Lagrange Points in KSP

[Fractal_UK]

No... Tiny invisible planets are not the same thing as Lagrange points... You don't orbit Lagrange points either. You need to continuously correct your orbit to stay there, which is something you can't really do unless you want to spend all your time in that mission and accomplish nothing else.

That depends on the Lagrange point. L1, L2 and L3 are not stable and any small perturbation toward one body or the other will cause you to drift out of position increasingly rapidly as your distance increases from the meta-stable point. L4 and L5 are completely stable and have some kind of effective gravitational potential, which would behave similarly to a tiny invisible planet. The L4 and L5 points are also known as the trojan points. This stability explains why there exists an accumulation of sizeable asteroids at Sun-Jupiter L4 and L5 - the Greek and Trojan camps of asteroids respectively (though it isn't just Jupiter that has these trojan asteroids but Jupiter has the largest accumulation due its enormous mass).

[iamaphazael]

ok. first. you often do orbit Lagrange points. 2. there is no station keeping anywhere in this game, so this would be no different, we just assume stable and that as close enough. 3. dont need n-body physics, just 3 body restricted... and often not even that.

1. No. You don't. Neither a "kidney bean orbit" nor a "horseshoe orbit" is the same as being in a circular orbit around a fixed, invisible point. The SOI around the lagrange point is a bad, bad approximation. Not to mention all the stupidity that would ensue from passing through that soi.

3. The 3 body restricted problem still does not have a closed form solution, which means that timewarp is either not possible, or timewarp is possible, but a ship's motion is affected by what warp level you are at, neither of which is acceptable

[Mephane]

I'd say even if a bad approximation, it is still better than having nothing at all.

[MR4Y]

And also this is on the "What not to suggest list"

[A Fat Pokemon]

And also this is on the "What not to suggest list"

It's not a suggestion, the OP was trying to find out how to calculate the lagrange points, but just didn't know that they didn't exist in KSP

[jheriko]

Is it not possible to add Langrange points without true multi-body physics? Like a mere dummy object, invisible with no hitbox, non-targettable, but with its own gravity, in the specific position, and then handle this object otherwise just like another moon or planet? You'd have stuff like a "L5 SOI" and you could orbit this dummy object, thus place probes or stations in this area, without invoking the actual physics.

As others have suggested this could work, but not by simply placing an invisible planet. What you want I think would be something to cancel out gravity within an SOI.

The real problem is time warp. There is nothing saying you can't have n-body physics in KSP, but you wouldnt be able to warp time since there is no analytical way to predict where you will be. It simply breaks the rails system.

Because you need to calculate 100000 steps per frame? With clever use of a rails system this becomes a non-issue, you have a wide enough time-step with interpolation so that the calculations fit within frame time.

3. The 3 body restricted problem still does not have a closed form solution, which means that timewarp is either not possible, or timewarp is possible, but a ship's motion is affected by what warp level you are at, neither of which is acceptable

You can solve this problem by calculating splines, which do have a closed form, and maintaining them during updates.

Why is everyone so inclined to come up with (poor) reasons why this impossible? I still don't want it in the game, but seeing a lack of knowledge accompanying such strong statements is... frustrating.

[tntristan12]

I'd say even if a bad approximation, it is still better than having nothing at all.

No... It's a terrible approximation and it is far better that KSP use patched comics which is a real world approximation - not some half baked nuttery dreamt up by people who don't understand Lagrange points. For all the times I have seen this suggestion I have never once seen any evidence that it would work or provide even the briefest modicum of resemblance to real life physics.

Why are we still having this conversation? It is on the do not suggest list, and ideas about implementing Lagrange points are a dime a dozen on these forums.

[Paul Kingtiger]

Why are we still having this conversation? It is on the do not suggest list, and ideas about implementing Lagrange points are a dime a dozen on these forums.

Because this is the general discussion forum not the suggestions forum. If you don't want to have the conversation any more by all means don't.

Anyway, L3, L4 and L5 you can already amoximate in game by parking in the same orbit as the body with the 60 degree phase angle. Likewise it would currently be possible for the devs to put some asteroids at the approximate L4 / L5 points for Jool in an analogue of the Trojan asteroids. They would be on rails so would stay in position.

That just leaves L1 and L2 which is a much smaller pay-off for the effort to implement and looking at it that way, may not be worth the effort.

