how much deltaV can you get out of a gravity assist?

[king of nowhere]

in moving from stock to rss, I noticed some weirdness in the effectiveness of gravity assists that brought me here to ask just that. i mean, of course the bigger (more massive) the body, the more of a slingshot you can get, but there are some additional factors I'm missing.

in stock, I started from duna to kerbin, wanting to move to a kerbin-eve hohmann orbit. for that, kerbin's gravity wasn't enough; I had to eject into a resonant orbit and take two gravity assists to complete the manuever.

i moved to rss, in a totally similar scenario: starting from mars, going to earth to take a gravity assist ad get into a earth-venus hohmann orbit. this time, a single earth flyby was enough to do the trick, and I didn't even need to get very close.

so I figured yay! gravity assists are a lot  more effective in rss. perhaps because everything is bigger and so you spend more time under the gravitational influence of the planet.

then I tried to take gravity assists from the moons of jupiter. it was an abject failure. oh, i can get assists, yes, but they are very small. I'm currently using ganymede, the biggest one, to reduce my injecton deltaV, and even though i'm making a close pass at 15 km from the surface to maximize the assist, I still am saving only 150 m/s. maybe 200. that's barely more than what you get from Mun in stock; and since everything in rss costs triple, it makes those assists a lot less effective than Mun gravity assists. attempts to use the moon for gravity assists - also frustrated by its highly inclined orbit - were equally fruitless.

on the other hand, Titan - which is also close in size to the moon - was quite effective, maybe 500 m/s of deltaV change in a single passage.

So I have this paradox; in going from stock to rss, gravity assists from planets appear to be a lot more effective. But gravity assists from moons appear to be a lot less effective. there also appear to be a huge variability between moons of similar sizes.

can anyone explain me why?

[king of nowhere]

update: now i'm using ganymede for a plane change, it would cost 900 m/s with rockets but ganymede is giving it for free in one pass. so how is it that I can get 900 m/s of gravity assist for changing plane, but I couldn't get more than 200 m/s for gravity capture?

[Terwin]

I believe that the max change in velocity that you can get from a fly-by/gravity assist is 2x the relative speed of the body in question.

At best you are making a U-turn around the body where your relative velocity compared to the moon is the same when you leave as when you arrived, but with a reversed direction compared to the body in question.

So, if you are approaching a body from behind with only 100m/s in relative velocity, then after the assist you will be going 100m/s slower than the body as opposed to 100m/s faster than the body when you started, for a total change of 200m/s.

The size/mass of the body only affects how low you need to get to achieve this perfect U-turn for a given relative velocity.  If it is a small/light body, you may not be able to get close enough without litho-breaking, and bodies with atmospheres increase your minimum altitude without aero-breaking. 

So choosing the correct moon is usually much more important than choosing the heaviest object available.

 

 

[king of nowhere]

16 minutes ago, Terwin said:

I believe that the max change in velocity that you can get from a fly-by/gravity assist is 2x the relative speed of the body in question.

At best you are making a U-turn around the body where your relative velocity compared to the moon is the same when you leave as when you arrived, but with a reversed direction compared to the body in question.

So, if you are approaching a body from behind with only 100m/s in relative velocity, then after the assist you will be going 100m/s slower than the body as opposed to 100m/s faster than the body when you started, for a total change of 200m/s.

The size/mass of the body only affects how low you need to get to achieve this perfect U-turn for a given relative velocity.  If it is a small/light body, you may not be able to get close enough without litho-breaking, and bodies with atmospheres increase your minimum altitude without aero-breaking. 

So choosing the correct moon is usually much more important than choosing the heaviest object available.

yes, if you could pass through rock, then you could get the same assist regardless of the mass of the body. but you yourself recognize that the practical limit is skimming the surface (or the atmosphere), and that defines how much you can get from a gravity assist.

as for 2x of the relative speed, that's not helpful. that's just a specific case of the more general principle "you leave with the same speed at which you arrive". relative speeds in rss are generally of many km/s anyway.

by "how much deltaV you can get from a gravity assist", I obviously mean by passing as close to the surface as safely possible. In stock, I was used to know how much I can get from a specific body. From Mun, I could get 100 m/s. To get to duna you need 1000 m/s, with a mun assist I could do it with 900 (yes, I know multiple assists make it cheaper, i never bothered for such a small gain). To get to jool i'd need 2000 m/s, with a mun assist I could still save 100. tylo gave... maybe 500? not sure, but it was consistent. Now in rss it doesn't seem consistent anymore, bodies of similar size giving wildly different results in different situations.

