## r^(-2.9)

### r^(-2.9)

I was playing with various gravity laws and found that r^(-2.9) was very strange. The orbit spirals inward, and it seems like it will collapse, but then it swings around the star several times and the comes back out. Why does it behave like this?

Binomial Theorem: ((a+b)^n)= sum k=0->k=n((n!(a^(n-k))(b^k))/(k!(n-k)!))

- testtubegames
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**Posts:**1008**Joined:**Mon Nov 19, 2012 7:54 pm

### Re: r^(-2.9)

That's really weird, isn't it?

I'd noticed this with General Relativity on, too. But showing it with an even simpler force law (like r^-2.9) helps cut through some of the mystery around it.

Looking at it, I think what we're seeing is just precession. So just as an orbit in r^-2.1 will slowly advance forward each cycle, like so:

An orbit in r^-2.9 will do that same thing, but to a greater extreme.

It's as if the asteroid is tracing out an ellipse, but an ellipse that's also spinning around the star. That makes it look like an inward spiral followed by an outward spiral.

Make sense?

I'd noticed this with General Relativity on, too. But showing it with an even simpler force law (like r^-2.9) helps cut through some of the mystery around it.

Looking at it, I think what we're seeing is just precession. So just as an orbit in r^-2.1 will slowly advance forward each cycle, like so:

An orbit in r^-2.9 will do that same thing, but to a greater extreme.

It's as if the asteroid is tracing out an ellipse, but an ellipse that's also spinning around the star. That makes it look like an inward spiral followed by an outward spiral.

Make sense?

### Re: r^(-2.9)

Yeah, I think I see what you mean. So the orbit itself precesses faster than the planet is moving and that makes it go around several times before getting farther again. I wonder what force laws can produce this effect, like if r^(-2.8) or r^(-2.5) will work.

Binomial Theorem: ((a+b)^n)= sum k=0->k=n((n!(a^(n-k))(b^k))/(k!(n-k)!))

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