I'm on a Free Return Trajectory (And so can you!)

[Rascal Nag]

I\'m sure quite a few of us know what a free return trajectory is, but to those who don\'t, sit back and listen, for this is quite the maneuver.

The idea behind the Free Return Trajectory is that once you make your burn so that your orbit takes you to your destination, if something goes wrong the gravity of that object alone will put you back on course for home. The result looks like a figure eight orbit:

But how does one achieve this orbit? You might notice that simply matching your Apoapsis with the Mun\'s orbit doesn\'t work. So how do you do it? Simple! You go farther than the Mun\'s orbit!

But why does this work? Wouldn\'t going further make you go faster, therefore flinging you into outer space? Yes, but at the same time, not at all! In this type of orbit, you still have a larger percentage of your velocity going into pushing you further away from Kerbin as you enter the Mun\'s SOI. This vertical velocity relative to Kerbin is lateral velocity relative to the Mun, allowing you to slingshot around it. You may speed up initially, but as you leave Munar orbit, the Mun slows you down, and moves along its own orbit, slowly causing you to point towards Kerbin. As you get closer to Kerbin, your top lateral speed cannot be greater than that of the Mun since you\'re escaping its orbit in a retrograde manner, plus you\'re getting closer to Kerbin, so this lateral speed is not only less than the Mun\'s, but closer in to Kerbin, so naturally your orbit is very elliptical. If you really did it right, your Periapsis will be deep enough in Kerbin\'s atmosphere to cause you to re-enter and land there.

Here are some pictures of my own FRT mission:

Liftoff!

Staging.

After the second stage put us in orbit, we now wait for the correct burn time.

Mun is rising! Burn!

Here\'s our Trajectory after the burn.

To show my confidence, I\'m only going to have the capsule.

Bye Kerbin!

We\'ve entered the Mun\'s SOI.

Look at that! A bit of a sloppy orbit, but we\'re coming home!

Approaching...

Oh man, high g-forces... they would probably be dead from that, but it\'s okay! Not modeled yet!

Chute is out!

Parachute now fully open.

And splashdown!

Mission is a success!

After a few runs, I\'m pretty convinced that a good rule of thumb is an apoapsis of about 14,500,000 m is sufficient, with the standard burn time for any Mun mission - right when it rises. My best one had a periapsis on return of 22,000 m. It\'s hard to predict exactly what you\'ll get, but follow these rules and you should be able to get at least some sort of FRT going.

[Huojin]

Not quite as easy as you make out. I just gave it a shot, it didn\'t go brilliantly. I\'ll post again if my next mission is a success, but when I did my last attempt, I shot straight past the Mun and looped back around to Kerbin, then was caught by the Mun the next time, but on the wrong side, then flung into a huge orbit of Kerbin.

[Rascal Nag]

Not quite as easy as you make out. I just gave it a shot, it didn\'t go brilliantly. I\'ll post again if my next mission is a success, but when I did my last attempt, I shot straight past the Mun and looped back around to Kerbin, then was caught by the Mun the next time, but on the wrong side, then flung into a huge orbit of Kerbin.

My gut says that our heights in orbit when we burned to the Mun were different, that\'ll probably have an effect on what happens.

[Huojin]

Not a brilliant collage, but it shows the mission. I managed to do it without any burn save for the TLI, but I missed the Mun on the first orbit out, had to wait for the third one before I intersected its path again. Might be I\'m going too high, I always seem to be too far from the Mun when it passes by.

[PD]

You genius... Do you realise how many 'experts' were saying an FRT was impossible with just 1 8-ball and the other information we currently have availible?!?!

I\'m so pleased to see our community constantly pushing the bounderies of what is 'possible'. I remember when people said we would never get to Mun on the instrumentation! Nice work indeed. I\'m going to give it a try RIGHT NOW!!!

---

*Mission controller walks into Jeb\'s room to wake him up*

'Jeb Its time to... umm what?!'

*Jeb is sitting in a meditative state on top of an armed nuclear warhead... in his space suit*

'Oh, of course you\'re right, I shouldn\'t be playing with nuclear warheads when there\'s a Free Return Trajectory to perfect.'

