Gravity Assist question

[numerobis]

A direct launch from Kerbin to Jool costs about 2km/s. Just fire up one of the launch window calculators and you're good to go.

I tried to be clever with a gravity assist, but failed. The concept: I'd go to Eve for 1km/s and then fly from there for about 500 m/s. A few people have done this. I thought I understood how to put this into action -- I have before. But this time I was going to be extra clever: I'd string up the Kerbin-Eve-Jool trip so that my Kerbals wouldn't have to while away the years waiting for the next encounter.

I fired up alexmoon's calculator. I told it I was parking at Kerbin 100km sometime in year 3, going to Eve with no final orbit. Best answer: leave on day 88, get to Eve on day 122. Then I told it to find me a path from Eve to Jool in year 3 after day 100, and it recommended leaving Eve on day 122. Perfect!

I launched to Eve at the appointed time, and with some twiddling set up a periapsis about 100km and an exit that points the right direction. Upon arrival, I was surprised at how low the unpowered boost would send my apoapsis -- only a bit higher than Kerbin. When put a node near Eve periapsis (at an escape angle about 120 degrees to prograde like you're supposed to), to get my heliapsis up to Jool's orbit costs me 1km/s due prograde -- which gets me an encounter. So it seems like everything worked, except that at that price, I should have just gone directly to Jool, not passed Eve, not collected 200 dollars.

So the question is: what additional piece of information am I supposed to be understanding to set up a powered assist?

[mhoram]

The only thing I can think of is the Oberth effect.

Try to set up your Eve-encounter in a way that increases the velocity at periapsis - for example by lowering the Eve-periapsis into the higher atmosphere of Eve (can't give you numbers at which altitude the drag-loss is greater than the Oberth-gain) or by changing the route so that you enter Eve's SOI with a higher velocity.

This should increase the gain from the planned periapsis 500m/s burn.

Edited September 26, 2015 by mhoram
typo

[tavert]

The insertion dV of that Kerbin-Eve transfer if you were to hypothetically burn into a 100 km Eve orbit at the end would be about 1540 m/s, and the ejection burn of the Eve-Jool transfer at that window is 2650 m/s (from 100 km). So the numbers all seem reasonable to me. And I don't think I've seen people get all that far from just the first Eve assist, from what I remember it usually takes one or two more Eve and/or Kerbin encounters to get all the way to Jool, depending how many powered flybys (and how large) you want to do.

How did the geometry of your encounter look inclination-wise? I'm not exactly an expert when it comes to gravity assists, but from what I've seen it helps to have some normal and/or radial component of your incoming trajectory for the gravity assist to bend around into a prograde component. In a normal Hohmann transfer you tend to come into the encounter mostly parallel with the planet's orbit, so it helps to actually go a bit past the optimal transfer on your initial burn.

[brooklyn666]

A direct launch from Kerbin to Jool costs about 2km/s. Just fire up one of the launch window calculators and you're good to go.

I told it I was parking at Kerbin 100km sometime in year 3, going to Eve with no final orbit. Best answer: leave on day 88, get to Eve on day 122. Then I told it to find me a path from Eve to Jool in year 3 after day 100, and it recommended leaving Eve on day 122. Perfect!

So the question is: what additional piece of information am I supposed to be understanding to set up a powered assist?

What was your Eve periapsis? The closer you are to your flyby planet, the more of a boost you get , the only caveat being that you need to avoid drag from the atmosphere, which in the case of Eve, can be extreme. Also, for a powered assist, you need to perform your burn at periapsis.

All told, a perfect direct slingshot from Kerbin to Eve to Jool is difficult. In real life, probes that use a Venus assist to Jupiter or Saturn often use a double or even triple assist. They'll swing by Venus, and then Earth a second time before they have enough energy to get to the outer planets.