[asmi]

To those who offering "phantom" planet to simulate Lagrange points - do you actually know how they work? L4/5 actually repells body out of that point (so it would be "anti-gravity"), and L1-L3 repells them in two directions and attract in two others. So there is only one way to get them - is to convince Squad to implement proper n-body physics (or it might be possible to implement in a mod?). People suggesting that it would "melt your computer" simply don't know what they are talking about. Orbiter has it implemented for years and it works fine even on 7-years old computer (and yes, it DOES have time warp). There is no question of whether it's possible - it's just requires some effort to implement. There are tons of papers on this matter.

Edited June 10, 2013 by asmi

[AceMgy]

Is it not possible to add Langrange points without true multi-body physics? Like a mere dummy object, invisible with no hitbox, non-targettable, but with its own gravity, in the specific position, and then handle this object otherwise just like another moon or planet? You'd have stuff like a "L5 SOI" and you could orbit this dummy object, thus place probes or stations in this area, without invoking the actual physics.

What you seem to want to do is find the effective potential of the Lagrange point, and have it project it's own "gravity" in a rotating reference frame, yes? The problem with this is that when you do the math to find this effective potential, it is certainly not gravity, not even close. While you can calculate this potential and get an accurate force out of it, there are several problems with this approach in patched conics:

1. The force on a body near a Lagrange point actually increases with distance from that body (at least until the centrifugal term cancels it out). So in that way it is totally unlike gravity, which decreases in strength with distance. This isn't totally unworkable, as it does eventually fall off with distance, so at first approximation one could define a hill sphere around the Lagrange point and work it in patched conics with a unique force. However, this hill sphere would be particularly large, and would intersect with other SoIs in the system (if you want to do it accurately enough), instead of being the nice little dummy planet you imagined.

2. Such a "hill sphere" used to approximate this would not be spherically symmetric, as the effective potential is not the same for all three axes. This makes the resulting "hill sphere" you'd have to make rather odd-shaped. While this isn't insurmountable by any means, it's more difficulty for the developers to code and debug. You'd have to go to all that effort if you want predictable orbits and preserve the on-rails system KSP has for orbits.

So you can see why they've cut that from development, as it doesn't have enough payoff for all the work involved. You're best bet would be to wait for an adventurous modder to spend a lot of time modding the physics for this. Plus the only two stable Lagrange points, L4 and L5, are stable in the current version. The points you're probably interested in, L1 - L3, would be unstable, and would require some kind of autopilot or fudging to make an object stay there when your focus is elsewhere.

Edit: I just remembered that "orbits" about Lagrange points are not periodic in nature. Look at the wikipedia article for Lissajous Orbits to see what I mean. I thought that using a patched conics system for Lagrange points would get around this but I was wrong. These non-repeating orbits are a consequence of the asymmetric potential. So you can either give up the on-rails simulation KSP has and have accurate Lagrange points, or have inaccurate Lagrange points and keep the on-rails simulation. Neither option is very satisfying.

Edited June 10, 2013 by AceMgy

[Space4Rockets]

I appreciate all the input from you guys. I wouldn't mind orbiting in the L4 or L5 points, I would need to find out where they would be. I wouldn't mind being out there without "orbiting" as long as i would be able to keep up with kerbin. I guess what im wanting to do is have a space station in interplanetary space as a refueling port for ship that couldn't make it all the way out crazy far. I just want some help calculating a point that would keep up with kerbin but out of all the SOI for the planets. Maybe its not possible, but anyone who could help me accomplish this would be my hero.

[Frederf]

Getting back on track about calculating LPs: the various types depend on the orbits and masses of the two bodies. LPs are where the effective force on the body is zero which is where the first derivative (i.e. gradient) of the potential is zero. The potential is a sum of gravity which is real and centrifugal effects which are because the system is in an accelerated (rotating) reference frame.

L1 is perhaps easiest. Objects orbit massive bodies faster than less massive bodies. Having a mass partially canceling the primary orbiting mass serves the same purpose as having the primary mass reduced. Far from the "lifter mass" the effect is less. Near to the "lifter mass" the effect is greater. For a given primary and lifter mass (really, just their ratio) there is only one spot a certain distance between them where the slowing effect caused by the lifter mass causes a test object to orbit at the same rate as the lifter mass. This is the L1 point. It turns out to be fractionally the cube root of one third times the mass ratio to first order approximation. The derivation is a little annoying but not too difficult. You start with an arbitrary point between the two bodies and write an expression for it's orbital angular speed as a function of it's position between the two masses and then constrain that angular speed to be the same as the second body.

