Emulated Lagrange Points

[Bedwyr]

I'd like to place some relay satellites in-line with points L4* and L5* in front of and behind the Mun. Assuming the usual 60 degree difference, how should I calculate the angle required from my parking orbit around Kerbin (usually 150km) to burn for an apoapse and reach either point at the correct angle?

Thanks!

 

 

*Emulated. Yes, I know; don't remind me. Single body physics.

[joshudson]

I recommend the following stupid approach: put it in about a co-munar orbit, quit, edit the save file to make the orbit exact. Due to single body physics it will stay there.

[Bedwyr]

Heh. That works.

I did figure in-game that I could create a transfer direct to the mun, get a periapse approach, and then offset to an appropriate number of degrees by eyeballing. Not perfect, but then real side-L points would be a bit outside the body's path at 60 degrees (I think it's 60 degrees for a two body L4/L5 right?).

[MarvinKitFox]

On 2016/10/24 at 1:06 AM, Bedwyr said:

Heh. That works.

I did figure in-game that I could create a transfer direct to the mun, get a periapse approach, and then offset to an appropriate number of degrees by eyeballing. Not perfect, but then real side-L points would be a bit outside the body's path at 60 degrees (I think it's 60 degrees for a two body L4/L5 right?).

The L4 and L5 points are trivial to locate:

They are coplanar with the intended orbit, and equidistant from both of the other objects.

Thus, for a perfectly equatorial circular orbit like Mun, simply place your satellite at the exact same orbit as the Mun, and exactly 60 degrees ahead(L4) or behind(L5)

 

While you are at it, you might as well also plonk in a satellite at L3, which is exactly 180 degrees from Mun

.

 

 

As for how to get there...

Put your sat in a *very* slightly lower orbit, let it catch up to the position you want.

When you are half-an-orbit from aligning with the perfect position, apply the needed prograde burn to raise apogee to the exact needed level.

When at apogee, burn prograde again to perfectly circularize your orbit.

(Mun make it easy, as it has a perfectly circular AND equatorial orbit. cheating, really!)