Is it possible for an object to orbit a stationary object?

[wasteofo2]

Is it possible for an object to orbit a stationary object? It seems to me that the reason for orbits is this: An object of greater mass pulls an object of lesser mass towards it. The object of lesser mass(B) heads towards the center of the higher mass object(A), but object A moves. Object B's inertia is sending it to the place where object A used to be, but gravity from object A starts to pull b towards it. A continues to move, and B's inertia keeps causing it to pass by A and then be pulled back. To me it seems that nothing could orbit around a stationary point because it would either go directly to the point or spiral steadily towards it.

Is this pretty much it?

 

[wasteofo2]

This is an overly simplified version of how I see it, of course the moon would make full orbits of the Earth many times by the time the Earth had almost completed it's orbit, but the basic concept can be discerned.

 

[Nereid]

Is it possible for an object to orbit a stationary object?

Stationary with respect to what?

To me it seems that nothing could orbit around a stationary point because it would either go directly to the point or spiral steadily towards it.

How about two compact objects, of exactly equal mass, orbiting about their common centre of mass?

 

[wasteofo2]

Originally posted by Nereid
Stationary with respect to what? How about two compact objects, of exactly equal mass, orbiting about their common centre of mass?

Stationary in an absolute sense, having no acceleration.

If you had 2 objects equal in every way, and they were stationary relative to their surroundings and each other, being somehow restrained and then let loose, wouldn't they just crash into each other? If they were already in motion wouldn't they just kind of spiral towards their central gravitaitonal point and eventually collide?

 

[Nereid]

How about a perfectly circular, thin ring, with a mass at the centre of the ring?

That would fit your requirement ("an object to orbit a stationary object")

IIRC, such an orbit would be unstable, no matter how fast the ring revolves (or the mass at the centre rotates).

 

[Jimmy]

If two masses were held at rest relative to each other and then let go, they would fall into each other. It would not matter if the objects were of equal mass or not. If one object were significantly more massive than another (the Earth and a person), for practical purposes, you could consider the less massive object to be accelerating toward the more massive of the two. In reality, both objects would be accelerating toward each other.

If the two objects of equal mass were already in motion, it would depend on their relative velocities as to whether they would crash into each other. Depending on their velocities, they might fall into a stable orbit, escape each other's gravitational pull, or crash into each other.

As far as one object being held stationary, do you mean one object would not be allowed to revolve around the common center of gravity? I'm not sure what would happen in that case. Two equal masses would revolve around a center of gravity that was halfway between them. You could consider the center of gravity to be stationary in that scenario. If somehow one mass was not free to move, I suppose as the other mass orbited the stationary mass, the center of mass would revolve around the stationary mass as well. I'm not really sure how that would work in reality.

 

[Nereid]

more specific?

Originally posted by wasteofo2
Is it possible for an object to orbit a stationary object? It seems to me that the reason for orbits is this: An object of greater mass pulls an object of lesser mass towards it. The object of lesser mass(B) heads towards the center of the higher mass object(A), but object A moves. Object B's inertia is sending it to the place where object A used to be, but gravity from object A starts to pull b towards it. A continues to move, and B's inertia keeps causing it to pass by A and then be pulled back. To me it seems that nothing could orbit around a stationary point because it would either go directly to the point or spiral steadily towards it.

Is this pretty much it?

Could you specify your context a little please? As you've posted this on "General Astronomy & Cosmology", I could assume your 'objects' are planet or star-sized in mass and composition. However, you may be looking for something general enough to apply to an electron and a proton, or two supermassive black holes, or a grain of sand and the Sun, or ...

 

[wasteofo2]

Yeah, I should have been more specific to begin with. I'm curious about planets orbiting stars and satellites orbiting planets. If the sun were stationary could the Earth orbit it or is it only to orbit the sun because the sun moves?

 

[selfAdjoint]

Imagine there are only two bodies in the universe, a very massive one (a star) and a less massive one (a planet). Assume they start with a relative velocity to each other. Then under Newton's inverse square law, and also to a high approximation under Einstein's General Relativity, They will attract one another and because of the relative velocity an orbital situation will be set up. If you assume the planet's mass is VERY much smaller thn the star's, then the planet will orbit the star according to Kepler's laws (elliptical orbit, equal areas swept out in equal times). If the planet's mass is big enough that you can't ignore it, then you have to include the fact that the star will move because of its attraction to the planet, and then both of the bodies will orbit around their common center of gravity.

In all of this, the only motion assumed was the relative motion between the star and the planet (an initial condition for the differential equations). That can be taken as the planet moving relative to the star or vice versa. But some relative motion is required so that the planet doesn't just fall into the star.

 

[ranyart]

Originally posted by selfAdjoint
Imagine there are only two bodies in the universe, a very massive one (a star) and a less massive one (a planet). Assume they start with a relative velocity to each other. Then under Newton's inverse square law, and also to a high approximation under Einstein's General Relativity, They will attract one another and because of the relative velocity an orbital situation will be set up. If you assume the planet's mass is VERY much smaller thn the star's, then the planet will orbit the star according to Kepler's laws (elliptical orbit, equal areas swept out in equal times). If the planet's mass is big enough that you can't ignore it, then you have to include the fact that the star will move because of its attraction to the planet, and then both of the bodies will orbit around their common center of gravity.

In all of this, the only motion assumed was the relative motion between the star and the planet (an initial condition for the differential equations). That can be taken as the planet moving relative to the star or vice versa. But some relative motion is required so that the planet doesn't just fall into the star.

Question?..would not the Star have an associated photon horizon that extends beyon the planet?..and thus a pressure shroud would exert some influence over the planet, as this shroud would envelope the planet and (pressuming that there is something outside this area?) then you would have an Universe that is acting like a solar system?

One can extrapolate further by stating that if the planet is reliant upon the Star as a centre of attraction, and settles into an orbit (your definition), then if the Star was to cease to exist( not the same as proposed in another thread wherby the light of a Star ceases, and Earth observers still see the light for a while), then the planet would instantly converge into the position of where the Star was, Whitehole>>Blackhole conversion.

The planet would be attracted (planet would be centre of where the Star was) to an area that is Blackhole(Star-collapse-zone), wherby its collapse would be sufficient to invoke 'elemental' reactions to the Planet, and would start to Radiate intensely!

 

[selfAdjoint]

Question?..would not the Star have an associated photon horizon that extends beyon the planet?..and thus a pressure shroud would exert some influence over the planet, as this shroud would envelope the planet and (pressuming that there is something outside this area?) then you would have an Universe that is acting like a solar system?

What is this about a photon horizon? When I said very massive I didn't mean a black hole, I meant a lot heavier than the planet. I wasn't trying to build a universe, just answereing the question is motion of the primary necessary to orbital mechanics.

 

[ranyart]

Originally posted by selfAdjoint
What is this about a photon horizon? When I said very massive I didn't mean a black hole, I meant a lot heavier than the planet. I wasn't trying to build a universe, just answereing the question is motion of the primary necessary to orbital mechanics.

Yes DickT sorry!

One small thing, is it correct that if I replaced the two bodies in your post, with two non-radiative Planets, one large and one small, then the result would be exactly as you state? would there be orbital correspondance?

Just a two or three digit word reply would be great DickT, thanks again.