r^1 Orbits
r^1 Orbits
Load this code:
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 35,ySet: 23], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 300,y0: 0,vx: 0,vy: 1,t0: 0,who: 3,m: 0]
r^1 seems to give stable, non-preccessing, symmetrical orbits with the star at the center.
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 35,ySet: 23], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 300,y0: 0,vx: 0,vy: 1,t0: 0,who: 3,m: 0]
r^1 seems to give stable, non-preccessing, symmetrical orbits with the star at the center.
Last edited by 19683 on Tue Jul 09, 2013 1:01 pm, edited 1 time in total.
Binomial Theorem: ((a+b)^n)= sum k=0->k=n((n!(a^(n-k))(b^k))/(k!(n-k)!))
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- Posts: 523
- Joined: Mon Jun 03, 2013 4:54 pm
Re: r^-1 Orbits
You mean r^1? I agree, r^1 is probably one of my favorite rules/exponents (besides r^-2, of course).
Edit: After more investigation, prograde motion can also cause decay:
- It acts like springs are joining each planet/star
- This means all orbits have equal periods, if the star's mass is held constant.
- Also, all orbits are ellipses, with the star at the center of the ellipse (where in r^-2, it's at the focus). The reason is left as an exercise for the reader. (Hint: Consider the properties of springs, sine waves, circles, and ellipses)
- Any multistar orbit acts like the object orbits a single star at the stars' barycenter (though I am unsure on the relationships of the masses):
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: -2277,ySet: -242], [x0: 2180,y0: 238,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2408,y0: 178,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2324,y0: 190,vx: -1.2,vy: -1.6,t0: 0,who: 3,m: 0]
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: -2276,ySet: -242], [x0: 2142,y0: 144,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2458,y0: 60,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2368,y0: 360,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2349,y0: 182,vx: -1.35,vy: -1.35,t0: 0,who: 3,m: 0]
- Resonance! Asteroids' orbits can grow infinitely large if they are orbiting a star prograde to a planet, and their orbits stretch if they're going retrograde! (They sometimes collide with the star, and other times may reverse direction and start going prograde)
(Delete one asteroid if you want.) Nothing special happens when the asteroid crosses the planet's orbit - It doesn't matter where the planet it, the orbits will still resonate. This also comes from the properties of springs.
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: -2276,ySet: -242], [x0: 2271,y0: 239,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2286,y0: 54,vx: -5.85,vy: -0.47,t0: 0,who: 2,m: 100], [x0: 2308,y0: 242,vx: 0.09,vy: -1.17,t0: 0,who: 3,m: 0], [x0: 2187,y0: 236,vx: 0.1,vy: -2.6,t0: 0,who: 3,m: 0]
Edit: After more investigation, prograde motion can also cause decay:
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 0.86,xSet: -2176.65,ySet: -253.4], [x0: 2112.93,y0: 295.07,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2374.6,y0: 112.29,vx: -5.78,vy: -8.27,t0: 33.3,who: 2,m: 100], [x0: 1964.34,y0: 291.72,vx: -0.11,vy: 4.7,t0: 56.7,who: 3,m: 0]
$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: r^-1 Orbits
Yes, I mean r^1.A Random Player wrote:You mean r^1? I agree, r^1 is probably one of my favorite rules/exponents (besides r^-2, of course).r^1 is actually a lot simpler than r^-2.
- It acts like springs are joining each planet/star
- This means all orbits have equal periods, if the star's mass is held constant.
- Also, all orbits are ellipses, with the star at the center of the ellipse (where in r^-2, it's at the focus). The reason is left as an exercise for the reader. (Hint: Consider the properties of springs, sine waves, circles, and ellipses)
- Any multistar orbit acts like the object orbits a single star at the stars' barycenter (though I am unsure on the relationships of the masses):
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: -2277,ySet: -242], [x0: 2180,y0: 238,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2408,y0: 178,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2324,y0: 190,vx: -1.2,vy: -1.6,t0: 0,who: 3,m: 0]
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: -2276,ySet: -242], [x0: 2142,y0: 144,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2458,y0: 60,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2368,y0: 360,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2349,y0: 182,vx: -1.35,vy: -1.35,t0: 0,who: 3,m: 0]
- Resonance! Asteroids' orbits can grow infinitely large if they are orbiting a star prograde to a planet, and their orbits stretch if they're going retrograde! (They sometimes collide with the star, and other times may reverse direction and start going prograde)
(Delete one asteroid if you want.) Nothing special happens when the asteroid crosses the planet's orbit - It doesn't matter where the planet it, the orbits will still resonate. This also comes from the properties of springs.Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: -2276,ySet: -242], [x0: 2271,y0: 239,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2286,y0: 54,vx: -5.85,vy: -0.47,t0: 0,who: 2,m: 100], [x0: 2308,y0: 242,vx: 0.09,vy: -1.17,t0: 0,who: 3,m: 0], [x0: 2187,y0: 236,vx: 0.1,vy: -2.6,t0: 0,who: 3,m: 0]
Edit: After more investigation, prograde motion can also cause decay:Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 0.86,xSet: -2176.65,ySet: -253.4], [x0: 2112.93,y0: 295.07,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 2374.6,y0: 112.29,vx: -5.78,vy: -8.27,t0: 33.3,who: 2,m: 100], [x0: 1964.34,y0: 291.72,vx: -0.11,vy: 4.7,t0: 56.7,who: 3,m: 0]
Wow! Can't wait to try some of those cool things you found!
