Request Tutorial for Lagrangian points

[ceauke]

Hi guys

I would like to fly my deltaglider to all of the L-points. I assume some are easier than others. But I have no idea how to aim for it. AFAICT there are no targets for setting these destinations.

(I tried to search the forums for it, but I couldnt' find a tutorial. I saw that one of the start scenarios start at the L4 point but it doesn't help me much.)

Can anyone tell me how to do this? Also, how do you prove/know you're there? Surely not by fast forwarding x100 and noticing that everything else is still in place.

The easiest one sounds like L1 between earth and the moon.

Thanks!

 

[jedidia]

It's a tough one, there are no solutions for orbiter that can pull that off currently.

Your best bet might be to place a vessel as a beacon at an L-point manually and then target it with transX, but even that will be full of problems as TransX will expect the vessel to propagate normally.

 

[Ripley]

Never tried these ones, anyway:
[ame="http://orbithangar.com/searchid.php?ID=3644"]Lagrange MFD 0.7[/ame]
[ame="http://orbithangar.com/searchid.php?ID=4582"]Lagrangian points MFD v0.2[/ame]

 

[ceauke]

Thanks Jedida. Good idea to park a ship there.

I guess transx is just a plugin. But surely in orbiter, the environment will simulate the gravity correctly. Does this mean if you 'by accident' traverse the L-point that most modules will calculate incorrectly? Wouldn't the L points be a 'standard' phenomena in their gravity models?

I'm not rocket scientist so maybe I have the wrong expectation of these points. Surely if you rocket past it, your trajectory should be affected by it. And the closer you fly by, the more it's affected. So I'd imagine that all plugins must be aware of this to be acurate. Maybe I'm missing something.

---------- Post added at 03:32 PM ---------- Previous post was at 03:28 PM ----------

Great MDF's ripley. I like that second one that teleports you to the L point!

I stil have one question though. How do you know you're at the point? Is the only way to FF? Or can I see somehwere on one of the 50 attributes of th orbit MDF that I'm at the L-point?

 

[jedidia]

Does this mean if you 'by accident' traverse the L-point that most modules will calculate incorrectly? Wouldn't the L points be a 'standard' phenomena in their gravity models?

That's pretty much what would happen, yes. The problem is that a Lagrange point is the result of an n-body situation, and the n-body problem is not solvable analytically. In essence that means that you can simulate a lagrange point with a very simple gravity simulator, but you can't predict its behaviour with standard propagation algorithms, as they can only calculate with two bodies (your ship and the core body, usually). Simulating gravity and propagating orbits mathematically are two entirely different pair of shoes, I'm afraid. For this reason, an analytical tool that predicts the behaviour of lagrange points has to be written specifically for this problem.

Or can I see somehwere on one of the 50 attributes of th orbit MDF that I'm at the L-point?

No, because an L-point isn't an orbital attribute. You can tell that you're there when your ship behaves like it's there.

 

[Tommy]

You might find this add-on useful for targeting L-Points:
http://orbithangar.com/search_quick.php?text=lighthouse&submit.x=0&submit.y=0

 

[ceauke]

Jedidia, you mention fascinating things. I'm really amused by the fact that the way the ship behaves is the way of knowing you're there. Is this just in Orbiter or in real life??

Still, I think there's something wrong with my perception of these L-points.
1. Maybe they are far weaker than I think. Maybe being in L1 is close to orbiting the sun/planet anyway. I'm wondering what will happen if your ship has significant mass? can you theoretically put another earth at the sun/earth L1 and it will still work on paper? For some reason I feel like SURELY it won't but then again, it doesn't matter what the mass is of the object, the effect of gravity yields the same accelleration.

2. If it's difficult to put a formula for it, does it mean that a space agency will run a 'gravity simulator' to see / finetune where they have to aim when traversing space with their rocket?

Btw, your mention of the n-body problem sent me to wikipedia and I found hill sphere and that seems to give me a lot of info (my next question to you was going to be why the moon is nor orbiting the sun or why the orbit around earth is not disturbed by the sun, but the hill sphere bit sorted me out ). This all has something to do with L-points.

