Optimising the slingshot effect ?

[flap]

Hello,

I wonder if we have any tool or good rule of thumb to optimize the slingshot effect we could get from the Mun... Or estimate how much energie we got / will get from it.

(take from the french version in wikipedia. I am not sure where to find those in the english version)

http://fr.wikipedia.org/wiki/Assistance_gravitationnelle

Edit :

One of the use for example, is the free return to Kerbin after visiting the Mun : http://kerbalspaceprogram.com/forum/index.php?topic=6058.0

Some others would be to launch further into space (then, predicting the course would be even more complicated...)

[StelarCF]

http://en.wikipedia.org/wiki/Gravity_assist

theres language options on the left of the wikipedia page

[Hypocee]

I\'m not an expert, but here\'s what I can say:

1. \'Optimise\' for what? Numerical velocity? Greatest periapsis? Right now nothing exists beyond the mün so there\'s not a lot to aim at.

2. Numerically you can gain up to 2 times its escape velocity (ca. 1400 m/s total?), but it\'s probably not most efficient to try that if you come on a Hohmann trajectory from Kerbin.

3. The only simple thing to optimise is the Oberth effect (effet d\'Obert), which I can\'t find in French. Efficient = fast = low. In theory you would like to do any burns as close to the body as possible.

[Iskierka]

It\'s not really possible to 'optimise' any kind of 'efficiency' here. Your final velocity, relative to the planet you\'re using for assist, is always identical to your initial velocity. What you -can- do, is alter your periapsis, to change the direction in which you leave the planet. By leaving in the correct direction, you can manage to leave either pointing directly along the line of travel of the planet - greatest final velocity relative to the solar system, or against the planet\'s travel, for minimum. Or anywhere between, to get wherever you want to get.

Also, you can get many times the planet\'s escape velocity, with the right periapsis - your momentum is conserved, which means the maximum change possible is two times your initial velocity, which is usually -at least- the planet\'s escape velocity. If you came in at 0.01 c, and could get a periapsis low enough, it would be very much possible to have a velocity change of 0.02 c.

[flap]

http://en.wikipedia.org/wiki/Gravity_assist

theres language options on the left of the wikipedia page

I knew someone would reply that... : I meant, those 2 graphics don\'t appear on any english pages in the wiki. Or at least I don\'t know where to find them.

True 'optimizing' is very vague and depends on your purpose. Well, what I meant was increasing as much as possible the rocket\'s energie in the original system (kerbin)

[Iapedus]

The 'true' slingshot effect implies a transfer of momentum from a planet or moon to the spaceship, increasing the total momentum of the ship and thus its velocity. Such an interaction is mathematically identical to a perfectly inelastic collision, with the initial and final directions influencing the outcome, however none of this is modelled in KSP.

In-game, craft can however still be 'slingshotted' by another body to usefully correct the direction of travel. Velocity relative to a third object can be maximised/minimised this way by either redirecting the ship along or against the other body\'s line of travel.

[flap]

The 'true' slingshot effect implies a transfer of momentum from a planet or moon to the spaceship, increasing the total momentum of the ship and thus its velocity. Such an interaction is mathematically identical to a perfectly inelastic collision, with the initial and final directions influencing the outcome, however none of this is modelled in KSP.

In-game, craft can however still be 'slingshotted' by another body to usefully correct the direction of travel. Velocity relative to a third object can be maximised/minimised this way by either redirecting the ship along or against the other body\'s line of travel.

Well, to the 'none of this is modelled in KSP', actually, yes it is :

It is a direct consenquence of the fact that you ship is being attracted by a moving object (the Mun) which has a limited sphere of influence (compared to Kerbin). So with movement and gravity, no need to add anything else in the model to have that effect. So actually, everytime a ship enters the infuence zone of Mun and leaves it, its mecanical energie compared to Kerbin would have been altered. The question, is how to make the most of (but I reckon : how would we define 'the most')

What isn\'t modelled though, is the Mun\'s change of velocity after after the slinghsot. But the mass of the craft is so small compared to the Mun, that it can be omitted.

(...)

Also, you can get many times the planet\'s escape velocity, with the right periapsis - your momentum is conserved, which means the maximum change possible is two times your initial velocity, which is usually -at least- the planet\'s escape velocity. If you came in at 0.01 c, and could get a periapsis low enough, it would be very much possible to have a velocity change of 0.02 c.

This is partly true. I have done calculations with the vectors (it wasn\'t that difficult, but it is the kind of exercise that I haven\'t done since 15 years...).

Actually, if the speed of you craft compared to the Mun (Vcm) is quicker than the speed of the Mun to Kerbin (Vmk), then after the slingshot, you would could have added or substracted twice the speed of the Mun to Kerbin to your original speed of to craft to Kerbin (Vck).