Binomial Theorem: ((a+b)^n)= sum k=0->k=n((n!(a^(n-k))(b^k))/(k!(n-k)!))
Re: r^1 Orbits
Woah, I already knew some of these, but others were unknown to me.
Also, I wonder. If r^-2 gives you orbits with one focus outside the star, r^1 with two foci, then does that mean there's a value where there are three?
Could you imagine a triangular orbit?
Also, I wonder. If r^-2 gives you orbits with one focus outside the star, r^1 with two foci, then does that mean there's a value where there are three?
Could you imagine a triangular orbit?
Convincing people that 0.9999... = 1 since 2012
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- Posts: 523
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Re: r^1 Orbits
An ellipse only has two foci. There isn't an ellipse with more than 2. Otherwise, it's not an ellipse...robly18 wrote:Woah, I already knew some of these, but others were unknown to me.
Also, I wonder. If r^-2 gives you orbits with one focus outside the star, r^1 with two foci, then does that mean there's a value where there are three?
Could you imagine a triangular orbit?
$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: r^1 Orbits
Try this:
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -11,y0: 9,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 142,y0: 8,vx: -0.03,vy: -4.84,t0: 0,who: 2,m: 100], [x0: 267,y0: 9,vx: 0,vy: -8.79,t0: 0,who: 2,m: 100], [x0: -129,y0: 7,vx: -0.06,vy: 3.73,t0: 0,who: 2,m: 100], [x0: -272,y0: 6,vx: -0.09,vy: 8.25,t0: 0,who: 2,m: 100], [x0: 63,y0: 8,vx: -0.03,vy: -2.34,t0: 0,who: 3,m: 0], [x0: 203,y0: 11,vx: 0.06,vy: -6.77,t0: 0,who: 3,m: 0], [x0: 341,y0: 11,vx: 0.06,vy: -11.13,t0: 0,who: 3,m: 0], [x0: -73,y0: 10,vx: 0.03,vy: 1.96,t0: 0,who: 3,m: 0], [x0: -202,y0: 7,vx: -0.06,vy: 6.04,t0: 0,who: 3,m: 0], [x0: -345,y0: 9,vx: 0,vy: 10.56,t0: 0,who: 3,m: 0]
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -11,y0: 9,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 142,y0: 8,vx: -0.03,vy: -4.84,t0: 0,who: 2,m: 100], [x0: 267,y0: 9,vx: 0,vy: -8.79,t0: 0,who: 2,m: 100], [x0: -129,y0: 7,vx: -0.06,vy: 3.73,t0: 0,who: 2,m: 100], [x0: -272,y0: 6,vx: -0.09,vy: 8.25,t0: 0,who: 2,m: 100], [x0: 63,y0: 8,vx: -0.03,vy: -2.34,t0: 0,who: 3,m: 0], [x0: 203,y0: 11,vx: 0.06,vy: -6.77,t0: 0,who: 3,m: 0], [x0: 341,y0: 11,vx: 0.06,vy: -11.13,t0: 0,who: 3,m: 0], [x0: -73,y0: 10,vx: 0.03,vy: 1.96,t0: 0,who: 3,m: 0], [x0: -202,y0: 7,vx: -0.06,vy: 6.04,t0: 0,who: 3,m: 0], [x0: -345,y0: 9,vx: 0,vy: 10.56,t0: 0,who: 3,m: 0]
Binomial Theorem: ((a+b)^n)= sum k=0->k=n((n!(a^(n-k))(b^k))/(k!(n-k)!))