L2 is just like L1 but instead of having to orbit slower due to being closer, it has to orbit faster because it is farther. The alignment of the two bodies on one side of the L2 point causes an increased mass and speeds up the orbit sufficiently so it keeps pace with the alignment of the two bodies.

L3 is very similar to L2 being more distant than normal being sped up by the fact that both bodies are on the same side of L3 but simply reversed in order which one is closer.

L4 and L5 are a pair. L4/5 can be seen as three objects having circular orbits around a common center of mass. Being equidistant from the other two masses, L4/5 orbits the CoM due to the bias of the differing masses at equal distances. Orbiting the CoM is what ensures invariance and a stable orbit. The proof of the triangle of the L4/5 and the two bodies being an equilateral triangle is beyond me to describe simply.

[CaptainBullet]

I appreciate all the input from you guys. I wouldn't mind orbiting in the L4 or L5 points, I would need to find out where they would be. I wouldn't mind being out there without "orbiting" as long as i would be able to keep up with kerbin. I guess what im wanting to do is have a space station in interplanetary space as a refueling port for ship that couldn't make it all the way out crazy far. I just want some help calculating a point that would keep up with kerbin but out of all the SOI for the planets. Maybe its not possible, but anyone who could help me accomplish this would be my hero.

In KSP you just have to match Kerbins Orbit outside kerbin's SOI. The phaseangle not important, since Kerbin's gravity is ignored once you left it's SOI. So for your interplanetary gasstation I'd just leave Kerbin along its orbit (prograde if you want to be behind kerbin, retrograde if you want to end up ahead) and do one (or several) orbit(s) around Kerbol, until you touch Kerbins orbit at the desired phaseangle. Then circularise your orbit until you get exactly 106d 12h 32m 24.6s of orbital period (or 53d 6h 16m 12.3s difference between time to Periapsis and time to Apoapsis, if you don't use a mod that calculates the period). There you go. Interplanetary spacestation with a fixed distance to Kerbin. No calculations needed.

If you want to get to a place where a Lagrange point would be, you need a phaseangle of +60° or -60° (which would be more or less L4 and L5). You can achieve that by setting your initial orbit to a period of (Kerbins Period)*5/6 or (Kerbins Period)*7/6.

Afaik, there is no way to set up an orbit that would resemble L1, L2 or L3, due to the largely discussed 2-body physics of KSP. You can sort of do as if you get to L3, but not really, since Kerbin's L3 is located slightly above Kerbin's Orbit, so in KSP kerbin will catch up slowly. But you can of course match Kerbin's orbin with a phaseangle of 180° and pretend its L3.

Btw. just to add to some of the comments above: just read the Wikipedia article about Lagrange points, if you don't really know how they work. For someone with limited knoledge about math and astrophysics (like me), it might be a bit complicated to really understand. But you get the general idea. And it prevents you from posting bull****

have fun out there

[CaptainBullet]

I guess what im wanting to do is have a space station in interplanetary space as a refueling port for ship that couldn't make it all the way out crazy far.

Oh, and I forgot to mention: I wouldn't recommend to refuel in Interplanetary space. getting an encounter with an interplanetary station, docking, refueling and accelerating back to your desired trajectory... all in iterplanetary space requires insane amounts of delta-V. You are usually more efficient, if you refuel in planetary orbit and use good old Oberth to kick yourself to the right trajectory.

If you want to do it, because you can: Go ahead, don't let me spoil your fun. But if you have the Delta-V to rendezvous an interplanetary spacestation, in most cases you should have well enough to get out to "crazy far" as well.

[Ravenchant]

Stuff

Epic necro is epic. How did you even find the thread?

But yeah, aside from the "messy" workaround of orbiting at the altitude of a moon outside of its SOI, Lagrange points aren't really doable.

[Sof]

blah blah blah

Hmm lets reply to a thread post from exactly 6 months ago. I'm sure that my input is completely relevant and I'm sure Space4Rockets will read this and/or care about my information.

~CaptainBullet logic

[vexx32]

While I appreciate that you most certainly did have something to add, this discussion has been long-dead. A search for lagrange points within the forums, or using Google to search the forums, will turn up several of the last incredibly long discussion threads. Seeing as this one here is in fact in the wrong section (stuff like this belongs in the Development section), and also lacking some of the finer points as to why this is not doable, I'm going to lock this. You can, if you wish, start up a discussion thread in the Development section -- but make sure you're not just re-hashing one of the many discussions we've already had, else there's really no point, is there?

As such, locked.