 

P.S. It just came to my mind that it may be possble to just aim for a lithobraking trajectory and use high time warp to glitch through the planet, getting a bigger boost from the gravity assist than otherwise possible. but here i'm talking of real physics; and for gaming purpose, I'm against exploiting bugs anyway.

[wumpus]

5 hours ago, king of nowhere said:

So I have this paradox; in going from stock to rss, gravity assists from planets appear to be a lot more effective. But gravity assists from moons appear to be a lot less effective. there also appear to be a huge variability between moons of similar sizes.

can anyone explain me why?

The planets are much smaller (Kerbin is 10% the size of Earth, and the rest are scaled to Kerbin).  My guess is if you scaled the moons down as much, you wouldn't be able to find them (especially Mar's moons), so they are likely much closer to reality.  So the bump thanks to Jupiter is huge (it will get you out of the solar system), while the bump from the Moons isn't so hot (I don't think NASA uses lunar gravity assists, even though they use multiple assists of various planets for a single mission).  I'm also reasonably sure that no gravity assist from a Galilean moon will get you anywhere near Jupiter escape velocity.  The gravitational field of Jupiter is huge.

PS: I think clipping on lithobraking  brakes most of the point of RSS.

[magnemoe]

1 hour ago, wumpus said:

The planets are much smaller (Kerbin is 10% the size of Earth, and the rest are scaled to Kerbin).  My guess is if you scaled the moons down as much, you wouldn't be able to find them (especially Mar's moons), so they are likely much closer to reality.  So the bump thanks to Jupiter is huge (it will get you out of the solar system), while the bump from the Moons isn't so hot (I don't think NASA uses lunar gravity assists, even though they use multiple assists of various planets for a single mission).  I'm also reasonably sure that no gravity assist from a Galilean moon will get you anywhere near Jupiter escape velocity.  The gravitational field of Jupiter is huge.

PS: I think clipping on lithobraking  brakes most of the point of RSS.

Yes the denser bodies let you get more out of the gravity assist but the bodies are also lighter and move slower, however Laythe and Tylo has earth level surface gravity, nothing like that among Jupiters moons but Jupiter "surface" gravity is 2.4 g.

Now an gravity assist does not change your absolute velocity, it just changes the vector, however this can be extremely useful.
One thing I wonder about in KSP is if its cheaper to do an orbital insertion burn with Pe, close to Jool and then use Laythe and / or Tylo gravity assist to make the Jool orbit more circular than an orbital injection burn on an Tylo flyby. 
 

[mikegarrison]

1 hour ago, magnemoe said:

Now an gravity assist does not change your absolute velocity, it just changes the vector, however this can be extremely useful.

That doesn't sound correct at all.

The idea with a gravity assist is that you are transferring energy from the body to the spacecraft. A tiny fraction of the kinetic energy of a planet can be a massive fraction of the kinetic energy of a spaceship.

(In KSP the planets are "on rails" so the energy is actually free. In the real world, a probe making a gravity assist at Venus actually slows down or speeds up Venus by a tiny, tiny amount.)

But it's definitely not just a change in vector direction.

I guess maybe it depends on reference frames. In the reference frame of the planet, maybe all you do is change direction around the planet. But in the reference frame of the sun, because the planet is moving relative to the sun, you have added speed.

Edited August 11, 2022 by mikegarrison

[king of nowhere]

1 hour ago, magnemoe said:

Now an gravity assist does not change your absolute velocity, it just changes the vector, however this can be extremely useful.
 

 

9 minutes ago, mikegarrison said:

That doesn't sound correct at all.

The idea with a gravity assist is that you are transferring energy from the body to the spacecraft. A tiny fraction of the kinetic energy of a planet can be a massive fraction of the kinetic energy of a spaceship.

a gravity assist does not change your velocity relative to the planet. it changes your velocity relative to the sun.

