Approximated Lagrange Points, keeping 2-body physics

[Heikman]

Hi there,

so as we know the problem with having real Lagrange Points is that they occur only in a (reduced) 3-body system, which unfortunatly is too complex to have a complete analytical solution, meaning we cannot predict a trajectory. This is why KSP approximates physics using a 2-body problem within a Sphere-Of-Influence (SOI), so that objects can be put on elliptical "rails".

Idea:

Why not implement Lagrange Points with their own SOI? Outside of it, ordinary 2-body physics reins, but inside there is an approximated harmonic potential also known as harmonic oszillator potential. This is the staight forward way to handle complex potentials in physics. Of course there is an error but in a reasonable small SOI it is neglectable. The advantage is that it has analytical solutions/trajactories in each dimension, e.g. oszillation in the attractive case: x(t) = x₀ * sin(w t). So we have rails again!

How could this look like in KSP?

Consider for example L1: Then between Kerbin and Mun there is a small region, where forces are slighty different. Two cases:

Case 1:

You pass the SOI of L1 with "normal" speed, like when you are going to land on Mun. You will not notice any difference.

Case 2:

You reach L1 at almost zero speed. Then the trajectory within SOI has an oszillating pattern. It can become quite long so KSP may not display it entirely. And it is always leaving SOI, because all Lagrange Points are unstable, but with tiny burns from time to time you can park the vessel there.

[Red Iron Crown]

Hi Heikman, and welcome to the forums!

This is actually a fairly common suggestion, so much so that it is on our What Not To Suggest list. It's been discussed several times, and I believe the consensus among the physicist types is that using SoIs to emulate lagrange points creates more problems than it solves (I don't have the physics background to give more detail, sorry). In the meantime, there is a mod for n-body physics that handles lagrange points nicely if you'd like to try it.