Interesting gravity laws

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NealCruco
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Re: Interesting gravity laws

Post by NealCruco »

Yes, stable orbits in r^0 are extremely easy. Since f(r) is always 1, the force of gravity never changes. In fact, I can't see how unstable orbits would be possible. Maybe wtg62 wasn't being serious?
A Random Player
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Re: Interesting gravity laws

Post by A Random Player »

exfret wrote:
ARP wrote:(That means only a line segment and a triangle. If the sim extends into 3D space, it also includes a tetrahedron.)
Wait, so how would you get a triangle?

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Gravity Fun at TestTubeGames.com: [ForceGr: r-1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -100,y0: 97.5,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: 0,y0: 97.5,vx: 0,vy: 0,t0: 8.800106,who: 2,m: 1000,c: 1], [x0: -52.5,y0: 192.5,vx: 0,vy: 0,t0: 75.59774,who: 2,m: 1000,c: 1]
One with L > 0

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Gravity Fun at TestTubeGames.com: [ForceGr: r-1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -100,y0: 2.5,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: 2.5,y0: 0,vx: 0,vy: 0,t0: 9.200115,who: 2,m: 1000,c: 1], [x0: -50,y0: 95,vx: -0.6,vy: 0,t0: 28.80056,who: 2,m: 1000,c: 1]
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
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AlternateGravity
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Re: Interesting gravity laws

Post by AlternateGravity »

I tried sending in a smaller planet to try to destabilize a planet orbiting with 1/r^2.9 and the larger planet continued to move with harmonic motion even when I crashed the smaller planet into it.

I also gave one planet a pair of moons that were 1/10th it's size using 1/r and the moons were able to stay in orbit around the planet even when the planet was also moving quickly around its star.
Gravitons would be my favorite particle as their existence could prove extra dimensions.
exfret
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Re: Interesting gravity laws

Post by exfret »

To ARP's post: Oh, that's what you mean by triangle. What about square?

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Gravity Fun at TestTubeGames.com: [ForceGr: r-1.1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -95,y0: 95,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: 0,y0: 95,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: -95,y0: 0,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1]
They only wobble because they aren't in precisely the right spot, but that doesn't matter much, it's still possible, as is any equidistantly spaced series of points. Still, it's cool how r-1 creates something akin to a spring.

To AlternateGravity's post: I don't think that would be harmonic motion. I think harmonic motion must be acceleration exactly opposite to position, not position^-2.9. Still, I'd think that a planet would be easily destabilized in a gravity law like that. In 1/r, I'd think that the moons would do that possibly by being pulled in a similar manner as their planet. It would be helpful to see the codes for these though so that I could take a look.

Also, I think I found a bug: changing the value of G doesn't seem to do anything. ):

Also, here's a nice spring-like gravity law:

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Gravity Fun at TestTubeGames.com: [ForceGr: 10*tan(r-pi/2),Qual: 1,Zoom: 0.5100285,xSet: 29.1995,ySet: -19.17115], [x0: 313.1603,y0: 257.9354,vx: -0.34,vy: 1.87,t0: 0,who: 3,m: 0,c: 0], [x0: 19.05904,y0: 248.132,vx: -1.71,vy: 2.1,t0: 0,who: 2,m: 1000,c: 2], [x0: -152.5,y0: 155,vx: 0,vy: 0,t0: 0,who: 1,m: 1000,c: 1]
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A Random Player
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Re: Interesting gravity laws

Post by A Random Player »

exfret wrote:To ARP's post: Oh, that's what you mean by triangle. What about square?

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Gravity Fun at TestTubeGames.com: [ForceGr: r-1.1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -95,y0: 95,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: 0,y0: 95,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1], [x0: -95,y0: 0,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1]
They only wobble because they aren't in precisely the right spot, but that doesn't matter much, it's still possible, as is any equidistantly spaced series of points. Still, it's cool how r-1 creates something akin to a spring.
Nope, even though perfect stability is possible, the distances aren't 1 because of the diagonals. The small (edge) lengths are about 0.85355 and the large (diagonals) are about 1.20710.
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
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exfret
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Re: Interesting gravity laws

Post by exfret »

Oh I see what you were saying now. I thought you were just talking about a rule for stable systems, but you were specifically stating that it was when r=1 at all distances.
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wtg62
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Re: Interesting gravity laws

Post by wtg62 »

Ah my bad... I'll fix it. (exfret is gravity master)

I usually put descriptions up based on what I experienced with the laws.
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wtg62
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Re: Interesting gravity laws

Post by wtg62 »

AlternateGravity wrote:*lots of stuff about inverse and reciprocal laws*
Heh, you get ellipses mostly because 1/r^2 is actually r^-2!
Anything you substitute x for here: 1/r^x
Will become: r^-x
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A Random Player
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Re: Interesting gravity laws

Post by A Random Player »

[*]cos(r) - No orbits... ever
cos(r) orbits:

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Gravity Fun at TestTubeGames.com: [ForceGr: cos(r),Qual: 1,Zoom: 1,xSet: -70.96354,ySet: -18.22917], [x0: 20,y0: 102.5,vx: -1.063219,vy: 0.8860161,t0: 24.80047,who: 3,m: 0,c: 0], [x0: 30,y0: 127.5,vx: -1.767923,vy: 0.9944564,t0: 66.79586,who: 3,m: 0,c: 0], [x0: 40,y0: 145,vx: -1.988211,vy: 1.123771,t0: 85.19979,who: 3,m: 0,c: 0], [x0: 7.5,y0: 87.5,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1]
Non circular:

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Gravity Fun at TestTubeGames.com: [ForceGr: cos(r),Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 30,y0: 145,vx: -0.96,vy: 0.34,t0: 24.40046,who: 3,m: 0,c: 0], [x0: 17.5,y0: 115,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1]
[*]r^0 - Creates flower patterns. Force is always 1. Infact, you can just write this as 1 (or any other constant if you're crazy enough)
Only positive constants. They change the scale.

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Gravity Fun at TestTubeGames.com: [ForceGr: -2,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -30,y0: 32.5,vx: -1.276042,vy: 0.07812507,t0: 0,who: 3,m: 0,c: 0], [x0: -30,y0: 15,vx: 0,vy: 0,t0: 0,who: 2,m: 1000,c: 1]
[*]sec(r) - Similar to tan(r). Can be written as 1/cos(r). Goes crazy when asymptotes are reached (Multiples of π, I believe).
Asymptotes are at π/2 + πn, n ∈ ℤ.
[*]r-1.1 - Well... we're getting some different shapes with different numbers apparently.
Just different stable lengths. All shapes from r-1 work here, with some space-time scaling (I made that phrase up)
[*]1/r^x - Substitute x with any negative number you'd like, and you get unstable orbit galore. Use a positive number and you get r^-x
1/r^x where x < 0 = r^x, which is stable(ish). I think you mean r^-x, or 1/r^x & x > 0, since you've already went over r^x & x > 0.
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
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wtg62
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Re: Interesting gravity laws

Post by wtg62 »

Ah, thanks for pointing that out.
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