Gravity Assist- Multiple Grav Assists on a Body

[NASAHireMe]

How do you perform multiple gravity assists on a single body to lower/raise your Kerbol-centric ap/pe?

For context, I know how GAs work in theory. I use them as much as possible on interplanetary missions. I've also mastered calculating resonant orbits so that I know when I will encounter a planet for a second gravity assist. What I've been struggling with is reconciling this: "If the secondary body already marks the apoapsis of our orbit, we cannot go any lower than that: to slow down we need to exit the secondary's SoI from the rear, but our pre-encounter trajectory is already crossing the secondary's SoI from front to back", taken from Part 2 of Stochasty's excellent post on gravity assists, with this:

, which used two Venus GAs to lower its orbit to Mercury's, or Metaphor's awesome eight-Moho-gravity assists voyage to Moho. Both examples seem to lower the Kerbol periapsis by performing a GA off of a higher body, which violate the first rule.

The answer has something to do with:

1. To perform a good GA, you can't approach a body exactly tangent.

2. I need to play around with the different conic draw modes more. The trajectory displayed in Mode 0 approaches reality the closer you get to the encounter, but before then, the trajectory lines don't match up with the planet pro/retro lines.

Anyone with a simple explanation?

[Itsdavyjones]

If you're not against mods, KSPTOT is a great tool for what you want.

http://forum.kerbalspaceprogram.com/threads/36476-WIN-MAC-KSP-Trajectory-Optimization-Tool-v1-1-8-Aerobraking%21

Otherwise, you can only try, for this in the only tool i know that can do multi-flyby calculations.

[Stochasty]

What you are missing from a theoretical standpoint is that both metaphor's Moho voyage and the MESSENGER mission were using gravity assists in combination with deep space maneuvers. This is a case that I didn't cover in my tutorial (I was more interested in looking at what could be done from a pure gravity assist standpoint).

Basically, the way these missions work is like this: suppose I'm in an orbit, where Moho marks my periapsis. I can use a flyby of Moho to drop my periapsis to inside Moho's orbit (simultaneously lowering my apoapsis). Then, on the next orbit, I can make a deep space maneuver at apoapsis to raise my periapsis back up to the level of Moho's orbit. By doing so, I will have lowered my effective closing velocity at my next Moho encounter by more (often much more) than the delta-V I spent during the deep space maneuver. With precision and timing, you can set things up so that, at each stage of this process, you end up in a resonant orbit and repeatedly encounter your target, slowly matching orbits with each pass; however, at some point, depending on the mass of the target body, the savings from the Oberth effect will outweigh the savings from the gravity assist process and you will be better off finishing the capture with a single burn.

This same process (in reverse) works going outwards, as well - I used this trick during the return phase of my Moho SSTO mission.

[NASAHireMe]

Thanks for the answer, Stochasty. I gradually figured this out myself by sending a couple of ion probes to Kerbol and playing with gravity assists along the way. Setting up assists so that you end up in a resonant orbit afterwards is the trickiest part, because the game engine isn't precise enough to calculate post-encounter trajectories with consistency. Going through the encounter at various timewarp speeds will screw it up, for example.

Each gravity assist also tends to have a small radial component to it. It twists the orbit slightly, either clockwise or counterclockwise. You've gotta then correct that radial twist at your deep space maneuver to raise your periapsis back up to Moho. All this would be a lot clearer and easier to visualize if Conic Draw Mode= 0 displayed the encounter as it would appear during the actual encounter. Instead, the lines are hard to parse because Mode=0 doesn't approach reality until you get close to encounter.

I was able to get the probes to 1GM from Kerbol (my target) using a couple Eve and Moho gravity assists, but I'm still kinda lost on HOW I did it. At least I know I can. It will take me a few more hours of thinking before I grasp it fully. Thanks anyway.

[vixr]

please excuse my dim bulb (I feel like a 40 watt in a room full of 100s) is the GA aimed at changing speed? direction? inclination? It seems like I could use the Mun to GA me into an encounter with Minmus if I'm understanding you guys...

[Jimbimbibble]

If your target is the Sun you could fly by Jool. Think of it as combining a bi-elliptical transfer with a gravity assist. You want to enter Jool's SOI from the rear and burn at Pe. The Oberth effect you get is huge and you can easily crash yourself into the Sun. I've gotten within 10km of the surface with 5k deltaV to spare. After burning that off I was still going 50km/s when I got back to Jool's altitude.

[cantab]

You can, though for the Mun-Minmus assist in that case you don't save an awful lot of delta-V, I think 150 m/s is the best case scenario.

For the Jool-sundive assist, the trick is that you want your apoapsis to be BEYOND Jool's orbit. That way you can get the gravity assist to knock down your periapsis. It then only needs a modest burn at periapsis to reraise apoapsis for a repeat assist.

Edited January 27, 2015 by cantab

[PLAD]

Multiple flybys of the same planet can change your Kerbol periapsis even if you do no maneuvers or encounters of other planets. What they cannot change is your speed at a given altitude above the flyby planet. I use the speed at the moment you enter (or leave) the SOI of a planet as the reference speed, I call it the VSOI. In the Moho Challenge that Metaphor won with style you will find that his VSOI at the two Eve flybys was the same, he just changed the direction he was going relative to Kerbol. I was in that challenge, as I recall the first pass was to match the plane of Moho but not reach its periapsis, the 2nd flyby lowered the Kerbol periapsis to Moho's orbit. The reason that two passes were needed is that Eve does not have the gravitational chops to change your path all at once- you'd have to flyby well below it's surface to do the plane change and periapsis change in one flyby. Mind you I've tried that, unintentionally.

Another example of this is my LKO to Jool for 1051m/s mission. I have to flyby Kerbin twice, notice I specifically show the direction and Kerbin-relative speeds I'm leaving Kerbin at after each pass, the first time is at a large angle from Kerbin's path around the sun and the 2nd pass departs much closer to parallel to Kerbin's orbit, thus the ship and planet velocities add up to a higher prograde speed around Kerbin and thus an apoapsis high enough to get to Jool.

And as noted, Metaphor's repeated Moho passes lower his Kerbol periapsis because he does a deep-space maneuver after each one. Flying by 2 planets has the same effect (the 2nd planet flyby is like a deep-space maneuver), by going Kerbin-Eve-Kerbin-Eve you can build speed up to Kerbol escape velocity if you do it right.

I know it's tooting my own horn but here is another extreme example of flybys, in my Jool-5 mission the carrier gets from LKO to a flyby of all 5 Jool moons and back to Kerbin on only 1415m/s by using 22 flybys. And there is a 2nd flyby calculator for KSP-Flyby Finder. It's not nearly as feature-rich as TOT but it's quick.

PS- "NASAHireMe"-you have my new favorite forum name.