a HVO Pe. The same? I'm not sure.

No, not unless the difference between the PE and AP radii is very small compared to the semi-major axis of the orbit and the change in either radius is also very small compared to the semi-major axis of the orbit. The magnitude of gravitational acceleration is proportional to the inverse square of the radius, so a change of 100 km very close to a planet involves much more energy than a change of 100 km very far from the same planet.

But once I posted and got it out it occurred to me, that (in simplest terms) the key must have to do with the Pe velocity to which the maneuver will be adding. Perhaps the Oberth effect is a more involved way of explaining this? I'm gonna have to experiment some to reach a complete understanding.

Basically, yes.

 

[RSWingman]

It starts you at about 115M alt. It costs roughly 1000 Dv to place Pe at 100k alt. To circularize, it costs roughly 2.6k in Dv. I'm assuming it would cost the same to restore Ap to 115M. So I'm seeing that there's about 2.6k of Dv that I already have at Pe toward my escape.

It seems to cost the same 2.8k at any orbit to reach earth (according to TransX). So it would appear, that all I have to add at Pe is about 200 Dv, making the total expenditure about 1200-1300 Dv.

It's interesting, that at 115M, the speed is about 1.644 k. While about 2/3 of it is removed in the retrograde, Pe speed is about 9.9k. About 2.6k of that would seem to already be in the parabola, giving me the Ap of 115M.

Looks like I got what I was looking for. Thanks all.