Flying to/from Lagrange points

[Cale]

Hi there,

Just wondering if Lagrange points can be targeted within the current version of Orbiter and if there are any MFD's (IMFD in particular) that are capable of doing so?

Thanks,

Cale

 

[agentgonzo]

I don't think that there are. One way to get there would be to put a ship there using the scenario editor or modifying the .scn file and then use normal MFDs (TransX, IMFD I presume would work too) to intercept it.

 

[Urwumpe]

Solving the real accurate position of a la-grange point is not an easy task, even though the rough targeting is easy. Also, more important, you even want to orbit this sneaky beast, which means you want to orbit something you cannot see.

 

[pattersoncr]

once again:

There was a topic on this at M6....

I have a technique for getting to an L4 point using IMFD:

Use the offset targeting function,
Set "Operation Modes:" under target intercept to "vel. frame"
Set "Lon" to -30deg
Set "Rad" equal to the moon's current orbital radius (from orbit MFD)
a similar procedure can be used for L5

This will get you pointed in the right direction, but as Urwumpe alluded to, figuring out when you're there is a bit tricky.

 

[Cale]

Ok, thanks for your help..that's what I figured...just trying to put together some scenarios using Simcosmos' Direct add-on. Based on their fall '07 presentation of Direct v 2.0, they're proposing to use EML1-EML2 points to stage rendezvous and/or refuelling...would be cool to duplicate this in Orbiter.

Cheers,

Cale

 

[n0mad23]

Here's the position for L5:

RPOS -148042329724.36 -26068996.18 11849461036.78
RVEL -2183.996 -56.285 -29104.261

 

[Urwumpe]

Here's the position for L5:

RPOS -148042329724.36 -26068996.18 11849461036.78
RVEL -2183.996 -56.285 -29104.261

At which time?

 

[n0mad23]

At which time?

I should finish my coffee before posting:

  Date MJD 52349.1257227511

  RPOS -148042329724.36 -26068996.18 11849461036.78
  RVEL -2183.996 -56.285 -29104.261

 

[Travis Reed]

once again:

There was a topic on this at M6....

I have a technique for getting to an L4 point using IMFD:

Use the offset targeting function,
Set "Operation Modes:" under target intercept to "vel. frame"
Set "Lon" to -30deg
Set "Rad" equal to the moon's current orbital radius (from orbit MFD)
a similar procedure can be used for L5

This will get you pointed in the right direction, but as Urwumpe alluded to, figuring out when you're there is a bit tricky.

I used this method to reach the Sun - Earth L4. I verified it with the CJP's Lagrange MFD. I did find a problem in reducing my velocity to 0, though. I'd hoped to use IMFD's Velocity Match to null this, however it only nulled the velocity on one axis. And without an indication as to which way to burn, there was no way to null them all. I rather miss the older IMFD Orbit Match...that probably would have done what I needed.

 

[HopDavid]

Solving the real accurate position of a la-grange point is not an easy task, even though the rough targeting is easy. Also, more important, you even want to orbit this sneaky beast, which means you want to orbit something you cannot see.

I recently found something by Szebehely published in 1967: "Theory of Orbits - The Restricted 3 Body Problem". Pages 133 to 138

Szehebely gives a power series expansion in terms of v (v = (µ/(3*(1-µ)^(1/3)) to the 6th power of v. As µ gets smaller, the series converges more quickly. In this case µ is the mass fraction of the orbiting body. µ = M2/(M1+M2) where M2 is mass orbiting body and M1 mass central body.

Distance of L2 from orbiting body: v(1 + v/3 - v^2/9 - 31v^3/81 - 119v^4/243 - v^5/9) + O(v^7)

Distance of L1 from orbiting body: v(1 - v/3 - v^2/9 - 23v^3/81 + 151v^4/243 - v^5/9) + O(v^7)

Edit: I typed big equations incorrectly on the 1st try.

Note: what I call L1 is the region between M1 and M2. I call L2 the region on the far side of M2. This is the convention I'm accustomed to. But those checking out Szebehely's book will find he names them vice versa. Szebehely does these expansions from a 5th order polynomial. His method remains opaque to me, else I would continue the expansion to the 7th power, etc.