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- Posts: 523
- Joined: Mon Jun 03, 2013 4:54 pm
Re: r^1 Orbits
Woah. The planets and asteroids do get out of phase though.19683 wrote:Try this:
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -11,y0: 9,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 142,y0: 8,vx: -0.03,vy: -4.84,t0: 0,who: 2,m: 100], [x0: 267,y0: 9,vx: 0,vy: -8.79,t0: 0,who: 2,m: 100], [x0: -129,y0: 7,vx: -0.06,vy: 3.73,t0: 0,who: 2,m: 100], [x0: -272,y0: 6,vx: -0.09,vy: 8.25,t0: 0,who: 2,m: 100], [x0: 63,y0: 8,vx: -0.03,vy: -2.34,t0: 0,who: 3,m: 0], [x0: 203,y0: 11,vx: 0.06,vy: -6.77,t0: 0,who: 3,m: 0], [x0: 341,y0: 11,vx: 0.06,vy: -11.13,t0: 0,who: 3,m: 0], [x0: -73,y0: 10,vx: 0.03,vy: 1.96,t0: 0,who: 3,m: 0], [x0: -202,y0: 7,vx: -0.06,vy: 6.04,t0: 0,who: 3,m: 0], [x0: -345,y0: 9,vx: 0,vy: 10.56,t0: 0,who: 3,m: 0]
Edit: And the inevitable:
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 10,y0: 0,vx: 0,vy: 0.316227766017,t0: 0,who: 3,m: 0], [x0: 20,y0: 0,vx: 0,vy: 0.632455532034,t0: 0,who: 3,m: 0], [x0: 30,y0: 0,vx: 0,vy: 0.948683298051,t0: 0,who: 3,m: 0], [x0: 40,y0: 0,vx: 0,vy: 1.26491106407,t0: 0,who: 3,m: 0], [x0: 50,y0: 0,vx: 0,vy: 1.58113883008,t0: 0,who: 3,m: 0], [x0: 60,y0: 0,vx: 0,vy: 1.8973665961,t0: 0,who: 3,m: 0], [x0: 70,y0: 0,vx: 0,vy: 2.21359436212,t0: 0,who: 3,m: 0], [x0: 80,y0: 0,vx: 0,vy: 2.52982212813,t0: 0,who: 3,m: 0], [x0: 90,y0: 0,vx: 0,vy: 2.84604989415,t0: 0,who: 3,m: 0], [x0: 100,y0: 0,vx: 0,vy: 3.16227766017,t0: 0,who: 3,m: 0], [x0: 110,y0: 0,vx: 0,vy: 3.47850542619,t0: 0,who: 3,m: 0], [x0: 120,y0: 0,vx: 0,vy: 3.7947331922,t0: 0,who: 3,m: 0], [x0: 130,y0: 0,vx: 0,vy: 4.11096095822,t0: 0,who: 3,m: 0], [x0: 140,y0: 0,vx: 0,vy: 4.42718872424,t0: 0,who: 3,m: 0], [x0: 150,y0: 0,vx: 0,vy: 4.74341649025,t0: 0,who: 3,m: 0], [x0: 160,y0: 0,vx: 0,vy: 5.05964425627,t0: 0,who: 3,m: 0], [x0: 170,y0: 0,vx: 0,vy: 5.37587202229,t0: 0,who: 3,m: 0], [x0: 180,y0: 0,vx: 0,vy: 5.6920997883,t0: 0,who: 3,m: 0], [x0: 190,y0: 0,vx: 0,vy: 6.00832755432,t0: 0,who: 3,m: 0]
Code: Select all
Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000], [x0: 4,y0: 0,vx: 0,vy: 0.126491106407,t0: 0,who: 3,m: 0], [x0: 8,y0: 0,vx: 0,vy: 0.252982212813,t0: 0,who: 3,m: 0], [x0: 12,y0: 0,vx: 0,vy: 0.37947331922,t0: 0,who: 3,m: 0], [x0: 16,y0: 0,vx: 0,vy: 0.505964425627,t0: 0,who: 3,m: 0], [x0: 20,y0: 0,vx: 0,vy: 0.632455532034,t0: 0,who: 3,m: 0], [x0: 24,y0: 0,vx: 0,vy: 0.75894663844,t0: 0,who: 3,m: 0], [x0: 28,y0: 0,vx: 0,vy: 0.885437744847,t0: 0,who: 3,m: 0], [x0: 32,y0: 0,vx: 0,vy: 1.01192885125,t0: 0,who: 3,m: 0], [x0: 36,y0: 0,vx: 0,vy: 1.13841995766,t0: 0,who: 3,m: 0], [x0: 40,y0: 0,vx: 0,vy: 