Gravity Assist From Minmus To Mun?

[The Flying Kerbal]

I've been playing with the KSP Demo these last number of weeks and have finally completed landings on both Mun and Minmus.  I'm planning to have a go at one last mission in demo before going back to the full game and need just a little advice from you good people.

The plan is to launch a rocket carrying two unmanned landers, one for Minmus, one for Mun.  The Minmus lander will be a very lightweight affair, basically a Science Junior on legs with a few essentials for power, control, etc.  The second lander will be a much more robust vehicle to be able to set down on Mun.  So what I was thinking was to attach the Minmus lander to the larger one, sending both to Minmus where the small one detaches and lands, while the second one heads for Mun.

Would a gravity assist be possible from Minmus to Mun?  I know it probably wouldn't be the most efficient way of doing it, but it just sounds like a fun thing to try; I've never used a gravity assist before.  I can find tons of stuff on assists going the other way, but nothing about trying one from Minmus to Mun.  There could be a very good reason for this, I expect the gravity of Minmus just isn't strong enough to be of very much help, but I thought I'd ask the experts and see what you think.

Edited January 10, 2017 by The Flying Kerbal

[FancyMouse]

In the form of just "going to Minmus then going to Mun", then it's definitely possible. All you need is a good timing, and if you do dozens of trips to Mun/Minmus you may even encounter a few by accident.

In the form of actually saving delta V by going to Minmus first - no. Going to Minmus already takes more fuel than going directly to Mun. And the whole point of gravity assist is to arrive at somewhere using fuel less than going directly there.

[Tex_NL]

Both Mun and Minmus are more than heavy enough to significantly alter your orbit. And in theory it is very possible to get an assist of either of them to reach the other. But it will take a lot of careful planning and the reward will be negligible.

Looking at your planned mission it might get even more tricky since one part needs to orbit/land while the other needs to continue. The landing/orbit insertion will be pretty much simultaneous with the low orbit coarse correction for the continuing part.
Much easier would be to get the entire craft in Minmus orbit and land the small lander. Then, at the appropriate time, leave Minmus orbit for and head for Mun. A Minmus to Mun transfer works in the same fashion as for example Kerbin to Eve or from Duna back to Kerbin. But it is dirt cheap.

[Zhetaan]

First, the terminology:  a gravity assist is only an assist when you exit the sphere of influence of the assisting body.  For this reason, you cannot get assists from the primary that you're both orbiting (usually the sun, but Kerbin counts if you're going from moon to moon), the body you're leaving (you started in orbit; you can't get an assist from that) or your destination:  it has to be a third party to that leg of the trip.

There are assists from the Mun to Minmus because you start at Kerbin and end at Minmus; the Mun is the assisting body because you both orbit the same primary (Kerbin) and the Mun isn't your destination.  You can also get an assist from the Mun going back to Kerbin for the same reason.  If you use the Mun to give you a braking assist to go back to Kerbin (essentially using the Mun to drop your periapsis into the atmosphere), that's called a free-return trajectory, and it's what the early Apollo missions relied on to insure against engine trouble when they tried orbital insertion at the moon.

If you want to waste the fuel and do it just because it can be done (which, let's be honest, is usually a good reason to do anything), you can get a braking assist from Minmus to help go to the Mun.  The trick is going to be timing it so that you don't shoot yourself into interplanetary space or go crashing into anything.  Minmus alone probably won't be enough, even if you do (almost) graze the surface.  It may end up looking weird like a free-return trajectory, which looks like a figure-eight.

There are efficient paths between the Mun and Minmus and back for when you begin orbiting one of them, but these are advanced transfers that require the use of a porkchop plot (that's alexmoon's Launch Window Planner) to describe fully accurately.  They're good to use as a test run for going interplanetary, though.

