are there any good tutorials on gravity assists?

[fommil]

I have always been scared of gravity assists, but when exploring the Jool system I was amazed to discover that I could get a free capture by flying close to Tylo or Laythe. Up until that point I had thought aerobraking was the only way to achieve this kind of thing.

So on my return journey, which was a 1k dv burn from Laythe back to Kerbin (incredible! especially when compared to the dv chart) I decided to do some playing around with the Kerbin insertion. I noticed that when I approach a body from the left (i.e. as if I were to insert into an inverted, or clockwise, orbit) my craft becomes more aligned with the body I'm flying past, as if I had burnt retrograde. It doesn't seem to matter if I'm jumping up (Kerbin to Jool via Tylo or Laythe) or down (the opposite) an orbit. And conversely, if I approach from the right (i.e. as if I were to insert into a normal, or counterclockwise, orbit) then the body is actually adding to my velocity and the gravity assist looks like I burnt to prograde. Is what I found generalisable or is it just working out this way by accident?

I managed to time a flyby of both the Mun and Kerbin on my return from Laythe, both pretty close and from the left, which brought me into an orbit with an Ap somewhere between Duna and Dres, which is a pretty big dv saving given that I was coming from Jool! I was impatient and wanted my next Kerbin approach within a year, so I spent about 300dv at that point to get a quick rendezvous but I could imagine waiting some more years and it would have come along naturally. My approach speed after doing this was very very safe for an aerobrake into Kerbin at that point, whereas it would have been touching cloth to have gone straight for the aerobrake first time.

However, it occurred to me that when doing an aerobrake it always has to be from the right (counterclockwise) to go with the surface movement. But that's actually counter-productive compared to the non-aerobrake scenario. Are there any situations where it's worth going into the atmosphere from the left, and staying quite high, to get the benefit of both kinds of decelerations at once? The GA effect from the left is definitely my preference when I can do it, because it is just so much safer than risking the craft on a high speed aerobrake.

Anyways, that's what I've figured out with experimenting. I'd be really interested in knowing if there are any in-depth tutorials that go into more detail than this. I watched Advanced Orbital Mechanics by Bradley Whistance (undoubtedly the king of gravity assists) but I found it lacking in detail... e.g. the approaching from the left vs right and tricks. On my return to Kerbin I ended up spending a bunch of dv to get an  intercept on the followup orbit , but is there maybe a trick to get that for free? e.g. maybe trading off some of the saving to get exactly the right orbital period to come back round again for the next pass (within 2 years), I wasn't able to get it to work.

My only remaining challenge in the game is the Grand Challenge, so I'm thinking of using some techniques to avoid having to mine for fuel along the way.

Edited November 15, 2022 by fommil

[Caerfinon]

13 minutes ago, fommil said:

I have always been scared of gravity assists

See: https://wiki.kerbalspaceprogram.com/wiki/Tutorial:_Gravity_Assist 

It clarifies most of the things you've already discovered. 

[king of nowhere]

2 hours ago, fommil said:

I have always been scared of gravity assists, but when exploring the Jool system I was amazed to discover that I could get a free capture by flying close to Tylo or Laythe. Up until that point I had thought aerobraking was the only way to achieve this kind of thing.

So on my return journey, which was a 1k dv burn from Laythe back to Kerbin (incredible! especially when compared to the dv chart) I decided to do some playing around with the Kerbin insertion. I noticed that when I approach a body from the left (i.e. as if I were to insert into an inverted, or clockwise, orbit) my craft becomes more aligned with the body I'm flying past, as if I had burnt retrograde. It doesn't seem to matter if I'm jumping up (Kerbin to Jool via Tylo or Laythe) or down (the opposite) an orbit. And conversely, if I approach from the right (i.e. as if I were to insert into a normal, or counterclockwise, orbit) then the body is actually adding to my velocity and the gravity assist looks like I burnt to prograde. Is what I found generalisable or is it just working out this way by accident?

