Interesting gravity laws
Re: Interesting gravity laws
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?
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Re: Interesting gravity laws
exfret wrote:Wait, so how would you get a triangle?ARP wrote:(That means only a line segment and a triangle. If the sim extends into 3D space, it also includes a tetrahedron.)
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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]
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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]
Always check your units or you will have no money!
Always check your units or you will have no money!
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Re: Interesting gravity laws
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.
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.
Re: Interesting gravity laws
To ARP's post: Oh, that's what you mean by triangle. What about square?
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:
Just add a bunch of dust and it looks pretty.
Another Glitch: I cropped off-screen objects and it cropped all the objects.
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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]
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]
Another Glitch: I cropped off-screen objects and it cropped all the objects.
Nobody ever notices my signature. ):
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Re: Interesting gravity laws
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.exfret wrote:To ARP's post: Oh, that's what you mean by triangle. What about square?
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.Code: Select all
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]
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
Always check your units or you will have no money!
Re: Interesting gravity laws
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.
Nobody ever notices my signature. ):
Re: Interesting gravity laws
Ah my bad... I'll fix it. (exfret is gravity master)
I usually put descriptions up based on what I experienced with the laws.
I usually put descriptions up based on what I experienced with the laws.
This message has been brought to you by wtg62, duh!
Re: Interesting gravity laws
Heh, you get ellipses mostly because 1/r^2 is actually r^-2!AlternateGravity wrote:*lots of stuff about inverse and reciprocal laws*
Anything you substitute x for here: 1/r^x
Will become: r^-x
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Re: Interesting gravity laws
cos(r) orbits:[*]cos(r) - No orbits... ever
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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]
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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]
Only positive constants. They change the scale.[*]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)
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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]
Asymptotes are at π/2 + πn, n ∈ ℤ.[*]sec(r) - Similar to tan(r). Can be written as 1/cos(r). Goes crazy when asymptotes are reached (Multiples of π, I believe).
Just different stable lengths. All shapes from r-1 work here, with some space-time scaling (I made that phrase up)[*]r-1.1 - Well... we're getting some different shapes with different numbers apparently.
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/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 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
Always check your units or you will have no money!
Re: Interesting gravity laws
Ah, thanks for pointing that out.
This message has been brought to you by wtg62, duh!