That being said, you can technically even use the Mun for a gravity assist to get to the Mun.  The requirement for an assist is that you must enter and exit the sphere of influence of the assisting body, so the only way to use the Mun to get to the Mun is to go twice.  That is to say, time your trajectory so that the Mun brakes your vessel and sets you up with a second Mun encounter; you can use this second one to reduce the needed draking delta-vee.  Just be sure you get the timing right; you don't want it to brake you so that you crash into Kerbin.

Edited January 10, 2017 by Zhetaan

[wumpus]

As stated, you really can only do this from Mun to Minmus.  You need to google the right angles they have to be in for this to work (it should be available, but isn't done enough to be common knowledge).

According to our handy cheat sheet: http://wiki.kerbalspaceprogram.com/wiki/Cheat_sheet It takes 860m/s to get to Mun and 930 m/s to get to Minmus, giving a maximal savings of 70m/s.  Note that you also need a 160m/s burn to match Minmus's angular velocity, and I'd suspect that a gravity assist helps even more here (you should wind up "chasing" Minmus).  Even so, most kerbanauts want plenty more reserve fuel than this so this is rarely done (although somehow I seem to encounter Mun a lot on the way home).

Note: edited thanks to Tex_NL's  warning.

Edited January 10, 2017 by wumpus
see note

[Tex_NL]

17 minutes ago, wumpus said:

 It takes 930m/s to get to Mun and 860 m/s to get to Minmus,

Don't you mean the other way round? 860 to Mun and 930 to Minmus!

Flying Kerbal is already mixing up the names. It doesn't help if we pile on with incorrect data.

Edited January 10, 2017 by Tex_NL

[Birdco_Space]

13 hours ago, wumpus said:

As stated, you really can only do this from Mun to Minmus.  You need to google the right angles they have to be in for this to work (it should be available, but isn't done enough to be common knowledge).

According to our handy cheat sheet: http://wiki.kerbalspaceprogram.com/wiki/Cheat_sheet It takes 860m/s to get to Mun and 930 m/s to get to Minmus, giving a maximal savings of 70m/s.  Note that you also need a 160m/s burn to match Minmus's angular velocity, and I'd suspect that a gravity assist helps even more here (you should wind up "chasing" Minmus).  Even so, most kerbanauts want plenty more reserve fuel than this so this is rarely done (although somehow I seem to encounter Mun a lot on the way home).

Note: edited thanks to Tex_NL's  warning.

A well executed gravity assist saves around 150-200 m/s over a straight shot to Minmus, because you can get the inclination change through your Mun gravity assist for a lot less delta v, and you can save around 60ms on the braking burn at Minmus.

A poorly executed gravity assist actually cost more because too much velocity is picked up on the Mun gravity assist, which needs to be bled off on the Minmus capture.  However, Mun gravity assists are almost always shorter flight times to Minmus (but not a big benefit when time acceleration is the norm)

The challenge is that the windows for these only occur once per Mun orbit, and some of these windows are much better than others.  Also, you only get the greatest savings when the intercept with Minmus occurs 90 degrees from either the ascending or descending node (where you save the most on the inclination change).  Given this, it frequently easier just to wait until a directs injection to Minmus results with an intercept on the AN or DN 

[The Flying Kerbal]

So what I'm planning isn't a gravity assist?  I honestly didn't know that, and I'm afraid there will be many similar gaffes on my part as I'm not as familiar with the correct terms used in space travel as you guys.

Also thanks to everyone who has so far taken the time to answer my question, all answers, advice and suggestions are very much appreciated.

[Zhetaan]

@theflyingkerbal:

Actually, I'm not sure whether you are planning a gravity assist.  It depends on how you fly the mission (okay, that should be obvious), and I'm not really clear on what you intend.

The mission you describe, and please correct me if I'm wrong, involves piggybacking a tiny Minmus lander on a larger Mun lander.  Whether this mission involves a gravity assist depends entirely on what you do when you get to Minmus.  The big difference is the number of destinations you reach with a single burn.  One destination is a transfer.  Multiple destinations is a gravity assist.