[SRV Ron]

Your are looking for a slingshot maneuver, not going into and leaving orbit. What is tricky is setting it up where one slingshot leads to another. When you reach Jool, you set up an aerobraking to get into orbit or use a retrograde slingshot with its moons to slow down.

[SSSPutnik]

Leaving retrograde from Kerb in aren't you losing energy due to reverse gravity assist?

[Superfluous J]

Leaving retrograde from Kerb in aren't you losing energy due to reverse gravity assist?

Yes, but not as much as you think. You lose 90 or so going down, and have to gain 90 or so going back up so you lose 180. All that matters is the location of your Apoapsis because you can either Aerobrake at Jool or get a lucky (or planned, but I'm not good enough to plan these things) set of Joolian moon encounters to get you into an orbit there.

Going to Duna instead of Eve, you chew 130 out of what you already need to go to Jool so maybe it's the better choice in this case, but you get less of an assist with Duna because it's smaller. Unless you could time a double assist from Ike AND Duna...

[numerobis]

The insertion dV of that Kerbin-Eve transfer if you were to hypothetically burn into a 100 km Eve orbit at the end would be about 1540 m/s, and the ejection burn of the Eve-Jool transfer at that window is 2650 m/s (from 100 km).

I'm not going into an Eve orbit, so I just left the final orbit field blank.

I don't think I've seen people get all that far from just the first Eve assist, from what I remember it usually takes one or two more Eve and/or Kerbin encounters to get all the way to Jool, depending how many powered flybys (and how large) you want to do.

Ah -- this is likely what I was missing! I thought it was one bounce, but if it takes two, that makes sense. And is going to be harder to get right.

How did the geometry of your encounter look inclination-wise? I'm not exactly an expert when it comes to gravity assists, but from what I've seen it helps to have some normal and/or radial component of your incoming trajectory for the gravity assist to bend around into a prograde component. In a normal Hohmann transfer you tend to come into the encounter mostly parallel with the planet's orbit, so it helps to actually go a bit past the optimal transfer on your initial burn.

Hmm... I didn't check for this explicitly.

So, I think I see an overall scenario:

1. from Kerbin to perihelion at Eve, intercepting Eve at the ascending node.

2. use Eve to bend my orbit to have a radial component. Burn a bit to get this new orbit to have a resonance so I can encounter Eve in the same place again.

3. use Eve again to convert that radial component back into a prograde component. Burn up to the Jool transfer on this one.

It sounds like a no-op, written this way. The win must come from being entrained along Eve's orbit during the encounter, but I'm fuzzy as to how to calculate that.

[numerobis]

Going to Duna instead of Eve, you chew 130 out of what you already need to go to Jool so maybe it's the better choice in this case, but you get less of an assist with Duna because it's smaller. Unless you could time a double assist from Ike AND Duna...

Hmm... the Duna assist I guess would be that you come in with a solar horizontal component that you convert into solar vertical speed to boost aphelion up near Jool (and lower perihelion, but we don't care about that). I don't see Ike making much difference to anything; it's tiny.

[numerobis]

A fun fact about patched conics: when you fly by a minor body (e.g. Mun), the major body's (e.g. Kerbin's) gravity doesn't affect you.

Say you're on an escape trajectory, you enter Mun's sphere of influence at altitude 9000 km, and leave it at altitude 14000 km. You exit Mun's sphere of influence at the same Kerbin-relative speed as you entered, but you're up at a higher altitude. Your potential energy grew without your losing any kinetic energy. ???. PROFIT.

Filling in the ??? that suggests that when I go to Eve, on the first encounter I should enter the Eve SoI with zero solar vertical speed, pass low on the day side of Eve, and thus get ejected with positive solar vertical speed -- exiting at higher altitude. On the second encounter I will then be coming up from the Sun, pass low on the night side of Eve, and get ejected due prograde, again at higher altitude than where I started.

I'm calculating that crossing the Eve SoI band should normally cost about 250 m/s solar vertical speed. So this energy cheat can be pretty significant.