Re: Planets and geodesic
- From: Ben Rudiak-Gould <br276deleteme@xxxxxxxxx>
- Date: Sat, 07 Oct 2006 16:12:10 +0100
sukhisoul@xxxxxxxxx wrote:
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimention, each planet is tracing a geodesic like a spiral
staircase.
My question , what kind of 3d surface has spirals as its geodesics?
Well, the Schwarzschild geometry, obviously. :-) Seriously, this really depends on what you mean by "spiral". For example, take a hollow cylinder embedded in 3-space, with the inherited metric; this has lots of geodesics that look like spirals in the embedding space. Or take a solid square cylinder, identify two opposite faces, and then twist it around to join those faces while preserving the original metric.
But the orbits in the Schwarzschild coordinates are spirals in a more subtle way that only depends on the internal geometry, and more specifically on how we establish a notion of space with surveying equipment. I don't know how to formalize that sense of spiral, and probably there's no analogous property for ordinary (positive definite) manifolds.
-- Ben
.
- References:
- Planets and geodesic
- From: sukhisoul
- Planets and geodesic
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