Originally posted by XanthosNZGood point. They clearly apply in the case of a circle (an infinitely thin torus) but, after some thought, I don't think everything cancels out for a torus of finite thickness. Things would be slightly off.
If you wish to use either the Shell theorem or converting to a point source you must prove that they apply in the case of a torus.
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Originally posted by GregMThe math would get very complex certainly because a torus doesn't resolve to a simple figure in spherical coordinates.
Good point. They clearly apply in the case of a circle (an infinitely thin torus) but, after some thought, I don't think everything cancels out for a torus of finite thickness. Things would be slightly off.
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Originally posted by Shallow BlueSo the coordinate system chosing doesn't matter then.
Because in that case the formula for the orbit would get rather complicated, or so I suspect.
Richard
I would put the torus, as a matrix, into a mathematical program, like MatLab or something, and do the math through numerical methods. Shouldn't be too hard. But this is an approximate method, that doesn't say anything for sure if the orbits are stable or not.
I did something like it in my university studies as a project and found some interesting result.
Originally posted by FabianFnasWhat was the 'something like it' study? Was it your dissertation?
So the coordinate system chosing doesn't matter then.
I would put the torus, as a matrix, into a mathematical program, like MatLab or something, and do the math through numerical methods. Shouldn't be too hard. But this is an approximate method, that doesn't say anything for sure if the orbits are stable or not.
I did something like it in my university studies as a project and found some interesting result.
Originally posted by sonhouseIt was a time ago, I don't remember the details. But it was a orbit analysis with more than two bodies, with a look ahead of some kind.
What was the 'something like it' study? Was it your dissertation?
Using the (more or less) same program I could do the calculations about orbits around a torodial shaped body, but I don't think I can find the papers anymore...
Originally posted by FabianFnasIt's clear an orbit aroung the 'equator' of a toroid woult be pretty much like a spheroid planet but it gets tricky when going over the
It was a time ago, I don't remember the details. But it was a orbit analysis with more than two bodies, with a look ahead of some kind.
Using the (more or less) same program I could do the calculations about orbits around a torodial shaped body, but I don't think I can find the papers anymore...
'poles' or 'holes' for sure, to say nothing of threading the needle kind of orbit.
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Originally posted by sonhouseWith numerical methods it's much easier. But you never get exact results, only approximated to a certain level.
It's clear an orbit aroung the 'equator' of a toroid woult be pretty much like a spheroid planet but it gets tricky when going over the
'poles' or 'holes' for sure, to say nothing of threading the needle kind of orbit.
Give a particle a location and a velocity, then you let it go and see what happens. Nice and fun to see the graph in 3d of the particles orbit, stable or not.
Originally posted by AThousandYoungWell, another question would be, can you establish a stable orbit around the 'flattened' part of the torous completely external, NOT going through the hole? It's clear an orbit around the toroid 'equator' would be stable because the gravitaional field would be more or less equal around the perimeter of the toroid. Gravity over the "poles" would vary from point to point in a "polar" orbit.
It seems to me that there will be unequal gravity from two directions; towards the opposing side of the torus there will be more gravity than the other way. This seems like it should prevent such an orbit.
No one has mentioned the obvious.
Imagine an orbit that is harmonic motion on a line tangent to the interior wall of the torus and directly through the centre of the hole. On this line all forces not on the line cancel and we are left with an "orbit" that is nothing but back and forth motion passing through the hole twice per period.
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Originally posted by XanthosNZThat's an orbit, but it isn't stable. A comet only has to breathe on this planet and it falls over.
No one has mentioned the obvious.
Imagine an orbit that is harmonic motion on a line tangent to the interior wall of the torus and directly through the centre of the hole. On this line all forces not on the line cancel and we are left with an "orbit" that is nothing but back and forth motion passing through the hole twice per period.
Richard
Originally posted by Shallow BlueI think I mentioned it a week ago:
That's an orbit, but it isn't stable. A comet only has to breathe on this planet and it falls over.
Richard
"Yes, you are right. In the middle of the torus hole, at the torus mass centre, the gravitation is zero. In the rotational axis the gravitation is pointed towards the mass centre. But off the rotational centre the gravitation is pointed towards the nearest surface. Correct me if I'm wrong."
The "In the rotational axis the gravitation is pointed towards the mass centre." means that you have a back and forth movement.
...and I think others has mentioned the samt thing too.