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# gravity slingshots for the outer planets and oberth effect

## Question

I'm trying to figure out the most effective trajectory to get far away from kerbol. the ultimate purpose would be to send a few relays farther than eeloo's orbit, so that they can cover pretty much all the outer planets; on the sun-facing side they are in sight of kerbin and its tracking station, and on the night side there is always some relay to pass the signal. anyway, not really important. what's important is that i was trying to figure out how to best optimize this launch.

I'm looking for an apoapsis of 140-150 million km. it would take me 2300 m/s to get there with a single big burn from LKO (and 1500 to circularize, but that applies always). I am trying to see if i can reduce that significantly with gravity assists

the problem with gravity assists is that they work well if you reach the planet relatively slowly. this way, the gravity and momentum of the planet have the time to give you a nice big push. if you zip past your planet super fast, you're not even going to feel it. you can also make a manuever at periapsis to take advantage of oberth effect, but then again, you also take advantage of oberth effect if you burn in LKO. and if you reach the target planet slowly, it means you burn less on LKO. I am coming to realize LKO is actually a great place to start, because while you have to pay a steep price to get out of a gravity well, you get a powerful oberth effect from a fairly big planet. on a big enough burn, this outweights the cost of getting out of kerbin.

so, i've been trying to use Mun for gravity assists. mun is a good source of assists if you don't need to go far. with 860 m/s you can get out of kerbin SOI, and already on intercept with Eve. however, even just for going to duna you'd have to make an additional burn at mun apoapsis. and you get less benefit from obert effect, because mun is less massive. it is more expensive to go to duna with a gravity assist from Mun than it is to just go straight there. For my purpose, the 2300 m/s that i'd need to get past eeloo's orbit won't even get me to jool. Of course, you can just make all your burn in LKO and zip past mun super fast, but it's not worth doing. i experimented, and i only gained a couple million kilometers of apoapsis. maybe 100 m/s of deltaV.

gravity assists on the outer planets all suffer the same problem. those planets are smaller than kerbin, and if their gravity assist is not enough to get me where i want (which is not) then i'd lose efficiency by burning close to them. and if i zip past at full speed i get a negligible benefit.

jool is the only planet suited for the purpose. so (barring some unlikely alignment of planets that would allow me to get to duna and from it get an assist to jool), it seems my best bet is to make a single manuever on LKO to get a jool flyby, then complete the rest of the burn on jool apoapsis. unfortunately, getting to jool from LKO is 2000 m/s, so even if the gravity assist get me already in the target trajectory (which is likely) i would not gain much.

If I had a refueling station on duna, i could get to jool with 1500 m/s from low duna orbit.so i'd have saved 800 m/s, although it is a bigger hassle as i would have to set up a refueling station and get a hohmann transfer window twice, not sure it's worth the effort.

is there anything better i could do?

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Couple points. Even if you have to drag your fuel up to LKO, deltaV in KSP is really cheap. If you mine either of the moons, then deltaV becomes almost free. So there really is no point in gravity assists, except for bragging rights, fun, or the satisfaction of solving a puzzle.

That said, Kerbin->Mun->Eve is not a particularly challenging slingshot. Eve has a very deep gravity well. Since all you are trying to do is raise your Ap super high -- I think that's the cheapest slingshot that will do what you want. Oberth at Eve is huge.

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11 hours ago, king of nowhere said:

it is more expensive to go to duna with a gravity assist from Mun than it is to just go straight there.

Rolling out that old screenshot again...

You see two trajectories that will ultimately lead to Duna, their arrival time differs by just a few hours. So they're virtually identical once they leave Kerbin SOI. They're also virtually parallel inside Kerbin's SOI, I guess that is not a coincidence.

A munar flyby like that is still pretty easy to plan: just delay the maneuver by +1 orbit until you come across the Mun, then refine a little. if you have a markup satellite with a standard transfer set up (like I do in that picture), this takes only a few minutes.

A burn near the Mun may be more efficient, but will be much harder to plan as you need to constantly jump back&forth between two maneuver nodes, one of which keeps shifting whenever you change the other. With stock KSP tools you can easily spend hours refining a flight plan that will ultimately save you very little ( I don't know what's even possible).

KSPTOT may make the process much easier, but I have zero first-hand experience with it.