it's not a matter of left or right, but of passing in front or behind a planet. if you pass behind a planet, you are accelerated, while if you pass in front of a planet you are slowed down. since all the planets rotate in the same direction, it translates to left and right

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I managed to time a flyby of both the Mun and Kerbin on my return from Laythe, both pretty close and from the left, which brought me into an orbit with an Ap somewhere between Duna and Dres, which is a pretty big dv saving given that I was coming from Jool! I was impatient and wanted my next Kerbin approach within a year, so I spent about 300dv at that point to get a quick rendezvous but I could imagine waiting some more years and it would have come along naturally. My approach speed after doing this was very very safe for an aerobrake into Kerbin at that point, whereas it would have been touching cloth to have gone straight for the aerobrake first time.

[...]

On my return to Kerbin I ended up spending a bunch of dv to get an  intercept on the followup orbit , but is there maybe a trick to get that for free? e.g. maybe trading off some of the saving to get exactly the right orbital period to come back round again for the next pass (within 2 years), I wasn't able to get it to work.

for a multiple gravity assist, you have to be ejected into an orbit with a duration multiple of the target body - a resonant orbit. that is, if you aim for kerbin and you want to take a second passage, you need to eject into an orbit that lasts exactly 2 years, or 3 years. or 2.5 years, in which case you will meet kerbin 5 years later in a 5:2 resonance. to see how long the new orbit would be, put a maneuver node after the planetary encounter, leave it at 0 m/s; when selecting it, you'll be able to see the orbital time in the lower left corner.

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However, it occurred to me that when doing an aerobrake it always has to be from the right (counterclockwise) to go with the surface movement. But that's actually counter-productive compared to the non-aerobrake scenario. Are there any situations where it's worth going into the atmosphere from the left, and staying quite high, to get the benefit of both kinds of decelerations at once? The GA effect from the left is definitely my preference when I can do it, because it is just so much safer than risking the craft on a high speed aerobrake.

this is a common misconceptions: a gravity assist will not slow you down compared to the planet. it will change your speed relative to the sun, or you can get one from a moon and change speed relative to its planet. but your speed relative to the celestial body providing the assist is always the same. so you still should enter aligned with the planetary rotation.

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My only remaining challenge in the game is the Grand Challenge, so I'm thinking of using some techniques to avoid having to mine for fuel along the way.

Even with gravity assists, a full grand tour requires more deltaV than a ship can reasonably have. so you have a few options if you don't want to mine fuel:

1) use lots of drop tanks

2) use ion engines and lots of xenon

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are there any good tutorials on gravity assists?

I'm not aware of any advanced one - the one linked by @Caerfinon is pretty basic and looks like stuff you already know - but, at the cost of looking crass for shipping my own content, I will point out that in my mission reports I do talk extensively of gravity assists with technical details, because I do think a mission report should allow someone else to replicate what you've done.

So I'll link a few chapters dealing with lots of gravity assists:

https://forum.kerbalspaceprogram.com/index.php?/topic/203233-lucy-in-the-sky-with-deadly-radiations-3-skys-just-got-a-lot-bigger-kerbalism-opm-grand-tour/&do=findComment&comment=4046683

this first one is a mission to moho using lots of conjoined gravity assists into resonant orbits to lower deltaV cost.

https://forum.kerbalspaceprogram.com/index.php?/topic/203233-lucy-in-the-sky-with-deadly-radiations-3-skys-just-got-a-lot-bigger-kerbalism-opm-grand-tour/&do=findComment&comment=4055758

this is the next chapter, detailing the return trip from moho to the mun using eve

https://forum.kerbalspaceprogram.com/index.php?/topic/203233-lucy-in-the-sky-with-deadly-radiations-3-skys-just-got-a-lot-bigger-kerbalism-opm-grand-tour/&do=findComment&comment=4068922

this chapter deals mostly with dwindling life support resources, but subchapter 19.2 uses a jool+tylo gravity assist to reduce speed and set up an encounter with kerbin, and 19.4 details a way to turn that into a low speed encounter with duna a few years later.