1.26491106407,t0: 0,who: 3,m: 0], [x0: 44,y0: 0,vx: 0,vy: 1.39140217047,t0: 0,who: 3,m: 0], [x0: 48,y0: 0,vx: 0,vy: 1.51789327688,t0: 0,who: 3,m: 0], [x0: 52,y0: 0,vx: 0,vy: 1.64438438329,t0: 0,who: 3,m: 0], [x0: 56,y0: 0,vx: 0,vy: 1.77087548969,t0: 0,who: 3,m: 0], [x0: 60,y0: 0,vx: 0,vy: 1.8973665961,t0: 0,who: 3,m: 0], [x0: 64,y0: 0,vx: 0,vy: 2.02385770251,t0: 0,who: 3,m: 0], [x0: 68,y0: 0,vx: 0,vy: 2.15034880891,t0: 0,who: 3,m: 0], [x0: 72,y0: 0,vx: 0,vy: 2.27683991532,t0: 0,who: 3,m: 0], [x0: 76,y0: 0,vx: 0,vy: 2.40333102173,t0: 0,who: 3,m: 0], [x0: 80,y0: 0,vx: 0,vy: 2.52982212813,t0: 0,who: 3,m: 0], [x0: 84,y0: 0,vx: 0,vy: 2.65631323454,t0: 0,who: 3,m: 0], [x0: 88,y0: 0,vx: 0,vy: 2.78280434095,t0: 0,who: 3,m: 0], [x0: 92,y0: 0,vx: 0,vy: 2.90929544735,t0: 0,who: 3,m: 0], [x0: 96,y0: 0,vx: 0,vy: 3.03578655376,t0: 0,who: 3,m: 0], [x0: 100,y0: 0,vx: 0,vy: 3.16227766017,t0: 0,who: 3,m: 0], [x0: 104,y0: 0,vx: 0,vy: 3.28876876658,t0: 0,who: 3,m: 0], [x0: 108,y0: 0,vx: 0,vy: 3.41525987298,t0: 0,who: 3,m: 0], [x0: 112,y0: 0,vx: 0,vy: 3.54175097939,t0: 0,who: 3,m: 0], [x0: 116,y0: 0,vx: 0,vy: 3.6682420858,t0: 0,who: 3,m: 0], [x0: 120,y0: 0,vx: 0,vy: 3.7947331922,t0: 0,who: 3,m: 0], [x0: 124,y0: 0,vx: 0,vy: 3.92122429861,t0: 0,who: 3,m: 0], [x0: 128,y0: 0,vx: 0,vy: 4.04771540502,t0: 0,who: 3,m: 0], [x0: 132,y0: 0,vx: 0,vy: 4.17420651142,t0: 0,who: 3,m: 0], [x0: 136,y0: 0,vx: 0,vy: 4.30069761783,t0: 0,who: 3,m: 0], [x0: 140,y0: 0,vx: 0,vy: 4.42718872424,t0: 0,who: 3,m: 0], [x0: 144,y0: 0,vx: 0,vy: 4.55367983064,t0: 0,who: 3,m: 0], [x0: 148,y0: 0,vx: 0,vy: 4.68017093705,t0: 0,who: 3,m: 0], [x0: 152,y0: 0,vx: 0,vy: 4.80666204346,t0: 0,who: 3,m: 0], [x0: 156,y0: 0,vx: 0,vy: 4.93315314986,t0: 0,who: 3,m: 0], [x0: 160,y0: 0,vx: 0,vy: 5.05964425627,t0: 0,who: 3,m: 0], [x0: 164,y0: 0,vx: 0,vy: 5.18613536268,t0: 0,who: 3,m: 0], [x0: 168,y0: 0,vx: 0,vy: 5.31262646908,t0: 0,who: 3,m: 0], [x0: 172,y0: 0,vx: 0,vy: 5.43911757549,t0: 0,who: 3,m: 0], [x0: 176,y0: 0,vx: 0,vy: 5.5656086819,t0: 0,who: 3,m: 0], [x0: 180,y0: 0,vx: 0,vy: 5.6920997883,t0: 0,who: 3,m: 0], [x0: 184,y0: 0,vx: 0,vy: 5.81859089471,t0: 0,who: 3,m: 0], [x0: 188,y0: 0,vx: 0,vy: 5.94508200112,t0: 0,who: 3,m: 0], [x0: 192,y0: 0,vx: 0,vy: 6.07157310752,t0: 0,who: 3,m: 0], [x0: 196,y0: 0,vx: 0,vy: 6.19806421393,t0: 0,who: 3,m: 0]
Code: Select all
import math
output = "Gravity Fun at TestTubeGames.com: [ForceG: 1,Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 1,m: 1000]"
step = 10
for a in range(step,200,step):
output = output + ", [x0: " + str(a) + ",y0: 0,vx: 0,vy: " + str(.001**.5*a) + ",t0: 0,who: 3,m: 0]"
print output
$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!