11 hours ago, king of nowhere said:

Of course, you can just make all your burn in LKO and zip past mun super fast, but it's not worth doing. i experimented, and i only gained a couple million kilometers of apoapsis. maybe 100 m/s of deltaV.

I've heard somewhere that 150m/s is the theoretical limit for what you can gain by that kind of assist. Getting 100m/s for an actual, real-life maneuver that's supposed to take you somewhere isn't bad.

11 hours ago, king of nowhere said:

gravity assists on the outer planets all suffer the same problem. [...] jool is the only planet suited for the purpose.

have you tried Eve? According to hearsay, it's trivially easy to get an AP outside of Jool's orbit from just a single Eve flyby. Ideally you want to line up an Eve + Jool assist.

Edited by Laie
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15 hours ago, bewing said:

Couple points. Even if you have to drag your fuel up to LKO, deltaV in KSP is really cheap. If you mine either of the moons, then deltaV becomes almost free. So there really is no point in gravity assists, except for bragging rights, fun, or the satisfaction of solving a puzzle.

That said, Kerbin->Mun->Eve is not a particularly challenging slingshot. Eve has a very deep gravity well. Since all you are trying to do is raise your Ap super high -- I think that's the cheapest slingshot that will do what you want. Oberth at Eve is huge.

actually a nice idea, i didn't think of going inward, and i will have a refueling station around Eve

unfortunately it does not work. from low eve orbit i need 2800 m/s to get the apoapsis where i want.

which surprises me a lot. it takes 300 m/s more to escape eve than to escape kerbin, and it takes 100 m/s to raise solar apoapsis from eve to kerbin. even if there was no oberth effect at all, i still should need 2700 m/s

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You don't want to stop in Eve orbit. When you get there, you already have an Ap that's outside Eve's SOI (beyond Kerbin, in fact), and you don't want to waste all that dV. Because speed is the source of Oberth. If you slow down to get into orbit, you are wasting Oberth. Adding a few hundred m/s at your Eve Pe should raise your Ap as high as you want. Additionally, the whole point of a gravity slingshot is not to stop. You want the velocity of Eve to add to your ship's velocity, or you get no points for a gravity slingshot.

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I don’t think you need any gravity assists at all to punt something into solar orbit beyond Eeloo. A cluster of NERVs and some big Mk3 liquid fuel fuselages will give you oodles of delta-V even if the TWR is low.

The question I have is- why are you putting relays outside of Eeloo’s orbit? The signal strength will be really low trying to relay from there unless you throw a lot of RA-100 relay dishes (or have the signal strengths turned up really high) and it would make much more sense to put a relay or two in a high polar orbit of each planet instead.

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I queued some Flyby Finder trajectory searches for you; a K-E-J assist window occurs approximately every 400 days, starting at day 0 (though the best assist that I found was at day 776).  I neglected to post any of them because they all required, at a minimum, 3,170 m/s of delta-V to get a Jool flyby.  The problem is that for Eve to raise your apoapsis to Jool orbit in one pass, you need to supply most of the energy yourself in the initial burn because the amount of velocity change that you can get from Eve is capped by Eve's own velocity.  If you need more than that, either because you're going farther away or because you're approaching at an angle or speed that is less than ideal, then you need to get orbital energy from somewhere else.

One place that you can go for that energy is Kerbin:  the K-E-K-J trajectory is much better.  I found quite a few paths that reduce your delta-V to less than 2,000 m/s.  Here is a selection:

Path Start Day 1st (Eve) Encounter Day 2nd (Kerbin) Encounter Day 3rd (Jool) Encounter Day Total Time (days) Initial dV (m/s)
1 1374 1564 2433 3187 1912 1338 m/s
2 1384 1568 2438 3168 1784 1358 m/s
3 1408 1568 2432 3249 1841 1621 m/s
4 1424 1572 2428 3235 1810 1920 m/s

For the first path, you'll need to start from an inclination of -2.6° and 75 km Kerbin orbit.  The path takes you to 120 km altitude at Eve, 284 km at Kerbin, and 1000 km at Jool.  Please note that these paths all lead to Jool, but not past Jool; for obvious reasons, Flyby Finder does not calculate trajectories to open space.  However, tweaking the encounter with RCS in order to tease out an assist to deep space is quite possible.