https://forum.kerbalspaceprogram.com/index.php?/topic/208134-lucy-in-the-sky-with-deadly-radiations-4-the-real-sky-this-time/&do=findComment&comment=4139639

4.2 details going from phobos to venus using an earth flyby, and 4.6 the reverse trip, still using an earth flyby

https://forum.kerbalspaceprogram.com/index.php?/topic/208134-lucy-in-the-sky-with-deadly-radiations-4-the-real-sky-this-time/&do=findComment&comment=4145720

this chapter is the trip to mercury, which entails the same amount of gravity assist as the trip to moho i linked earlier

https://forum.kerbalspaceprogram.com/index.php?/topic/208134-lucy-in-the-sky-with-deadly-radiations-4-the-real-sky-this-time/&do=findComment&comment=4166092

and this final chapter is my greatest achievement in gravity assists: reaching Io, the innermost moon of jupiter, with limited fuel. It includes 30 gravity assists.

 

I do believe you can find more informations there than in most guides.

 

[fommil]

2 hours ago, king of nowhere said:

this is a common misconceptions: a gravity assist will not slow you down compared to the planet. it will change your speed relative to the sun, or you can get one from a moon and change speed relative to its planet. but your speed relative to the celestial body providing the assist is always the same. so you still should enter aligned with the planetary rotation.

This is very interesting. I'd like to understand this a bit more. In my return back to Kerbin I noticed that the assist off Kerbin itself (before I came back for the second pass) definitely reduced my Ap and made my next pass be at a much lower relative speed, but maybe there was something else at play there. It's probably, like you say, because I got a different relative speed to the Sun that it gave me a lower energy orbit around the sun but at that particular moment in time I didn't get any advantage relative to Kerbin which is why I only reaped the rewards on the second pass.

Something else I'd like to understand would be how much of  a gravity assist I can reasonably expect off any given body, in dv. Presumably the limit is whatever that body's speed is relative to their parent, but it'd be good to know what some typical values are. e.g. how much can the Mun give depending on how close you get, if it's pointing in the right direction.

Edited November 15, 2022 by fommil

[king of nowhere]

58 minutes ago, fommil said:

This is very interesting. I'd like to understand this a bit more. In my return back to Kerbin I noticed that the assist off Kerbin itself (before I came back for the second pass) definitely reduced my Ap and made my next pass be at a much lower relative speed, but maybe there was something else at play there. It's probably, like you say, because I got a different relative speed to the Sun that it gave me a lower energy orbit around the sun but at that particular moment in time I didn't get any advantage relative to Kerbin which is why I only reaped the rewards on the second pass.

 

actually, this is a trick I myself only learned recently, and the physics behind it is a bit complicated. But it goes like that.

when you take a gravity assist, you never change your speed relative to the target body. you chain up two consecutive gravity assists with a resonant orbit, second assist you're going to have the same intercept speed you had the first time. On the orbit itself, you lowered both apoapsis and periapsis, which resulted in a less-than-ideal Hohmann intercept, which resulted in having the same intercept speed despite the lower apoapsis. Or maybe you gained some inclination.

But! now that you are in a new orbit with lower apoapsis and periapsis, you can raise periapsis with a burn in solar orbit. and since your periapsis was only lowered by a small amount, this burn is cheap. and at this point you lowered your periapsis a lot, you have the same periapsis for an ideal hohmann transfer, and you spent less fuel than if you had just lowered apoapsis with rockets.

so, you cannot change your speed relative to the planet you are using for the assist, but you can set yourself in a trajectory where there is a sequence of burns resulting in a cheaper capture.

