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### Re: Gravity Art Megathread

Posted: Thu Feb 04, 2016 12:09 pm
Stargate38 wrote:It seems to be in a perfect 7:5 resonance with the secondary star.
It's taking me way to long to parse this. (Assuming this isn't too necro of a thread that you've forgotten all about it... )

I think what 7:5 resonance means is that one object goes around the 'central' star 5 times, in the same time it takes the other to go around 7 times. But for some reason that's not what I'm seeing? Am I confused? (Answer, yes, yes, I am)

I just counted (non-ptolemy and non-lagrangian) as each went around the star, and I didn't see the 7:5 resonance. The blue one went around 7 times, and the star went around... 3-ish times? No dice there.

Then I watched it in Lagrangian, and got this...
Screen Shot 2016-02-04 at 10.49.35 AM.png (55.13 KiB) Viewed 19433 times
Woo - seven loops before the blue orbit perfectly lines up!

So I went to Ptolemy and watched...
Screen Shot 2016-02-04 at 10.50.39 AM.png (65.81 KiB) Viewed 19433 times
Woo - five loops before the blue orbit matches up!

Five and seven. That's the point at which I started to doubt reality, and threw my cards in with numerologists. Is this a coincidence? Is this why I *should* be seeing 7:5 resonance? Help!

### Re: Gravity Art Megathread

Posted: Fri Feb 05, 2016 3:29 pm
What I meant was as follows:

The resonance can be calculated from the number of loops the object makes in Lagrangian mode. You put the total number of pericenter passes (cycles) before the orbit lines up again on the bottom. The top can be calculated from how many loops it skips with each pass:

(Total):(Total-Skipped-1)=7:(7-1-1)=7:5

In this case, it skips every other loop as it orbits, so the bottom number is 7-1-1=5. Look at the orbit of Venus in Earth's Lagrangian mode (assuming you have a simulation of those 2 planets). Venus appears to be in an 8:5 resonance, but it's not. Its orbit skips every 3 "points", but never lines up with itself, so it's not exactly in an 8:5 resonance.

The pentagram/flower orbit in Ptolemy mode is just a coincidence of said gravity law. That has nothing to do with the resonance.

### Re: Gravity Art Megathread

Posted: Tue Feb 16, 2016 1:28 am
I was curious to see if planets could have moons assuming a reciprocal law considering that the moon would be more effected by the gravity of the star then the planet it orbits. I found that the answer is actually yes.
Screen Shot 2016-02-16 at 12.14.01 AM.png (303.85 KiB) Viewed 18707 times
This is a planet orbiting around a star with its moon using F=r as the law for Gravity.

### Re: Gravity Art Megathread

Posted: Tue May 31, 2016 12:47 pm
Kind of looks like an earthworm (Select yellow star, click Lagrange, click blue star):

Code: Select all

``Gravity Fun at TestTubeGames.com: [ForceGr: abs(1000*((r^3-1)*abs(ln(r))+(1+r^3)*ln(r)))/(2*r^1.99*(1+1000*abs(ln(r)))),Zoom: 1], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 4,m: 1600,c: 1], [x0: 400,y0: 0,vx: 0,vy: -22.627416997969520780827019587355,t0: 0,who: 4,m: 1600,c: 3], [x0: -200,y0: 0,vx: 0,vy: 45.25483399593904156165403917471,t0: 0,who: 4,m: 1600,c: 2], [x0: 100,y0: 0,vx: 0,vy: -5.656,t0: 0,who: 3,m: 0,c: 2]``
Without the asteroid:

Code: Select all

``Gravity Fun at TestTubeGames.com: [ForceGr: abs(1000*((r^3-1)*abs(ln(r))+(1+r^3)*ln(r)))/(2*r^1.99*(1+1000*abs(ln(r)))),Zoom: 1], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 4,m: 1600,c: 1], [x0: 400,y0: 0,vx: 0,vy: -22.627416997969520780827019587355,t0: 0,who: 4,m: 1600,c: 3], [x0: -200,y0: 0,vx: 0,vy: 45.25483399593904156165403917471,t0: 0,who: 4,m: 1600,c: 2]``
Worm.png (225.65 KiB) Viewed 13320 times

### Re: Gravity Art Megathread

Posted: Wed Aug 17, 2016 12:15 pm
Stargate38 wrote:Kind of looks like an earthworm (Select yellow star, click Lagrange, click blue star):
Love it -- and for whatever reason it looked a bit different when I ran it. (I might have lagrange-ed the wrong pair? Or ran it at x2 speed, that might have affected it?) In any case, still really striking, thought I'd share. Looks like the caterpillar (aka the 'worm') turned into a butterfly
screenshot_17 08 16 12 09 18.png (186.03 KiB) Viewed 12630 times
Also, I'm glad I took physics courses in *our* world instead of this one. You'd fill up half the blackboard just writing the equation of gravity.
Spoiler
Show
abs(1000*((r^3-1)*abs(ln(r))+(1+r^3)*ln(r)))/(2*r^1.99*(1+1000*abs(ln(r))))
(And that's presumably just the Newtonian approximation! )

### Re: Gravity Art Megathread

Posted: Wed Jan 25, 2017 4:06 pm
Gravity: r^100

Code: Select all

``````_settings(gravity: r^(100));
_type1(m: 0, col: 1, lcol: 3, pic: 2);
_add(m: 1000, col: 2, lcol: 3, pic: 0, noGrav, x: 0.83, y: 2.5, t: 0);
_add(type: 1, x: 71.67, y: 25, vx: -6.6, vy: 10.9, a: 185, t: 74.8);
_add(m: 0, col: 1, lcol: 0, pic: 0, x: 51.67, y: 15.83, vx: -0.367994, vy: 1.201153, t: 106.8);
_add(type: 1, x: 20.83, y: 100.83, vx: -21.93, vy: 4.3, a: 36, t: 113.6);
_add(type: 1, x: -15.83, y: 105.83, vx: -23.4, vy: 0.67, a: 154, t: 146.4);
``````

### Re: Gravity Art Megathread

Posted: Mon Mar 06, 2017 5:44 pm
Oooh, neat, thanks for sharing! I posted the pretty result on my twitter feed