Multi-planet gravity assists

[TJPrime]

I have installed Krags planet factory and a certain pack into my game - the titan system. I was wondering how I could time my gravity assist from Jool to get an encounter with Titan. Is there a way to calculate the time? I don't really want to install any sort of software, by the way.

Edited July 12, 2014 by TJPrime

[allmhuran]

The easiest way is not to time it such that you immediately go from one gravity slingshot into the next, but rather go from one gravity slingshot into a couple of solar orbits before getting the next one.

You might think this seems boring, since you have to sit around in 100,000 times warp in solar orbit for a few minutes. But if you want perfectly timed gravity slingshots you need a perfect launch window and a perfect initial position for the targets, which means sitting around in 100,000 times warp in the tracking station for at least as long (usually longer).

I won't try to describe it in words, because I have several videos on the subject. The best explanation is probably to be found midway through my starting parts grand tour, here's a link to the point in the video where I describe in detail how to chain slingshots together:

http://youtu.be/HcWwWAJt4dM?t=10m42s

There's another briefer example in that video here http://youtu.be/HcWwWAJt4dM?t=17m5s

Or I have a video that is entirely devoted to this topic here http://www.youtube.com/watch?v=mnPSNH8zlmw

Edited July 12, 2014 by allmhuran

[purpletarget]

You'd probably have to did out the phase angle calculations for the planets in question.

You'll need to determine the phase angle based and transfer time between Jool and Titan. (Where Titan needs to be when you do Grav assist at Jool)

Then you'll want to calculate the Transfer time & Phase angle between your origin and Jool... (To line up initial transfer to Jool)

You'll need to backing off the time for origin to Jool, and add it to the Jool/Titan phase angle caculation. That'll tell you where Titan/Jool need to be in relation to each other when you leave the origin

The combined times, Origin to Jool, and Jool to Titan will give you the time required, and you should have the relative phase angles that both Jool and Titan need to be in before you leave. Fortunately they're probably so far out that the origin angle (presumably Kerbin) can be cycled 2-3 years before the outer planets get out of the window.

Check here for the equations, mostly in section 1 of Kosmo-ot's guide: http://forum.kerbalspaceprogram.com/threads/16511-Tutorial-Interplanetary-How-To-Guide

[allmhuran]

Oh, in case you don't want to watch a video and would prefer a text answer, I looked up the answer I gave someone in the reddit thread related to that video. This is probably a better explanation than the commentary in the video, but is obviously lacking the visual advantage:

Short answer: Ignore the timing.

Longer answer: Watch the section at 10:44 again http://youtu.be/HcWwWAJt4dM?t=10m44s

Long answer:

Let's go back to the basics of how an encounter happens. For an encounter to happen, you and your target have to be in the same place at the same time.

First let's work on "same place". To be at the same place as your target, your orbital path must cross the target's orbital path. Let's say you're at Jool and you want to get to Kerbin as per your example.

If you like, you can Just burn away from Jool (leave Jool so that your ejection angle is solar retrograde) for long enough that your solar periapsis gets down to Kerbin. Or, to save many-a-delta-V, you can slingshot off Tylo. But for now let's just say you burn your way down for simplicity.

OK, now you're in a solar orbit with a periapsis near Kerbin's orbit, so if we look "down on the map from above", your orbit lines will appear to cross. But what about if we look from the "side"? Where does your orbit pass above or below Kerbin's orbit?

To get an intercept, the point where you pass above or below Kerbin's orbit (ie, the ascending or descending node) must also be the point where you pass inside or outside Kerbin's orbit. So you need to make a normal plus or normal minus correction until the ascending or descending node moves around to the point where the orbits appear to cross when looking from above. Note that you do not have to match planes with Kerbin.

OK, so now your orbit line passes exactly through Kerbin's orbit line at one point, or in other words we have the "same place" part all figured out. But what about the "same time" part?

Well, this is actually pretty easy. The time it takes you to complete an orbit depends on how big the orbit is. And you can change how big the orbit is by burning prograde or retrograde.

Of course, we don't want to mess up that "same place" part, so we're going to perform that burn right at that point we set up earlier, where the orbits cross.

Put a maneuver node down at the crossing point. It doesn't have to be absolutely perfectly there, just "pretty close". When you place that down, you will get a "closest approach" marker on your orbit, and a "target position at closest approach" marker on Kerbin's orbit.

Now put down another maneuver node on your orbit. I usually place it 270 degrees in front of that first node. This represents a maneuver that happens after that first maneuver.

Now click the "one orbit ahead" button on that second maneuver. You will see the approach markers move. Keep clicking it until the two markers are "pretty close" to that first node we put down at the crossing point.

Now all you need to do is change your orbital period until the two markers come together at that point. Do this by pulling the prograde or retrograde handles of the first maneuver, the one at the crossing point. When you see an intercept happen, use the second maneuver to tweak your trajectory into Kerbin's atmosphere so you can aerobrake.

Small changes to the first maneuver will have big changes on the intercept, and it can be difficult or impossible to get a perfect encounter periapsis. But you can always get a perfect encounter periapsis using the second maneuver, and it is much less sensitive.