If you go to Minmus, make orbit, detach your Minmus lander, and burn to break orbit and send the rest of the stack to the Mun, then that is an advanced transfer which requires a porkchop plot to plan accurately.  It is not a gravity assist because you burn to brake at Minmus.  A proper advanced transfer to drop from Minmus towards the Mun will point your trajectory along the same vector as you would get from a gravity assist, but it is not a gravity assist in the popular sense because you're doing the trajectory pointing with rocket fuel, not ballistics.

If, on the other hand, you set up a manoeuvre at Kerbin that sends you through Minmus's sphere of influence in such a way that it bends your trajectory back to get an encounter with the Mun, and while you are travelling through Minmus's sphere of influence, you decouple the Minmus lander and have it burn to make orbit on its own while the Mun lander goes on to the Mun, then yes, that is a gravity assist--for the Mun lander part only, but it is still a gravity assist.

If that second one is what you plan, then there are some things to keep in mind as you design the mission:

• First, the Minmus lander will need to have fuel not only to land, but also to brake to orbit and possibly also to alter the orbit to what you want for a good landing spot.  Maybe you don't care where you land, but it may work out that the flyby you need puts you in high Minmus orbit and you'll need to come down to close orbit for the landing (unlikely, but you need to consider it).

• Second, Minmus is a little space pebble:  it doesn't have enough gravity to bend your trajectory as much as you need for good assists.  The amount of speed you can get from a body is limited to exactly double your closing speed for a theoretical ideal of an assist that spits you out on a vector precisely 180° from a sphere-of-influence entry point exactly at the prograde or retrograde vector of the assisting body.  Getting the entry point right is easy; that's what you do with a (theoretically ideal) simple transfer orbit.  Getting the right amount of deflection is the hard part.  The faster you go with respect to the assisting body (this is the closing speed) the more assist you can get, but the faster you go, the less time the assisting body has to warp your trajectory.  The less warp you have, the less assist you get (and the more you have to alter your entry point so your exit is in the correct direction), so there is a definite optimum that balances the speed you approach against the direction it spits you out.  Low gravity only magnifies the problem, and that's why assists work so much better with massive bodies.

• Third, the space pebble orbits far away:  its orbital speed is so low that what it can give you just isn't very much if you're starting from Kerbin.  Minmus orbits at a snail's pace of 274.1 m/s.  Using the cheat sheet that @wumpus provided for the rough figures, the ideal Hohmann transfer (also known as a minimum-energy transfer) requires 160 m/s to capture and circularise.  In effect, capture is the same as making your orbital velocity equal that of the thing you want to capture you, so the difference between these two numbers is our rough closing speed.  It isn't exact because you usually want to be on one side or the other of the thing you're capturing around (you could go for the middle but that's hard on the paint job) and Oberth has an effect as well, but the point is that our closing speed is 114 m/s.  A perfect Minmus assist would give us a total possible change of something a little over 228 m/s, but that's not possible.  It's still doable--for this job, we actually don't want a perfect assist--but it will be tricky.  Aim for the idea that a Minmus assist will help you a very little, but you're probably still going to need to do the lion's share of the job yourself.  Also, while it is possible to get more closing speed by going with a less-than-ideal Hohmann transfer, you definitely don't want to do this, for two reasons:

1. The Mun orbits closer in than Minmus, so any energy you add to the orbit beyond the minimum, you'll need to take away again. It's inefficient to put energy into an orbit that you don't intend to use, and we've already gone over how Minmus can't give you a perfect assist, so that means more burns and more wasted fuel.
2. The difference between reaching Minmus orbit and Kerbin escape velocity is 20 m/s of dV by the chart.  You're too close to the edge of Kerbin's sphere of influence to go fiddling with inefficient transfers.  It's different if you are trying to go interplanetary, but you're not, so there it is.

