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Orbital mechanics - Gravity Assist/Brake


imWACC0
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I've been having trouble rapping my head around slingshot maneuvers. Enter Sphere of Influence (SoI) and exit SoI with changed velocity. It basically breaks down to four maneuvers.

slingshot.jpg

A and B are from a higher (faster) orbit, C and D are from a lower (slower) orbit. A and C are leading the object, B and D are trailing.

 

There are some hints in https://wiki.kerbalspaceprogram.com/wiki/Tutorial:_Gravity_Assist It shows C and D. but what about A and B?

 

Which ones will increase my exit velocity? C

Which ones will decrease my exit velocity? D

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Imagine that the planet has 10km/s orbital speed, and is traveling from left to right.

Further, let us imagine our spacecraft has a relative velocity to the planet of 2km/s

In A and C, the spacecraft has an orbital velocity that is faster than the planet, 12km/s.  It then catches up to the planet, wraps around, and heads off back the direction it came.  Instead of 2km/s faster (12km/s orbital speed) it is now going 2km/s slower (8 km/s orbital speed), so we lost speed overall.

In B and D, the opposite occurs, we are going slower, the planet catches up to us, then flings us forwards. So we gain speed.

 

The way I like to look at it is this:

Compared to the orbital path of the body we are assisting off of around its parent, was our trajectory bent so that it is closer to prograde than before (ie, did the angle between the bodies prograde, and our prograde, get smaller)? If so, we gained speed.  Was it bent closer to retrograde than before (ie, did the angle between the bodies retrograde, and our prograde, get smaller)? If so, we lost speed.

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18 hours ago, Lt_Duckweed said:

The way I like to look at it is this:

Compared to the orbital path of the body we are assisting off of around its parent, was our trajectory bent so that it is closer to prograde than before (ie, did the angle between the bodies prograde, and our prograde, get smaller)? If so, we gained speed.  Was it bent closer to retrograde than before (ie, did the angle between the bodies retrograde, and our prograde, get smaller)? If so, we lost speed.

This.  Exactly this.


Happy landings!

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On 1/27/2022 at 1:03 PM, Lt_Duckweed said:

In A and C.......we lost speed overall.

In B and D.......we gain speed.

To paraphrase, in front of body slow down, behind body speed up?

 

On 1/28/2022 at 7:56 AM, king of nowhere said:

you change speed compared to the sun main body.

Sorry, this works for moons also.

 

 

May your god go with you.

W.A.C.Co

 

 

 

P.S. Sorry it took me a bit to get back here, Real Life SUX. And I'm in the middle of a different mission. to Eve. Forgot to add coms, and getting a resupply ship to it has been FUN. See

 

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21 hours ago, imWACC0 said:

To paraphrase, in front of body slow down, behind body speed up?

If you mean passing in front and passing behind, then ... roughly, yes.

It would be more accurate to say that your exit speed relates to how close your exit direction is to the celestial body's prograde direction.  If they are roughly parallel, then you speed up in the primary sphere of influence.  If they are anti-parallel (meaning that you're aligned with the body's retrograde), then you slow down.  B and D show the craft leaving the body in something like the body's own prograde direction (it isn't exactly parallel, but it's obviously more prograde than retrograde), so the craft speeds up.  A and C show the craft leaving roughly retrograde, so it slows down.

There's a whole list of caveats and addenda to that, mostly relating to your speed, angle of approach, and periapsis (and a lot of it deals with the fact that, being in three-dimensional space, you can do other things like change inclination with a gravity assist).

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8 hours ago, Zhetaan said:

There's a whole list of caveats and addenda to that

Brother, don't I know it. At least I'm not trying to get an answer to the 3 body problem :D

 

Thank you for taking the time to spell it out in more technical terms. I knew I had to spend the ∆v, for inclination, early so I can get into the correct plain of destination. I'm trying to do the KEKKJ shot that Matt Lowne talks about.

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On 2/23/2022 at 6:26 PM, imWACC0 said:

I'm trying to do the KEKKJ shot that Matt Lowne talks about.

In that case, this is pretty much the definitive post on the subject.  It's also the case that you'll be looking for something more nuanced than just passing in front of or behind celestial bodies, because the main trick to those multiple-assist trajectories is getting the timing right for the intermediate legs.

For example, there's a multiple assist to get to Moho by way of Eve:  you can get to Moho by way of Eve but the problem is that Eve cannot, on its own, slow you down enough on an infalling trajectory from Kerbin to both get you to Moho in one pass and save enough propellant to be more worthwhile than just flying there directly.  So the way to do it is a K-E-E-M assist.  For that middle leg from Eve to Eve again, the exact flyby orientation is less important than the timing of the interval, which needs to be exactly 65.5 days (one Eve year) or else you'll miss the Moho encounter (or make it very expensive, at least).  But that means that you need to take the assist that will give you that interval, not the one that reduces your solar speed the most.

It's not so bad as it sounds, because the assist that gives you the right interval will put you in the right place for the next assist, which is the point.  But it means that you're not looking for the maximum possible effect on the flyby, either.  That's okay, since multiple assists are really just chained transfer windows, and transfer windows are mainly about timing.  Your mission may be about propellant efficiency and delta-V budgets, but the windows don't care one bit about that because the planets move and align regardless.

Unlike, for example, a Tylo gravity brake to get into Jool orbit, where it's ideal to approach Tylo from directly behind (if possible), swing round at nearly ground level (if possible), and exit exactly in Tylo's retrograde (more or less required), you may find yourself exiting (or approaching) the intermediate celestial bodies at a weird angle, because that's the angle that gives you the right timing for the next encounter.  Do not neglect your course correction budget, and remember that when you correct for an upcoming encounter, you should really be looking at the encounter after that.

Well, maybe glance back to ensure that you're not getting that 'encounter' via a collision course with Kerbin or something.  Otherwise, this encounter should be all about setting up the next encounter.  Do that and you'll be fine.

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On 2/25/2022 at 8:55 AM, Zhetaan said:

 It's also the case that you'll be looking for something more nuanced than just passing in front of or behind celestial bodies, because the main trick to those multiple-assist trajectories is getting the timing right for the intermediate legs.

But that one answer just cut my "hunt & peck" time in half. I know there's all sorts of fun to have with multiple-assist trajectories, and the difference of >0.01m/s can mean success or fail. (and don't use RCS) See xkcd #1356

Thanks for the link*. I've been brute forcing KSP for 9ish years, now that I'm "retired" I'm going to do a lot more of fine tune stuff.

 

May your god go with you,

WACCo

 

*Oh, look, a rabbit hole! :D

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