*The mission controller looks at the clock ticking down with about 6 days left on it. Jeb looks at him and says as he saunters out:*

'Ahh don\'t worry.. I\'ll get that when we\'re back.'

*With that, he put on his shades. Leaving the controller to wonder how Jeb already knew about the new mission. It was the least of his concerns*

[Cepheus]

You deserve this.

I managed to do it without any burn save for the TLI, but I missed the Mun on the first orbit out, had to wait for the third one before I intersected its path again. Might be I\'m going too high, I always seem to be too far from the Mun when it passes by.

The best time to burn for a TMI is immediately after the moon rises over the horizon. Works every time.

[chimpychimp]

Ive just tried this out now, I think I had the same problem Huojin in that the height of our orbits when starting the burn was different, I think I was in a fairly high orbit (200,000m?)

[PD]

Yep, I did it from 120,000 and it works perfectly.. I was a little fast by accident, so my AP was about 15,000,000. But, it was a free return.

PD

[Huojin]

The best time to burn for a TMI is immediately after the moon rises over the horizon. Works every time.

Yeah, I did that, but maybe ever so slightly late and a little too far out. I\'ll give it another shot soon. But it\'s doable, certainly. I love it :3

[Huojin]

Yeah, I did that, but maybe ever so slightly late and a little too far out. I\'ll give it another shot soon. But it\'s doable, certainly. I love it :3

Just gave it another shot. Worked like a charm. It\'s absolutely perfect. Made my TLI burn, then detached everything to see what would happen. Went up, around the Mun, and back to Kerbin.

Rascal, it\'s amazing.

EDIT: Hit 41.2 G when my I popped the chute, which was fun :3

[Rascal Nag]

Just gave it another shot. Worked like a charm. It\'s absolutely perfect. Made my TLI burn, then detached everything to see what would happen. Went up, around the Mun, and back to Kerbin.

Rascal, it\'s amazing.

EDIT: Hit 41.2 G when my I popped the chute, which was fun :3

Thanks! Glad it\'s working.

[PD]

Having massively loved your technique I\'ve decided to write a tutorial on the wiki covering this topic. I hope you don\'t mind?

here it is: Free Return Trajectory

Also, I think that we might be able to tweak our entry speed to the Mun\'s ZOI by bringing the apoapsis in to about 12,000,000. I\'m hoping we\'ll make orbit? This might... not work

Plan B is to shoot for about 11,100,000m, as we might be able to orbit in the opposite direction. We\'ll see what happens!

PD

[Rascal Nag]

Having massively loved your technique I\'ve decided to write a tutorial on the wiki covering this topic. I hope you don\'t mind?

here it is: Free Return Trajectory

Also, I think that we might be able to tweak our entry speed to the Mun\'s ZOI by bringing the apoapsis in to about 12,000,000. I\'m hoping we\'ll make orbit? This might... not work

Plan B is to shoot for about 11,100,000m, as we might be able to orbit in the opposite direction. We\'ll see what happens!

PD

I\'ve got no problem with it being on the wiki. Also, I\'m not sure 12,000 km will work, that\'s what I usually do for landing missions. I was thinking not too long ago to maybe try 14,000 km apoapsis, to try to raise my periapsis when coming back. I might just do it in the middle, at around 14,200 km - 14,250 km.

Also, just to be safe I\'ve searched the forums with regards to whether or not I proved it was possible or not, because I vaguely remembered an old thread on the same subject.

http://kerbalspaceprogram.com/forum/index.php?topic=4449.15

Page 2, PakledHostage has done it just under two weeks ago.

[PD]

ohh interesting..

yeah 12,000,000 didn\'t work. I\'m going to 'shoot short' tomorrow

PD

[Guest Flixxbeatz]

Free return trajectory...

[Rascal Nag]

Free return trajectory...

No, the free return trajectory is when after doing the burn to reach the Mun from Kerbin, you can just let the capsule free with nothing attached (except a parachute) and you\'ll be slingshotted by the Mun, taken back back Kerbin\'s gravity and land safely.

[PD]

Yeah, that\'s close but no cigar. You you let Jeb use his boosters from Kerbin and then just chill with no engines all the way to the Mun and back? With just shades and a parachute to get him home safe? That my friend.. is the challenge 8)

PD

[closette]

Success - thanks to the posts on this thread! Boosting from circular Kerbin orbit at 150km to a 15 million km apoapsis at Munrise seems to do it - nice round numbers.