Edited by Zhetaan
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i tried to get an eve slingshot to outer space: it takes 900 m/s to get to 140M km apoapsis. in addition to the 1050 needed to get in eve flyby, that's a bit less than 2000, at least in theory; in practice, orbital plane correction and course correction manuevers eat up all that i would gain. from eve flyby it would instead be 600 m/s to get to jool, but setting up that kind of path is beyond me. even setting up the eve flyby so that i can accelerate close to periapsis and get a good trajectory is challenging: made more so because, when i am planning the eve flyby, i see the trajectory compared to the current position of eve, not with its predicted future position.

K-E-K-J trajectory... very convoluted. looking at it, i can see that the first eve flyby would put me in an elliptic orbit where i would then wait two or three orbits to get the second kerbin flyby. i would probably have to set up a course correction during that time to get it right. ultimately, i think course corrections will end up eating whatever advantage i gain. it is the most efficient, most elegant solution. but refueling at duna is probably still the compromise i like most between efficiency and practicality.

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22 hours ago, king of nowhere said:

K-E-K-J trajectory... very convoluted. looking at it, i can see that the first eve flyby would put me in an elliptic orbit where i would then wait two or three orbits to get the second kerbin flyby. i would probably have to set up a course correction during that time to get it right. ultimately, i think course corrections will end up eating whatever advantage i gain. it is the most efficient, most elegant solution. but refueling at duna is probably still the compromise i like most between efficiency and practicality.

Fair enough.  There's also a K-E-K-K-J trajectory that more or less gets everything that you can get out of repeated Kerbin flybys before you reach maximum velocity (and minimum assist), but just the paths I showed you earlier involve waiting a bit over two years between the Eve and the second Kerbin encounters; a third Kerbin encounter would add another two years to the flight time (or three; I don't remember).  Do note that course corrections probably are not so bad as you fear; Eve and Jool are both inclined but still arguably in the plane of the solar system, and the flyby paths are designed to be flown on inertia alone.  You'll need some manoeuvring reserve for corrections anyway, but the essence of it is that after the big burn at Kerbin, you don't light the engines again until Jool (or later).  Most who fly these paths well use less than 100 m/s total for corrections, and most of that is in RCS.

But there is, as usual, the trade-off between efficiency and time, and if you want to move more quickly, Duna is certainly an option.  It will still take time (windows between Kerbin and Duna occur somewhat infrequently because they are next to one another in orbit) but it's a viable, albeit unusual, choice.  I will suggest that you consider refuelling at Ike instead, though.  The lower gravity and lack of atmosphere could be great helps to you.

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5 hours ago, Zhetaan said:

Fair enough.  There's also a K-E-K-K-J trajectory that more or less gets everything that you can get out of repeated Kerbin flybys before you reach maximum velocity (and minimum assist), but just the paths I showed you earlier involve waiting a bit over two years between the Eve and the second Kerbin encounters; a third Kerbin encounter would add another two years to the flight time (or three; I don't remember).  Do note that course corrections probably are not so bad as you fear; Eve and Jool are both inclined but still arguably in the plane of the solar system, and the flyby paths are designed to be flown on inertia alone.  You'll need some manoeuvring reserve for corrections anyway, but the essence of it is that after the big burn at Kerbin, you don't light the engines again until Jool (or later).  Most who fly these paths well use less than 100 m/s total for corrections, and most of that is in RCS.

yes, if all is set up perfectly. i have no doubt the real nasa would do it. and perhaps i will do it too, eventually. as it is, i just started doing real interplanetar trips. oh, i know a lot about hohmann transfer, launch windows, gravity assists and the like, but one thing is knowing the theory, putting it to practice is another thing entirely. so far i am quite happy with what i achieved, but i haven't yet the precision to pull that kind of stunt. not with the precision necessary. and i learned that in interplanetary space a course correction manuever that looks tiny on the map will still eat hundreds of m/s.

i am happy to learn of those trajectories, it's interesting and cool, but i don't feel up to replicating them.

plus, i'm still close to the optimal duna launch window, so it's a convenient solution to go there.

Quote

I will suggest that you consider refuelling at Ike instead, though.  The lower gravity and lack of atmosphere could be great helps to you.

of course. when i say "refuel at duna" I really mean "refuel at duna's orbit".

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