 

[boogabooga]

An orbit in L1 IS an orbit around the major body, 'perturbed' by the presence of a minor body to have the same (more or less) effective period as the minor. When your effective period is reduced to that of the minor body, you know you're in the L point by definition. If you have the same mass as the minor body, the L point concept doesn't make sense because the two bodies will attract each other. You will alter the minor's orbit as much as it will alter yours.

Here is a scenario with (from Velcro Rockets or CVEL Titans) in Earth moon L1:

BEGIN_DESC
Probe in Earth Moon L1
END_DESC

BEGIN_ENVIRONMENT
  System Sol
  Date MJD 55975.8529655927
END_ENVIRONMENT

BEGIN_FOCUS
  Ship Probe
END_FOCUS

BEGIN_CAMERA
  TARGET Probe
  MODE Cockpit
  FOV 60.00
  BEGIN_PRESET
    Ground:Earth:30.00:Earth -84.40000 39.12000 2.00 1.58 0.14
  END_PRESET
END_CAMERA

BEGIN_HUD
  TYPE Orbit
  REF Earth
END_HUD

BEGIN_MFD Left
  TYPE Orbit
  PROJ Frame
  FRAME Ecliptic
  REF Sun
END_MFD

BEGIN_MFD Right
  TYPE OAlign
  REF Earth
  TARGET Moon
END_MFD

BEGIN_SHIPS
Probe:probe
  STATUS Orbiting Sun
  RPOS -127169737232.46 16516580.17 74927398879.28
  RVEL -14831.016 59.430 -25458.146
  AROT 179.86 30.22 152.78
  AFCMODE 7
  PRPLEVEL 0:1.000000
  NAVFREQ 0 0
END
END_SHIPS

Take a look in external view, and if you have Videnie that's even better. For a few days, notice that you'll essentially "keep pace" with the moon, orbiting the earth at the same rate. This is the Lagrane point concept. Since L1 isn't stable, after a few days probe will drift out of the L1 point and probably enter a proper orbit around earth (less often around the Moon). Notice how different the orbit is once you leave L1. You don't keep pace with the moon at all, the period is something like half of that of the moon.


BTW, it's fun to see what happens for a few years of sim time after ejection from L1, since it seems to act like a chaotic system. The moon can pick you up out of earth orbit and do all sorts of things. Sometimes you transition from earth orbit to lunar orbit and back. I've seen ejections from the earth moon system, too (occasionally you get recaptured). Sometimes, you enter into a near resonance with the moon that can last quite a while. You can even end up back in another L point for a time. Or, you can end up crashing into the moon.:lol:

 

[jedidia]

Still, I think there's something wrong with my perception of these L-points.

I think the major misconception is that you try to understand an L-point as an orbiting object. An L-point doesn't orbit, it is defined by the position of two or more sufficiently massive bodies to each other.

I.E. the moon orbits the earth, and thus creates a stable L-point between earth and moon. The L-point itself is not an object that orbits, its position is solely defined by the orbital elements of the bodies involved.

So if you hold a position at an L-point, you are no longer orbiting in the strict sense, because now your trajectory is dependant on the attributes of at least two bodies. So while you're at the L-point, your "orbital velocity" for example will be significantly different than it would have to be if you'd be orbiting earth at the same distance. This is why standard orbital propagation cannot be used to predict it (not without further calculations, anyways). It simply isn't an orbit, and its behaviour is defined by utterly different parameters than a simple orbit.

If it's difficult to put a formula for it, does it mean that a space agency will run a 'gravity simulator' to see / finetune where they have to aim when traversing space with their rocket?

Space agencies allways do that, for anything. Orbital propagation is an approximation that holds only true as long as there are no more than two bodies involved (one of them usually being you), which in reality is never the case. They give you good first estimate, but the real situation cannot be analytically calculated (n-body problem), it can only be simulated. That's why we practically always need course corrections in Orbiter: The simulated "reality" is more complex than the calculated propagation (and the physical reality is still a lot more complex than what's simulated by orbiter).