[Superfluous J]

To know your exit velocity, you need to know your entry velocity and location, and the location of the planet/moon on its orbit. Luckily KSP gives you all of these in the orbit diagram (with a level 2 tracking station) so you don't have to math. I know the basics of how to do the math, but I'm about 30 years away from college so I'm very rusty, and won't even try it here.

But it's "just" vector math:

1. Your ship has a velocity (and location) relative to the sun when you enter the planet's SOI.
2. Your ship has a velocity (and location) relative to the planet when you enter the planet's SOI.
3. The planet has a velocity (and location) relative to the sun when you enter the planet's SOI.
4. Your ship has a velocity (and location) relative to the planet when you exit the planet's SOI.
5. The planet has a velocity (and location) relative to the sun when you exit the planet's SOI.
6. 1+(2-4)+(3-5) = your ship's velocity (and location) relative to the sun when you exit the planet's SOI.

1, 2, and 3 you can find out by knowing when you enter the planet's SOI, which you are in control of.
4 and 5 you get by doing orbit math in the planet's SOI. Good luck with that

Note I didn't actually take location into account relative to the sun, but that technically matters. It matters more in KSP's smaller solar system than it does in the real one, but it still matters there.

Edited August 12, 2022 by Superfluous J

[Hannu2]

16 hours ago, magnemoe said:

Now an gravity assist does not change your absolute velocity, it just changes the vector, however this can be extremely useful.

It is little bit dangerous to think absolute velocities in space. There is no absolute velocity but velocity depends always on frame of reference. Gravity assist do not change magnitude of velocity vector in the frame of reference of body used to assist. But it can change magnitude and direction of velocity referenced to common center body, which makes it useful.

 

16 hours ago, magnemoe said:

One thing I wonder about in KSP is if its cheaper to do an orbital insertion burn with Pe, close to Jool and then use Laythe and / or Tylo gravity assist to make the Jool orbit more circular than an orbital injection burn on an Tylo flyby.

I have not calculated the math but have a gut feeling it is better to time encounter so that you can brake near Tylo or Laythe at optimal position relative to planet (at periapsis of spacecraft trajectory). It takes single meters per second if you adjust it in midcourse few hundreds of days before encounter. It is pretty difficult to achieve with vanilla adjustment tool but very easy with mod which gives you possibility to increase and decrease of velocity components by 0.1 m/s (or smaller) steps. I use Mechjeb.

It is also practical because one of those moons is the primary target for most trips to Jool system and it can decrease number of maneuvers.

[magnemoe]

4 hours ago, Hannu2 said:

It is little bit dangerous to think absolute velocities in space. There is no absolute velocity but velocity depends always on frame of reference. Gravity assist do not change magnitude of velocity vector in the frame of reference of body used to assist. But it can change magnitude and direction of velocity referenced to common center body, which makes it useful.

I have not calculated the math but have a gut feeling it is better to time encounter so that you can brake near Tylo or Laythe at optimal position relative to planet (at periapsis of spacecraft trajectory). It takes single meters per second if you adjust it in midcourse few hundreds of days before encounter. It is pretty difficult to achieve with vanilla adjustment tool but very easy with mod which gives you possibility to increase and decrease of velocity components by 0.1 m/s (or smaller) steps. I use Mechjeb.

It is also practical because one of those moons is the primary target for most trips to Jool system and it can decrease number of maneuvers.

I agree with the invalidity of  absolute velocities but still don't think you don't change the vector length much, now you could reverse the vector direction if the target was heavy and dense enough. Or simply how an Mun flyby coming in behind the Mun will kick you out into solar orbit but using more dV and coming in in front can give you an free return trajectory back to aerobrake. And yes you are stealing energy from the object you are flying past but this can be ignored for spaceflight for the foreseeable future  

Now my Jool or Tylo question was related to an KSP event there I sent 5 ships/ bases to Jool, doing orbital injection by burning at Tylo, initial goal was Pol with Bop as an secondary. 
I miscalculated total dV, an problem using ore as part of your fuel reserve  
Now I was able to get two on my bases down on Pol and one of the tugs so was able to capture the reminding ship in Jool orbit then they came close to Pol. 
But I know that KSP calculates burns based on instant force at burn point not over 5 minutes who lessen the oberth effect so my thought was that the much higher velocity low at Jool would magnify the  oberth effect letting me get into an orbit then using gravity assist to make the resulting orbit more circular. 

