An Solution to add Lagrange Points easily to KSP2.

[Raphael Weinmann]

Hello dear all.

I apologize in advance for my not quite perfect English gramatic. I am working with an online translator from German to English. Since I am not very good in English writing.

 I have now spent a few hours with KSP2 and KSP1 and I noticed that also this time the Lagrange points are missing.
Or are not provided.
Which is a pity because then missions like deep space telescope / James Web Like and so on. Are not possible this time.
And i Think there can be an big Part of an Story to find interstellar systems with mission to reach

 That's why I thought with my rudimentary programming knowledge how these points, at least the Kerbin Lagrange Points can be simulated without changing the physics system to Kerbin only where enough i think.

 My solution: There must be added objects at the Lagrange points with the properties of very small moons without a hit box and without a visible image but with an active sphere of influencer.
Maybe big enough to simulate Shadow (Light)  problem at the second point.

These objects then move with the exact same speed around the sun as Kerbin. On the there own Orbits- Like Plantes or Moons.

This does not bring the special physics of the Lagrange Points into the play but the special function for space traveling would be possible.

About the size of the Sphere and the strength of the gravity I can´t make astatement.
But one should get points then if necessary, in the science  property tree or over the locating map indicated around them also to hit to be able.

Good wishes from Germany. I Have an lot of fun with KSP. Thanks for the second part.
Raphael Weinmann

[Guest]

You'd have to mask the singularity though, otherwise you would get some very strange effects when getting close to it!

I'm a bit in two minds about this though. On the one hand I would like Lagrangian points even at a very basic level, so I could park something there. On the other hand, this solution is really so different from how the actually behave that it might be more misleading/bad than good.

I mean, patched conics are different from n-body or even restricted 3-body physics, but they're still close enough that most of the time there isn't going to be a dramatic difference. But these fake Lagrangian points would be pretty different from the real ones. I mean, L4 and L5 kind of behave like that, but even they're pretty different not least because the "sphere of influence" isn't a sphere, it's very elongated, and L1, L2, and L3 are unstable, you have to continuously station-keep so you don't slide off them. 

[Raphael Weinmann]

Ok Periple, you mein an Fake is more worse then No one? 
the Instability of L1,L2L3 come in Real from the. Moon and other opjekts. But KSP there no mutual influence. So eye See not why there can‘t be in the Game. 
 

have you an other idear about an Fake Point without killing the Simulation? 

[kicka55]

Dude, use ChatGPT to translate stuff.

As mentioned using a fake Moon would mean you can get very close and being very close not good when it comes to Newton. Formula for acceleration

a = MG/r²

r -> 0 
=>
a -> inf

When you hit the center of that fake Moon you'd accelerate to infinity. So in order to solve this problem they had to come up with a new formula for gravity for that special case like for example. Or using two formulas. One for being far away that acts normally and one for being very close.

a1 = GM/r²
r > 10 km

a2 = GM*(1-(sin(pi*r/10km)/(pi*r/10km))^2)
r <= 10 km

Gravity would approach to 0 when near the center while being being  a = GM at the boundary condition of 10 km. The next problem is to deal with the difference between a = GM/(10km)² and a=GM when you switch from one formula to the other. I has to change unnoticed! For that you have to simply divide the whole term by 100km or 100,000m. So the final equation is

a2 = GM*(1-(sin(pi*r/10)/(pi*r/10))^2)/100
r <= 10 km
   

The gravity from 10km to 0km goes from GM/100 to 0.

The gravity from inf to 10km goes from 0 to GM/100

You can further tweak the numbers to enhance smoothness at 10km. There would be a bit of a bump right now. Until a1'(10km) = a2'(10km). Easy optimization problem.

I tried some ChatGPT but it calculates nonsense lol Bing Chat not much better. The green function is what you're looking for. Could be a simple Sinus to be honest. That's why you sketch before you think.

 

Edited March 15, 2023 by kicka55

[Guest]

1 hour ago, Raphael Weinmann said:

Ok Periple, you mein an Fake is more worse then No one? 

It depends how fake! If it's close enough to the real thing that it "feels right" then fake is very good. If it's so different from the real thing then yes I think it's worse. 

1 hour ago, Raphael Weinmann said:

the Instability of L1,L2L3 come in Real from the. Moon and other opjekts. But KSP there no mutual influence. So eye See not why there can‘t be in the Game. 

The difference is that L4 and L5 are attractors and could kind of be simulated with a sphere of influence with a masked singularity at the center, but L1, L2, and L3 aren't attractors, they're like mountain peaks or a saddle. If you drop a marble into L4 or L5, it'll stay there, rolling around in the "trough", but if you try to balance it on L1, L2, or L3, it'll roll off even if nothing perturbs it as it's not possible to get it exactly there at infinite precision. With the "masked singularity" solution, L1-L3 wouldn't behave at all like the real Lagrangian points. You'd actually have to make them repulsors, where repulsion is exactly zero at the point, increases as you fall away from it, then falls back to zero towards the edge of the "sphere of influence." 

The other thing is that the "spheres" aren't spheres at all, L4 and L5 are shaped like bananas. But maybe that's less important than the attractor/repulsor things.