- If you were moving in the same direction then, you would have slowed down (see second animation in first post).

- If you were moving opposit to the movement of the Mun, then, you would have accelerated.

If speed of the Mun to Kerbin was higher than the speed of your craft to the Mun, then the max change of speed would have been twice the speed of your craft to the Mun.

You would get the optimal change of speed if you were moving exactly on the same axis as the Mun, and would leave on the same axis, but in the opposit direction :

(Taken from the article http://en.wikipedia.org/wiki/Slingshot_effect )

So, if I sum up the words above :

Lets have :

Vck : the initial speed of your craft to Kerbin

V final : the speed of you craft to Kerbin after the slingshot

Vcm : the inital speed of your kraft to the Mun

Vmk : the speed of the Mun to Kerbin

Then :

If Vcm > Vmk and you originally move in the same direction as the Mun,

then V final = Vck - 2*Vmk

If Vcm > Vmk and you originally move int the opposit direction of the Mun,

then V final = Vck + 2*Vmk

If Vcm < Vmk and you originally move in the same direction as the Mun,

then V final = Vck - 2*Vcm

If Vcm < Vmk and you originally move int the opposit direction of the Mun,

then V final = Vck + 2*Vcm

But this is theoritical, and it doesn\'t really tells how to use it...

Edit :

Check out the deepspace manual at this page. It is originally written for orbiter, but contains interresting technics related to slinghsots.

[boolybooly]

You can use the Mun to slingshot in KSP if you make an eccentric orbit with PE over 600km and AP past the Mun orbit you can use 10,000x warp and can watch many orbits in a few minutes. Where these intersect the Mun SOI you can see the effect.

If you orbit to 90°, same orbit as Mun, then you can pass behind the Mun and get a pull from it and watch your AP increase. If you make a pass in front of the Mun you lose AP. I havent compared the magnitudes. They should be different in theory. I also havent tried the reverse orbit.

IMHO in KSP its got a lot to do with the geometry of the place you enter and exit the Mun SOI relative to the Kerbin orbit. Your path is going to be defined by the point you enter the SOI and on what vector. Intuitively I reckon the biggest net velocity gain is going to be a pass which exits the outward side of Muns SOI on the line between Kerbin and Mun. But if you are going too fast to start with you will exit behind the Mun and miss some acceleration time and too slow you will exit ahead of it and lose some of the Kerbin relative speed you gain on the escape vector.

[Ydoow]

So this could not only be used to be slingshot outside of an SOI, but could also be very useful for requiring a smaller burn to make a Munar Orbit as well, correct?

Entering the Mun\'s SOI traveling in the same direction as the Mun\'s travel would mean you\'d lose speed/energy, and therefore require a smaller burn to make a stable orbit, correct?

That could be very useful.

[flap]

Not really. Or not in one go at least : during a slingshot with the Mun, your trajectory your mechanical energy with the Mun, and trajectory with will stay the same.

But once you would have escaped its SOI, you would have lost energy compared to Kerbin (slowed down compared to it).

But it could have slowed down you enough compared to Kerbin so that you periapsis is now in the planet. Hence the free return flight back home after a Mun flyby (you won\'t even need to lower you periapsis to land).

As far as I understood, in real life, slinghsots are mostly used to alter energy to reach a third body (slingshoting around Jupiter to reach Pluto, or even reach the solar system escape velocity). They also are used ot get enough energy to change the plan in which the probe is orbiting (slingshot with jupiter to to able to have the probe flying above the pole of the sun). Though, in that case, I am not sure that the slingshot (change in energy) is really the main effect. It might just be that a slight change in the plan of the orbit around the sun is amplified when flying close to a planet...

[Nurb]

I don\'t know how I did it, but after my first munar landing I took off with too little fuel left and ended up having a path way to the right of Kerban, but its gravity still captured me and flung me out 25 million K. I warped time just to see what happens next and it turns out after a few orbits, the mun caught me just right (like in the first animation in the OP), and hurled me out at over 10,000 m/s into a near perfect circular Solar orbit the same distance as Kerbin. If this happened after I pre-ordered and not in the demo, I\'d have left their flight in process just to see if they\'d eventually intercept Kerban as I continued playing

It was the last I saw of those brave Kerbonaughts. Bob and Bill were screaming... Jebediah was characteristically optomistic...

[flap]

Well, if before your flyby with the Mun you were orbiting around Kerbin, and after, without thrusting, you have left Kerbin sphere of influence, then it is likely to have been a slingshot.

Unless you were very close to escape velocity, and when you left the system was toward the sun, lowering just enough the escape velocity so you escaped Kerbin. (Though, I don\'t know if this is likely)