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Ekim
2008-Mar-26, 05:34 PM
If the Moon orbits the earth, would a solid ring also orbit the earth?

I want to say no because an orbiting body is actually spiraling towards the center of mass. If it were a ring it would have to remain the same distance at all points at all times which doesn't sound like it should work.

Forgive me if the question is too weird or not worded in a way that is easily understood.

NEOWatcher
2008-Mar-26, 05:44 PM
If the Moon orbits the earth, would a solid ring also orbit the earth?
It might be possible to do it, but I think it would be highly unstable.

I want to say no because an orbiting body is actually spiraling towards the center of mass.
Spiral?

If it were a ring it would have to remain the same distance at all points at all times which doesn't sound like it should work.
Not exactly. It would be based on its center of gravity which would be at the center of the Earth.

Now; I wait for a better explaination.

Ekim
2008-Mar-26, 05:46 PM
It might be possible to do it, but I think it would be highly unstable.

Spiral?

Not exactly. It would be based on its center of gravity which would be at the center of the Earth.

Now; I wait for a better explaination.

I am under the impresion that the moon is getting closer to earth on every orbit. Spiraling towards the center of gravity because it can't maintain a permanent orbit forever.

Trocisp
2008-Mar-26, 05:54 PM
The moon is actually, very, very slowly, spiraling away from the earth.

A few CM per year, I believe.

Ekim
2008-Mar-26, 05:55 PM
The moon is actually, very, very slowly, spiraling away from the earth.

A few CM per year, I believe.
I suppose it would have to be either/or in all gravitational systems.

NEOWatcher
2008-Mar-26, 05:56 PM
I am under the impresion that the moon is getting closer to earth on every orbit. Spiraling towards the center of gravity because it can't maintain a permanent orbit forever.
Just the opposite. It is spiraling out due to tidal forces (2-3 cm/yr IIRC)
But, the spiral is the tidal effect and has nothing to do with the basics of a stable orbit.
If both objects were gravitationally spherical, with no tidal effects, then there would be no spiraling.

Grey
2008-Mar-26, 06:06 PM
If you're imagining something like a version of Saturn's rings, where the ring is a single, rigid object, the answer is "not very easily". A solid ring around a massive object is gravitationally unstable, like a pencil balanced on its point. If it's exactly balanced, it will stay there, but if you give it the slightest nudge it will fall over.

EvilEye
2008-Mar-26, 06:16 PM
I picture it this way. The center of mass for BOTH objects would be in the same place (center of the earth) if the ring was exactly centered both up and down, and distance from the earth all the way around.

One of two things would probably happen.

1. - If the ring moved north or south of center, it would begin to wobble like a poorly thrown frizbee, and the two would slip apart or crash into each other.

2. - If the ring deviated left or right causing an uneven distance away from the earth on either side (closer on one side, and further on the other), the ring & Earth would wobble like somone using a hula hoop....eventually touching and destroying both.

Trocisp
2008-Mar-26, 06:18 PM
It would also be dependent on the mass of the ring, if you're talking about a single massive space station that would orbit the earth in that manner, it's possible, but it would have to have very, very, very interesting engineering and maintenance.

Noclevername
2008-Mar-26, 06:31 PM
If the Ringworld is unstable (http://en.wikipedia.org/wiki/Ringworld#Instability), any solid ring around a gravitational body would be.

neilzero
2008-Mar-26, 07:35 PM
The ring would eventually turn slower (due to windage) and become increasingly unstable, but a real ring with a circumfrence of about a million kilometers would not be rigid. It would have stretch transients and other oscillations which complicate the analysis. As long as the ring was kept rotating slightly faster than orbital speed, it should not fall toward Earth and would have at least a slight gravity away from Earth. Some energy would need to be added periodically, to maintain the faster than orbital speed. Neil

Noclevername
2008-Mar-26, 07:47 PM
The ring would eventually turn slower (due to windage) and become increasingly unstable, but a real ring with a circumfrence of about a million kilometers would not be rigid.

Close enough for jazz.

It would have stretch transients and other oscillations which complicate the analysis. As long as the ring was kept rotating slightly faster than orbital speed, it should not fall toward Earth and would have at least a slight gravity away from Earth. Some energy would need to be added periodically, to maintain the faster than orbital speed. Neil

No, the speed is irrelevant, it's still unstable. If one side moves further away from Earth, that means the other side is getting closer, and pulled more by gravity (whose strength varies by distance.) It's been mathematically proven. The speed doesn't matter, the center of mass is what does.

Tim Thompson
2008-Mar-27, 01:27 AM
If the Moon orbits the earth, would a solid ring also orbit the earth?
Not by itself. A solid ring is unstable. James Clerk Maxwell demonstrated this in 1856 in a discussion of Saturn's rings (which were long thought to be solid rings). I can't find Maxwell's paper, but Jeffreys, 1947 (http://adsabs.harvard.edu/abs/1947MNRAS.107..263J) analyzes the difference between an extremely viscous fluid (almost solid) and separate particles for the rings of Saturn, showing that the fluid ring is unstable. Of course by then it was known that Saturn's rings could not be solid anyway, since we can see stars through them even from Earth. But Jeffreys' discussion might be helpful in understanding the nature of the instability of a solid ring.

I want to say no because an orbiting body is actually spiraling towards the center of mass.
In the ideal case of point masses, or spherically (radially) symmetric masses, there will be no spiraling, in or out. In those cases, absent external forces, the orbits are eternal. In all of the real cases, like Earth & moon, tidal forces will cause an outward or inward drift of the satellite.

In the case of Earth, the moon is moving away at the currently anomalously high rate of 3.82±0.07 cm/year (Dickey, et al., 1994 (http://adsabs.harvard.edu/abs/1994Sci...265..482D); see The Recession of the Moon and the Age of the Earth-Moon System (http://www.talkorigins.org/faqs/moonrec.html), one of my Talk.Origins entries). The moon will continue moving away from Earth until the two are completely locked, one side of the moon facing one side of Earth (terrestrial day = lunar day = lunar month). If it were a 2-body problem that would be the eternal, stable configuration. But the introduction of solar tides causes the moon to start falling slowly inward towards Earth. In about 100,000,000,000 years from now the moon would collide with and re-join Earth. But since both will be destroyed by the AGB phase of solar evolution in about 5,000,000,000 years, that won't happen (Solar System Dynamics, C.D. Murray & S.F. Dermott, Cambridge University Press, 1999 & 2001, pp. 163-166; the despinning time for Earth is 50,000,000,000 years, and the reverse process should take the same amount of time).

The return trip is already on the way for Phobos, which is spiraling in towards Mars. Phobos will collide with Mars somewhere between 40,000,000 and 43,000,000 years from now (Efroimsky & Lainey, 2007 (http://adsabs.harvard.edu/abs/2007JGRE..11212003E)).

a1call
2008-Mar-27, 02:13 AM
The wikipedia Orbital Ring (http://en.wikipedia.org/wiki/Orbital_ring) might need correctional details. Not exactly an orbit but somewhat related.

John Mendenhall
2008-Mar-27, 08:28 PM
As Tim Thompson posted, a solid ring is unstable. Worth noting that Larry Niven got this wrong in Ringworld, and when it was pointed out to him, he then wrote a Ringworld sequel to take care of the problem.

frankuitaalst
2008-Mar-27, 09:16 PM
I wonder if there is any reference available about the dynamics of a ring world ie. concerning the instability of such a structure ?