Super Fancy Orbital Mechanics

[Alpheratz]

Hello everyone,

I've recently learned about the Rosetta spacecraft en route to a comet. In a descriptive video (below), it shows a series of very complicated gravity assists. Now, how can I plan such a thing in KSP? I realize some gravity assists require a specific planetaty alignment. On the other hand, the first gravity assist of the video is with earth itself, which should be doable any time. It would be nice to be able to do such a thing on a regular basis to boost a spacecraft out to the edge of the Kerbol system!

Imagine you launch and set yourself in an orbit whose orbital period is a multiple of Kerbin's. And you repeat the process at each gravity assist. This could potentially save thousands of delta-v! The problem is: when you make the first burn to leave Kerbin's SOI, you can't target Kerbin to get back at it! And every time you reach Kerbin's periapsis to make a correction burn, you can't target Kerbin...

Maybe I could calculate the Sun apoapsis needed to get an orbital period that is a multiple of Kerbin's, but I'd need help with the math.

Now, how should I do that?

Alpheratz

[KerikBalm]

The concept of getting gravity assists from the point of launch seems weird to me... it seems like a losing proposition, can you actually get more dV out of it than the dV needed to set up the maneuver?

[How2FoldSoup]

Iirc ( no guarantees that I do) both voyager satellites used gravity assists of the Moon, Venus, and then back with the Earth or some such to fling them into the outer solar system...It's not weird at all it's pretty normal for NASA do to such a thing.

Disclaimer: This is from memory and I could be wrong.

[Starstrider42]

The Voyagers didn't use any inner-system gravity assists. You're thinking of Galileo and Cassini, both of which happened in a much more budget-conscious era (and which needed a lot of on-board fuel for orbital maneuvers).

To answer the OP, a gravity assist by Kerbin is likely to only work once, because your orbit changes with every assist (I think somebody told me your trajectory specifically gets more parallel to Kerbin's). So you won't save a whole lot of delta-V. And chaining gravity assists would require more computational resources than any KSP player has at the moment. I'm pretty sure NASA has people whose *entire job* is to work out clever launch windows, it's not something you can do on the back of an envelope.

With that disclaimer, here's how to get the orbit you want:

1. Kepler's third law says the semimajor axis of an orbit, cubed, is proportional to the period, squared. So to get an orbit with double Kerbin's period, you want 2^(2/3) = 1.5874... times Kerbin's semimajor axis.
   
2. The semimajor axis is the flat average of the periapsis and apoapsis. If the periapsis is at Kerbin's orbit, the apoapsis must be at 2.1748... times its orbit for things to work out.
   
3. Kerbin's semimajor axis is 13,599,840,256 m, so you want to set your apoapsis to 29,576,961,202 m.
   

In practice, it's probably easier to set your orbit by the period, not the apoapsis, if you have a mod that lets you do that.

[Kasuha]

Gravity assists in KSP work slightly differently than gravity assists in reality. Fortunately they are actually simpler.

There are some tools available to pre-calculate optimal gravity assists when going on certain route but it is also possible to just plan them hop-by-hop using just a few m/s of dv to correct for each next assist.

My approach is this:

1/ eject from Kerbin on a trajectory which crosses trajectory of some other body (Eve is a good candidate).

2/ at the crossing point perform correction to get intercept (if you did not eject to intercept right away)

3/ fine-tune the intercept so it sends you on trajectory crossing the trajectory of some other planet. Use maneuver nodes for rough setup, and RCS for fine tuning. Good places to fine-tune are one orbit (for timing), half orbit (for periapsis), and quarter orbit (inclination) ahead.

4/ continue from point 2

Each gravity assist can only deflect you by certain angle (depending on your speed and the body gravity), if you need to be deflected by more, you need to use multiple passes or your own thrust.

Another point is that - at least for unpowered gravity assists - the speed at which you enter the SOI (relative to the central body) is the same as the speed at which you exit it. It's the direction what changes your orbital parameters in the higher SOI, with one extreme having your periapsis at the point where you used the slingshot (if you exit the SOI exactly prograde) and the other extreme with your apoapsis at the same point (if you exit the SOI exactly retrograde).

[Supernovy]

I've answered a similar question before here.

The main thing to keep in mind is the angle of intercept and ejection. You want to change non-prograde velocity to prograde velocity, that is, leave more parallel to your solar orbit than you arrived.

EDIT: Leaving Kerbin (anti)radial rather that pro/retrograde benefits this, you can have a very similar period with slightly different eccentricity to get a large change from the Kerbin assist, and only after a single orbit.

Edited March 31, 2014 by Supernovy

[LethalDose]

Gravity assists also require a fairly substantial body to make them work appropriately. IIRC, Scott Manley has stated repeatedly that using the Mun to slingshot vessels into interplanetary space is a losing proposition in terms of dV. I forget the reasoning though. I think it has to do with the dV cost of the adjustments that have to be made to make it work larger than the dV savings.

I think gravity assists around Eve to loose velocity going deeper into the solar system (e.g. to reach Moho) should work. I've only tried once, but had to abort because my Eve approach got screwed up.

But Kashua is absolutely right in that for unpowered assists, direction is the only thing that changes, not speed within the SoI of the body around which you're doing the assist... unless you're also aerobraking (which sheds velocity and changes specific orbital energy).

[Kasuha]

Actually...

The main thing to keep in mind is the angle of intercept and ejection.

Angle of intercept is only significant in the sense that you can only be deflected up to certain amount so at certain angles you may not be able to achieve ideal ejection angle.

You want to change non-prograde velocity to prograde velocity

That depends on what you want to achieve by that slingshot. If you just want to set as high apoapsis as possible then it is true, but when you want to do something else, such as set your apoapsis/periapsis at certain point (e.g. to touch orbit of other planet) or to get another intercept right away then the angle you need to use is just the angle which will eject you on the right trajectory.

EDIT: Leaving Kerbin (anti)radial rather that pro/retrograde benefits this, you can have a very similar period with slightly different eccentricity to get a large change from the Kerbin assist, and only after a single orbit.

I don't think this is true. If you exit Kerbin SOI radially, then your Sun-relative velocity will be almost exactly the same one orbit later when you return there. And your Kerbin-relative speed when you enter the SOI again will also be the same and if you turn it to prograde, it will be still the same Kerbin-relative speed, so you'll be on exactly the same trajectory as if you ejected from Kerbin SOI prograde initially.

The only difference will be that you'll exit Kerbin SOI at the "top" of the SOI and enter it at the "bottom" of the SOI, so your velocity will be a tiny bit higher given the difference in distance from Sun. I did not do the math but I think the effect will be a few m/s.

... unless you're also aerobraking (which sheds velocity and changes specific orbital energy).

That's right, I should have mentioned that. But to be honest, you rarely need to aerobrake during gravity slingshot. It will only lower your range, regardless of direction you're going. So the only thing I can think of is when you're performing gravity slingshot from Jool to Moho around Eve, in that case you might want to aerobrake to set your periapsis exactly at Moho and apoapsis exactly at Eve. Because without aerobrake your energy is too high.

Edited March 31, 2014 by Kasuha

[Alpheratz]

Thank you for all the useful comments. There's what I think I learned, correct me if I'm wrong. If I set my ship on an orbit that is tangent to Kerbin's at periapsis, any gravity assist would get me into a lower orbit. This happens because my velocity vector has the same orientation as Kerbin's velocity vector. Any gravity assist would change my velocity vector relative to Kerbol and thus slow me down. Am I right?