Using a gravity well for a Jool arrival

[uncle_jew]

Hello,

I am trying to arrive at Jool by a Hohmann transfer from Kerbin so that my spacecraft would end up in the same orbit as Pol.

If I adjust my arrival trajectory so that it "touches" the Pol orbit, I can get into the Pol orbit by doing a retrograde burn at the periapsis with a delta-v of 1329 m/s.

Is it possible to use the gravity well effect to insert into the Pol orbit with a smaller delta-v? Burns done inside a gravity well are supposed to be more efficient due to the exhaust being left with less total energy, right?

I tried nudging the arrival trajectory so that it passes by Jool inside the Laythe orbit. If I do this, I can get into an elliptical orbit touching the orbit of Pol from the inside by doing a retrograde burn at the periapsis with 537 m/s. However, to circularize the resulting elliptical orbit, I need another burn with 865 m/s at the apoapsis. So the total delta-v in this case is 1402 m/s, which is even higher than 1329 m/s needed for a direct insertion into the Pol orbit.

Is there anything I am missing here, or is a gravity well generally unusable to get into circular orbits?

Thanks

 

[Snark]

What you're doing is an Oberth maneuver.  Unfortunately, Pol is poorly placed for that.

An Oberth maneuver is good for getting into a very low circular orbit-- for example, if you wanted to end up in a circular orbit just above Jool's atmosphere, you'd want your Jool-approach periapsis to be down there and do your whole burn at periapsis.

An Oberth maneuver is also good for getting into a very high circular orbit-- for example, suppose Pol had an orbit that was waaaaay up near Jool's SoI boundary, where orbital velocity is only a few meters per second.  In that case, an Oberth maneuver would work great:  you do your capture burn at a very low Jool periapsis, putting your apoapsis right out by Pol.  Then when you coasted up to Ap, you'd have only a very small and cheap circularization burn (since the orbital velocity is so slow up there).

What Oberth maneuvers are not good at is in-between circular orbits, which is where Pol is.  If you dive low enough to Jool to get a decent Oberth effect for your capture burn, then your resulting ellipse (with its apoapsis at the target orbit) will be so eccentric that you'll have to do a big circularization burn to match orbits.

Now, one thing you can do that can give you quite a boost is a gravity assist maneuver, using Tylo or Laythe.  The idea is to use the heavy moon's gravity in a sort of "reverse slingshot" to slow you down enough to capture to the Jool system even without using any rocket power at all.

An example of such a maneuver:  approach Jool in such a way that your descending orbit (on your way to Jool Pe) passes right in front of (not behind!) Tylo, with the lowest possible Tylo periapsis that you can manage.  This will cause Tylo's gravity to slow you down.  You'll also take advantage of a mathematical inaccuracy of patched conics, in that you will re-enter Jool's SoI (from Tylo's) at a much lower Jool altitude than the point at which you entered Tylo's SoI, without having actually fallen that distance in Jool's gravity and thereby picked up more speed.

Since you're passing really low to Tylo, you can give it a double-whammy by doing a retro-burn at low Tylo Pe to further slow yourself down, if necessary (e.g. to fine-tune your resulting orbit to put your Ap out by Pol), thus taking advantage of Oberth effect at Tylo rather than Jool.

 

 

[uncle_jew]

Will try that, thanks! 

After more trying, I also did manage to use the Jool gravity well to my advantage - my mistake was choosing the apoapsis of the initial elliptical orbit around Jool to match the Pol orbit - this way, raising the periapsis became too expensive.

If instead I enter the elliptical orbit with the highest possible apoapsis after passing by Jool, then raise the periapsis to match the orbit of Pol, then lower the apoapsis, I am able to shave off around 460 m/s from 1329 m/s required for a direct Pol orbit insertion.

[Plusck]

Yes, Tylo every time. Even if you give Tylo a relatively wide berth (several hundred kilometres), it'll slow you enough for a Jool capture. Take it too tight in and your periapsis will be inside Laythe's orbit, which will cost you to raise it back up to Pol.

It's very easy to do, but a bit finnicky. Simply drop a maneuvre node about three-quarters of the way to Jool, and play with a combination of radial/prograde burns. Prograde will get you to Jool slightly faster, therefore with Tylo further back in its orbit. Radial in will delay the moment you intersect Jool's orbit (assuming you're hitting it straight on, and not after looping behind) and so will bring Tylo further forward in its orbit. It doesn't matter what kind of intersect you started with, it just takes a few dozen m/s to set up the perfect Tylo encounter to send you wherever you want in the Jool system.