The new Wiki entry looks pretty good. Keeping Munrise as the datum, it would be interesting to explore the possible ranges of {starting orbit, boost apoapsis} values where this works.

Also a 'Mun direct' approach from launch to main engine cut-off, without establishing Kerbin orbit first, would be quite a challenge.

[PD]

Both things I shall now work on. That seems to be a more useful challenge that the (as far as I can tell) not yet possible transfer into orbit trajectory without a burn.

Perhaps the wiki entry could have a table of successful figures?

I\'m going to try the direct shot now, I shall let you know.

PD

[chimpychimp]

I will try the 150km and 15km apoapsis later on closette, they are very nice round figures.

I need to figure out a reliable way to predict a good kerbal orbit from the moon, my current method basically involves jeb pointing the rocket at the kerbal and yelling 'FIRE ALL THRUSTERS' at the top of his lungs.

[PD]

I\'m just wondering if we can take a mathmatical approach now that we have a few known orbit altitudes and speeds for Free return? I\'m no mathematician but I\'m thinking if I find the relationship between Circular orbit speed (as shown in the Basic orbit tutorial table) for the altitude, and the free return trajectory speed from the same height, that might be translatable to all other altitudes and related speeds. I am going to try this by doing the maths (as well as I can) and then testing the returned figures.

EDIT: Either I\'m doing the wrong maths, or that idea doesn\'t work.

What I did: I took the speed used in the original example by the OP. And took the percentage of that to the Basic Orbiting Table\'s idea of a circular orbit. It was about 132% (or close enough).

I then boosted a rocket up to an 80,000m orbit, took the speed from the table and multiplied it by the answer from before (so something like 1.327...)

This did not work. my Apoapsis ended up at like 9.5M. Clearly a little 'more' needs to be added on for that one, which suggests a non-linear relationship? Anyone with any expertise able to step in at this point?

PD

P.S. @Chimpychimp

You should find that boosting retrograde to the Mun\'s orbital path, will mean that you end up slowing down on the Mun\'s gravity, before leaving it\'s SOI. Once that happens, you will naturally fall back to Kerbin. Hope that helps.

[Cezary]

Wicked cool. I was looking for a new challenge. Going to try this right now. ;P

[closette]

@PD - I should have said this earlier, but your Wiki tutorial is GREAT. 'Can I do a free return?' was one of the first questions I asked myself about this game, and your tutorial would have answered it. This opens up yet another educational aspect of the game, exploring parameter space to find out what works.

I would not have expected a linear relationship between Kerbin orbit altitude, boost velocity, and apoapsis, although they are clearly calculable. The artificial switch from {spacecraft-Kerbin} to {space-craft-Mun} gravity and back though is abrupt, and very likely makes the parameter space for 'successful free return' more complicated.

An experimental approach of throwing spacecraft at the problem would work almost as well. At least the parameters do not include spacecraft size or mass.

Perhaps to start the ball rolling and help PD with the Wiki entry, my parameters once again were:

Circular orbit at 150 km altitude prograde, boost prograde at Munrise until apokerb = 15 million km -> successful free return (final periapsis less than Kerbin\'s radius, so not shown).

[Rascal Nag]

I think that the longer you wait to burn to the Mun, while still staying in the window where it is feasible, the higher the periapsis is when coming back to Kerbin. My line of thinking is simply that waiting longer allows you to go further out from the Mun, causing it to slow you down a bit less relative to Kerbin, therefore raising the periapsis. I\'ll have to test this later.

[closette]

Good point Rascal - and needs thorough testing!

When we get persistence in v0.14 it will be easier to start from Kerbin orbit each time as opposed to launching from scratch. (I\'ll be annoyed at having to rebuild all my spacecraft though).

I just tried:

Prograde circular orbit at 100km -> boost at Munrise to 15 million km apoapsis -> failure to be captured by the Mun, so I\'m thinking that 15 million km, although a nice round number, may be at the high end for which this is possible.

Also, orbiting below 150 km takes too long in the game, so I\'ll be conducting all my tests at just above 150km starting orbit, so I can time-warp a bit faster.