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Something else I'd like to understand would be how much of  a gravity assist I can reasonably expect off any given body, in dv. Presumably the limit is whatever that body's speed is relative to their parent, but it'd be good to know what some typical values are. e.g. how much can the Mun give depending on how close you get, if it's pointing in the right direction.

there are two limits. the first is, indeed, speed relative to parent body. if you are moving very slowly compared to your target, you'll end up ejecting very slowly too. so, for example, if you want to go to jool using a gravity assist from duna, you cannot do it by taking a normal hohmann transfer, because you'll arrive to duna with 600 m/s intercept speed, and to reach jool from duna you need 1 km/s ejection speed, so you are too slow compared to duna to reach jool. you need to use a different trajectory resulting in a higher speed relative to duna.

the second limit is the gravity of the body. predictably, a smaller body gives a smaller gravity assist. for this reason you can gravity capture on jool using tylo or laythe, but you can't do it with vall. and a flyby of bop or pol will leave your orbit almost unchanged. I can't give any hard data on this; by experience, I know that with mun you can gain beteen 50 and 100 m/s, with tylo/laythe you can gain around 500 m/s, with kerbin a bit more. Still, when I wanted to make a duna-kerbin-eve assist, one single kerbin flyby wasn't enough and I had to eject into resonant orbits and make, like, three assists. And I had to use mun in one of them to increase my velocity relative to kerbin, otherwise i didn't have enough speed to reach eve.

of course i'm talking here of going as close to the surface as you can. if you pass more distant, you get less change. if you could pass underground, you could get a huge deltaV even from a small moon, unfortunately there's that pesky surface along the way.

 

[fommil]

9 hours ago, king of nowhere said:

On the orbit itself, you lowered both apoapsis and periapsis, which resulted in a less-than-ideal Hohmann intercept,

oooh, that is true! The Pe is indeed lower and the reintercept would not be on the Pe, I'd be at an angle (non-ideal as you say).

But when I GA from the right, the Ap gets a lot bigger and I don't know how to explain that, I'd need to go and look at the quicksave to see what happened to the Pe.

Or maybe I was actually observing the effect from the Mun GA and confusing it with the impact from the Kerbin one. I should investigate again in isolation.

9 hours ago, king of nowhere said:

which resulted in having the same intercept speed despite the lower apoapsis. Or maybe you gained some inclination.

Because I did a correction burn (like you say, at Ap to raise Pe), I can't confirm this first point, but of course it would make logical sense because (assuming I were to reintercept exactly in phase) it would be with exactly the same relative speed as before. Thank you for the explanation, it's really good to hear that what I did wasn't in my imagination!

And totally ironic that I discover this on my final manned return mission (to Tylo) and can now consider the game somewhat complete :-D ... if only I'd known earlier. But to be honest I think GAs (or, rather, their consequences to spacetravel, since the principal itself is simple) are the most complicated part of the game so it makes sense to only learn this latterly.

9 hours ago, king of nowhere said:

the second limit is the gravity of the body. predictably, a smaller body gives a smaller gravity assist. for this reason you can gravity capture on jool using tylo or laythe, but you can't do it with vall. and a flyby of bop or pol will leave your orbit almost unchanged. I can't give any hard data on this; by experience, I know that with mun you can gain beteen 50 and 100 m/s, with tylo/laythe you can gain around 500 m/s, with kerbin a bit more. Still, when I wanted to make a duna-kerbin-eve assist, one single kerbin flyby wasn't enough and I had to eject into resonant orbits and make, like, three assists. And I had to use mun in one of them to increase my velocity relative to kerbin, otherwise i didn't have enough speed to reach eve.

this is great insight, thank you!

9 hours ago, king of nowhere said:

of course i'm talking here of going as close to the surface as you can. if you pass more distant, you get less change. if you could pass underground, you could get a huge deltaV even from a small moon, unfortunately there's that pesky surface along the way

Elon Musk owns SpaceX and the Boring Company. The sink just got in.