[Leganeski]

On 8/11/2022 at 8:17 AM, king of nowhere said:

update: now i'm using ganymede for a plane change, it would cost 900 m/s with rockets but ganymede is giving it for free in one pass. so how is it that I can get 900 m/s of gravity assist for changing plane, but I couldn't get more than 200 m/s for gravity capture?

I think that what's going on here is that if your trajectory around Jupiter meets Ganymede at periapsis, the assist can change your velocity vector (relative to Jupiter) by 900 m/s, but almost all of the change is perpendicular to the velocity. This is perfect for a plane change, but it doesn't change your speed by very much, so it's not very helpful for a gravity capture.

If you intercept Ganymede away from periapsis, then the change in velocity can be aligned with the initial velocity vector. However, the intercept speed (relative to Ganymede) is much faster, making the total change in velocity much smaller (i.e. the assist is less effective because the craft spends less time in Ganymede's gravity well).

This problem is particularly relevant for the moons of Jupiter because they orbit so fast. For example, Ganymede's escape velocity (~2730 m/s) is quite small compared to its orbital speed around Jupiter (~10880 m/s). In contrast, Titan has a comparable escape velocity (~2370 m/s) but orbits Saturn much less quickly (~5570 m/s), meaning that overly fast intercept speeds are not as much of a problem there.

In summary: the variability in gravity assist effectiveness between moons of similar sizes is likely caused by their different orbital speeds around their planets, with very fast-moving moons not being as effective because intercepts with them are faster and therefore don't spend as long near the moon.

(If I'm right, this should also appear in OPM, although at a much less important location: Eeloo is about the same size as Mun but orbits almost four times faster, which means that it should be less effective for gravity assists going to or coming from interplanetary space.)

Edited August 13, 2022 by Leganeski
Added summary

[king of nowhere]

10 hours ago, Leganeski said:

I think that what's going on here is that if your trajectory around Jupiter meets Ganymede at periapsis, the assist can change your velocity vector (relative to Jupiter) by 900 m/s, but almost all of the change is perpendicular to the velocity. This is perfect for a plane change, but it doesn't change your speed by very much, so it's not very helpful for a gravity capture.

If you intercept Ganymede away from periapsis, then the change in velocity can be aligned with the initial velocity vector. However, the intercept speed (relative to Ganymede) is much faster, making the total change in velocity much smaller (i.e. the assist is less effective because the craft spends less time in Ganymede's gravity well).

This problem is particularly relevant for the moons of Jupiter because they orbit so fast. For example, Ganymede's escape velocity (~2730 m/s) is quite small compared to its orbital speed around Jupiter (~10880 m/s). In contrast, Titan has a comparable escape velocity (~2370 m/s) but orbits Saturn much less quickly (~5570 m/s), meaning that overly fast intercept speeds are not as much of a problem there.

In summary: the variability in gravity assist effectiveness between moons of similar sizes is likely caused by their different orbital speeds around their planets, with very fast-moving moons not being as effective because intercepts with them are faster and therefore don't spend as long near the moon.

(If I'm right, this should also appear in OPM, although at a much less important location: Eeloo is about the same size as Mun but orbits almost four times faster, which means that it should be less effective for gravity assists going to or coming from interplanetary space.)

the thing about alignment of the velocity vector is a good point. my periapsis was at Io's level, and I could get less help from Io than I could from Ganymede.

I guess I never realized this because I had many Jool missions when I took gravity assists from Tylo at periapsis; but tylo is a lot bigger than any of the real life moons, so perhaps it's strong enough that even an inefficient assist is enough for gravity capture.

as for the intercept speed, I'm not sure it actually affects gravity assist. I used Mun for a lot of manuevers, some of them even at very high speeds. There was one instance where I zipped past Kerbin at 4 km/s intercept speed, and I used a Mun flyby to refine the gravity assist, and I could squeeze some deltaV from it even though it was five times faster than the normal speed of a Mun intercept. On the other hand, it certainly makes intuitive sense that spending less time close to the body will result in less change in trajectory. Do you know this for sure, or is it a speculation?

Spheres of influence may be relevant here too - though of course they don't exhist in real life, they affect how this game calculates trajectories. Ganymede is close to Jupiter, and its sphere of influence is rather small.

