Challenge: Lagrange Points

[A Random Player]

I say we just give up and do this in r^1. That should prove easier.

r^1 isn't the most stable of rules either...

[robly18]

Guys, I may have a lead!
I'm assuming you've been using stars for the most massive body. If not, feel free to disregard this.

If so, use a planet instead. We (as in, I) haven't been taking into account the movement, or lack thereof, of the star.

[A Random Player]

Guys, I may have a lead!
I'm assuming you've been using stars for the most massive body. If not, feel free to disregard this.

If so, use a planet instead. We (as in, I) haven't been taking into account the movement, or lack thereof, of the star.

We've all been using stars. The problem is it's not very easy to do the calculations with a planet instead.

[robly18]

We could replace the star with a planet of the same mass...

[A Random Player]

We could replace the star with a planet of the same mass...

However, many formulas aren't the same with two bodies in motion, like the orbital period, for instance.

Edit: I actually think this is a bug with the simulator itself. I'll go post it as a bug report (or at least a question).
Edit2: For the benefit of people in the future, this is that bug report.

[testtubegames]

Random, that was the trick. Phew, it feels great to have found that (very major) bug. A complex issue, but basically, planets weren't working with the precision we expected (and they had only 1/6 the pull to boot). So the formulas weren't working for us... and even formulas aside, the precision was crud.

But it is fixed. And the Lagrange point code from way early on in this thread now works. To restate what Robly had posted:

Code: Select all

Gravity Fun at TestTubeGames.com: [ForceG: -2,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 100,y0: 0,vx: 0,vy: -3.1622776601683795,t0: 0,who: 2,m: 100], [x0: 135.23367415675359103,y0: 0,vx: 0,vy: -4.2764642668839177,t0: 0,who: 3,m: 100]

This now makes a functional Lagrange Point. Note, the (un)stability issue still comes into play... but now it breaks down after about 3 orbits instead of immediately.

Thank you all for keeping on this and trying to figure out what the problem was. These forums are certainly earning their keep here on the site!

[A Random Player]

Woah, that was major. Glad it's fixed though.
And the inevitable: Here's L1-L3.

Code: Select all

Gravity Fun at TestTubeGames.com: [ForceG: -2,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 100,y0: 0,vx: 0,vy: -3.1622776601683795,t0: 0,who: 2,m: 100], [x0: 135.23367415675359103,y0: 0,vx: 0,vy: -4.2764642668839177,t0: 0,who: 3,m: 100], [x0: 71.565667180446301657,y0: 0,vx: 0,vy: -2.2631051055977070779613,t0: 0,who: 3,m: 100], [x0: -100.83329985830060355,y0: 0,vx: 0,vy: 3.18862891542963407822029,t0: 0,who: 3,m: 100]

L2 fails first, then L1, and L3 hasn't failed yet.

I'm not that sure how to calculate L4/5 yet.