| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
07 Oct 2006 04:23:57 AM |
| Object: |
Planets and geodesic |
Hello,
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?
Thanks
Milind
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| User: "Hero" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 05:48:52 AM |
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schrieb:
Hello,
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?
On a spiral staircase the inner railing - to be more exact and on the
surface, the footline/projection of it - is the shortest path up and
down.
Have fun
Hero
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| User: "Uncle Al" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 10:03:04 AM |
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wrote:
Hello,
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?
Trans. Am. Math. Soc. 19(4) 315 (1918)
http://arxiv.org/abs/math.DG/0602435
http://mathworld.wolfram.com/Helicoid.html
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz3.pdf
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| User: "Ben Rudiak-Gould" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 10:12:10 AM |
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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
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| User: "Sam Wormley" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 09:06:56 AM |
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wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
My question , what kind of 3d surface has spirals as its geodesics?
Thanks
Milind
.
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| User: "Mike" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 09:25:34 AM |
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Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
My question , what kind of 3d surface has spirals as its geodesics?
Thanks
Milind
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| User: "Sam Wormley" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 09:29:30 AM |
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Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
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| User: "Mike" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 09:46:45 AM |
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Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Mike
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| User: "Sam Wormley" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 09:52:01 AM |
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Mike wrote:
Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Mike
Light travels faster than sound. This is why some people appear
bright until you hear them speak (or write, as the case may be).
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| User: "Mike" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 10:25:14 AM |
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Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Mike
Light travels faster than sound. This is why some people appear
bright until you hear them speak (or write, as the case may be).
Some people never get it straight:
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Answer the question
stooooooooooooooooooooooooooooooooooooooooooooooooopid.
Mike
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| User: "Sam Wormley" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 10:30:28 AM |
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Mike wrote:
Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Mike
Three-body problem solutions are not required! Any third body with
gravitational influence will prevent a circular orbit.
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| User: "Mike" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 11:38:02 AM |
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Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Mike
Three-body problem solutions are not required! Any third body with
gravitational influence will prevent a circular orbit.
If you do not know any physics learn at least how to google:
"The discovery of planets in circular orbits is exciting because they
are so rare," Butler added. " Of the published planets with orbital
periods longer than a month, only HD 27442 and this system are in
circular orbits. From this we can make a preliminary guess that about
five percent of planetary systems are in circular orbits."
http://exoplanets.org/esp/47uma/47uma_announce.html
You are an empirical fool in addirtion to
stooooooooooooooooooooooooopid.
Mike
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| User: "Sam Wormley" |
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| Title: Re: Planets and geodesic |
07 Oct 2006 12:11:16 PM |
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Mike wrote:
Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
Mike wrote:
Sam Wormley wrote:
sukhisoul@yahoo.com wrote:
Hello,
Assume that planets go around sun in a perfect circle. Then, in
2+1 dimen[s]ion, each planet is tracing a geodesic like a spiral
staircase.
This more than one planet, there can not be any perfect circle
orbits. Impossible. Stable orbits don't exist for n spatial
dimensions other than n=3.
In theory yes, you can have perfect circle orbits when the eccentricity
epsilon of the orbit is zero and the energy E of each planet satisfies
a certain equation (E = mu^2/2k^2, where mu = G(M+m) and k is the
angular momentum per unit mass)
Mike
Not with the gravitational effects of other planets--get real!
Have you solved the three-body problem (not the restricted one) and
found out that circular orbits are noit possible?
Mike
Three-body problem solutions are not required! Any third body with
gravitational influence will prevent a circular orbit.
If you do not know any physics learn at least how to google:
"The discovery of planets in circular orbits is exciting because they
are so rare," Butler added. " Of the published planets with orbital
periods longer than a month, only HD 27442 and this system are in
circular orbits. From this we can make a preliminary guess that about
five percent of planetary systems are in circular orbits."
http://exoplanets.org/esp/47uma/47uma_announce.html
You are an empirical fool in addirtion to
stooooooooooooooooooooooooopid.
Mike
In context, "circular orbits", means that the eccentricity of the
elliptical orbits is small, like the planets of our solar system.
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