[Leganeski]

4 hours ago, king of nowhere said:

On the other hand, it certainly makes intuitive sense that spending less time close to the body will result in less change in trajectory. Do you know this for sure, or is it a speculation?

I haven't tested it directly, but this has certainly been my experience when exploring GEP (particularly the inner planets, which orbit their star really fast, leading to the same problem when trying to use them for gravity assists). To make sure I wasn't just imagining it, I ran the numbers for Mun, and found that when coming to Mun from LKO via a direct Hohmann transfer (that is, an intercept speed of 365 m/s), an assist can change the craft's velocity by more than 500 m/s. It's not in the optimal direction, but it is still enough to get to Minmus. In contrast, for an intercept speed of 3000 m/s (for instance, when coming from Jool), the change in velocity is only 200 m/s. (If this assist is performed on the way to or from LKO, it's not in the optimal direction either, which might explain why you're only saving 100 m/s.) 

Of course, as @Terwin pointed out, if your relative velocity is too slow, you can't get as much out of the gravity assist either. It seems that the intercept speed (at SOI entry) that maximizes the total change in velocity is equal to the orbital speed at the periapsis altitude, resulting in a change in velocity equal to that amount. (For Mun, that's about 560 m/s.) I have no idea why it works out so nicely, but it appears to get more and more accurate the larger the SOI is.

[tomf]

The maximum change in velocity is going to occur when you change direction by exactly 180°, i.e. the the orbit at the SOI crossover is parallel to the centre line. This can only happen when the orbit is in fact an ellipse cut off by the SOI meaning that the relative velocity is always low.

For hyperbolic orbits the deflection angle is always less, but it is at a maximum when the pe of the orbit skims the surface/atmosphere. 

For a given relative velocity you can work out the maximum angle of deflection and hence the maximum change in velocity. If you can only deflect 90° at a given relative speed of V then your Delta v is ✓2 * V by simple trig.

This matches the observations above.

 - a massive body is good, it deflects more at a given speed

- a denser body is better, pe can be lower giving more deflection

- If the speed is to high deflection angle is low giving little DV

It's bedtime here which is definitely the only reason I'm not going to do it but it ought to be possible to work out for any given body what relative speed gives the highest change.

----------------

Working out how to get the Delta v to point in a useful direction is an entirely different matter in my experience.

Edited August 14, 2022 by tomf
I wanted those to be separate posts

[tomf]

.For capturing as I mentioned above getting that Delta v to point in the right direction that is hard, and is related to the velocity of the assisting body.

Imagine a very massive but distant and slow assisting body orbiting at speed V. We can get a good angle of deflection if we wish, but that just leaves us in almost exactly the same orbit just going the other direction with a 2v difference. E.g a previously prograde hyperbolic orbit about the primary is now an only very slightly less hyperbolic retrograde one.

We could go for a smaller degeneration angle but then the Delta v of the assist is limited.

[king of nowhere]

33 minutes ago, tomf said:

The maximum change in velocity is going to occur when you change direction by exactly 180°, i.e. the the orbit at the SOI crossover is parallel to the centre line.

 

yeah, but that wasn't my question. This is of little practicall relevance, because you very rarely want to use a gravity assist to pull a 180° flip.

My question arose because I came to a gas giant with 500 m/s intercept speed and I used a large moon for gravity capture and it worked fine, and then I came at another similar gas giant, with a similar intercept speed, and I tried to use a similar moon for a similar gravity capture, and this time I could only get a minor saving.

@Leganeskianswer about intercept speed is probably it

[Leganeski]

1 hour ago, tomf said:

it ought to be possible to work out for any given body what relative speed gives the highest change

 

On 8/13/2022 at 8:18 AM, Leganeski said:

It seems that the intercept speed (at SOI entry) that maximizes the total change in velocity is equal to the orbital speed at the periapsis altitude, resulting in a change in velocity equal to that amount.

 

I just did the math to try to confirm this, and got a complicated expression that I can't simplify by hand. I graphed it with Desmos, and found that this is indeed the optimal relative speed (when SOI issues are ignored). The resulting trajectory around the assisting body has an eccentricity of 2 and a deflection angle of 60 degrees.