• Fourth, remember that gravity assists still depend on transfer windows.  It's not a once-a-decade thing, but Minmus's orbit is inclined by 6° from the Mun's orbit, and you need to take that into account:  it does not good to arrive with perfect timing at the Mun's orbit only to find the Mun a few million metres to your celestial north.  You need to start from Kerbin at a point that will put you at Minmus in a way that will throw you to the Mun at a time that both the Mun and Minmus will be there when you're there.  If the trajectory isn't getting you anywhere close, you may need to change the time of Munth (or Minth, or both) that you go.

• Lastly, decoupling the Minmus lander needs to be done in a way that it does nothing to the Mun lander's trajectory.  This means either turning the decoupler force to zero in the VAB or using docking ports.  Don't turn on RCS until you've undocked.

All of this is probably intimidating; don't let it be so.  Gravity assists are a fun, though advanced, way to play the game, and you can get a lot out of them if you learn how to do them correctly.  All that is really required is experience with transfers; with that, the next step is to grasp how to squeeze several transfers out of one rocket burn.  The real issue here is not that gravity assists are too difficult; the issue is that the gravity assists available from Kerbin's moons simply aren't very good.  It's just the same as how rendezvous leads to docking leads to orbital space station assembly:  you need the right skills, but you also need the right tools.  Imagine trying to dock using only solid rocket boosters and you can see what I'm trying to describe.

The Mun can send you to Minmus with little trouble (in fact, you may want to try that one first), but that's the end of it.  It can send you interplanetary, but it won't get you anywhere else.  If you can reach Eve, on the other hand ... well, then you can go anywhere.  Eve is a high-gravity world, easy to reach (under 1400 m/s), inclined with respect to Kerbin (this is needed for gravity-assisted inclination changes) and though it has a moon, it's nearly impossible to hit that moon accidentally (it's also nearly impossible to hit it deliberately--rotten 125 km sphere of influence!--but that's beside the point).

Have fun! 

[The Flying Kerbal]

13 hours ago, Zhetaan said:

Actually, I'm not sure whether you are planning a gravity assist.  It depends on how you fly the mission (okay, that should be obvious), and I'm not really clear on what you intend.

What I'm planning is to launch from Kerbin into LKO.  Sort out my burn to Minmus, drop off the Minmus lander and then use the Minmus gravity to set me on course for Mun.  In theory, if everything worked according to plan, after my injection burn from LKO to Minmus, there would be no more engine firing until the Mun lander reached its final destination and fires retro to slow down in preparation for landing.  However I do intend to take enough fuel with me so that if push comes to shove (as we say in Northern Ireland), I'll be in a position to fire up the engine to make any corrections necessary to set me on course for Mun.

Your posting was really brilliant - as indeed was everyone else's - packed full of information and facts I wasn't aware of, although being in the office isn't exactly the ideal place to study everything you said in great depth.  However the one bit that has really stuck in my mind is to maybe try shooting something at Mun first with the intention of going for an assist to Minmus, just to have a go at trying a manoeuvre such as this.  That sounds like a plan to me!

I do realise what I'm thinking of doing is probably not the way you professionals would do this, but as I said in a previous comment, it just sounds like a bundle of fun and will give me an excuse to pat myself on the back if I should manage to pull it off!

Edited January 12, 2017 by The Flying Kerbal
As usual I can't spell :O(

[Zhetaan]

4 hours ago, The Flying Kerbal said:

professionals

I'm only a professional if you pay me, and if you make me laugh too hard, then I can't type.

Anyway, this is how the real professionals do it.  The animations do a great job of showing just how much you can gain (or lose) from a gravity assist; you ought especially to take a close look at the encounters for Saturn and Neptune.  Saturn shows a near-perfect example of a gravity assist done to gain speed and Neptune shows how a gravity assist can make you lose speed (this wasn't intentional, per se, but since Neptune was the last stop and the mission planners wanted to see Triton up close, it didn't matter to them that the probe lost speed there).