Confusion About the Physics of Orbiting Bodies

[ScientificMind]

I hope this is in the right thread, I wasn't sure which one to put this in but this seemed like the most likely one to be right, so I'm sorry if this is in the wrong thread.

Anyway, my question basically amounts to this: what is the difference between something orbiting around a still planet and something hovering over a rotating planet? On one hand, it seems like both situations would appear exactly the same, but on the other hand what happens is incredibly different (i.e. one plummets to the ground, while the other remains in orbit) In part, I suppose, this questioned formed because of the idea of a geostationary orbit, and partly from becoming accustomed to the logic behind relativity. Because the outcomes are so different, I know there must be some sort of objective observable difference, but for the life of me, I can't think of what it might be.

 

[olivermsun]

The geostationary object is also orbiting around the planet. The planet just happens to rotate at the right rate so that people on the planet's surface can always look up and see the object in the same relative location.

 

[newjerseyrunner]

Relativity is not needed to explain geosynchronous orbits, just classical Newtonian gravity.

 

[ScientificMind]

The geostationary object is also orbiting around the planet. The planet just happens to rotate at the right rate so that people on the planet's surface can always look up and see the object in the same relative location.

I'm aware of that, what I want to know, though, is, what is the difference from the point of view of the thing orbiting? If something is orbiting a non-rotating planet, it seems like from the point of view of the satellite, it would look the same as if they were hovering in the air above a rotating planet, except they would remain in orbit instead of plummeting to the ground, so what is the difference in how it looks to the satellite.

 

[rootone]

A completely non rotating planet would be a rare thing though not an impossibility.
In the usual case of a planet which IS rotating there there will be some particular altitude at which it is possible for a satellite to be in geosynchronous orbit around the equator.
The exact altitude will depend on the gravity of the planet and the mass and velocity of the satellite, in other words it's angular momentum.

If the planet is not rotating it has NO angular momentum or velocity, so to match the planet the satellite also must have and orbit with zero angular momentum.
So a geosynchronous orbit would be at ground level!
If you launch it into space it will orbit alright, but it can't be geosynchronous orbit.

 

[Bandersnatch]

The 'point of view' of the satellite doesn't matter as far as its ability to stay in orbit goes*.

What matters is how far it is from the centre of the gravitational field, and how fast it's moving w/r to it.
The planet may be rotating or not, or it can be put in a non-transparent box that doesn't let you see what's going on with it. None of it changes the ability of the satellite to orbit the planet.

That the observer in the satellite may see the ground as stationary doesn't change his ability to stay in orbit in the same way as sitting in a moving train, looking out the window and seeing another train moving in parallel (which gives the illusion of being stationary) doesn't change the fact that you're going to get from your point of origin to the destination in the same time as you would without the second train giving you the illusion of not moving.

In more precise terms, changing the frame of reference (here: to a non-inertial, rotating one) doesn't change the dynamics of the system.* it does affect that in some senses, if you're orbiting something like a black hole (see: frame dragging) or if you're considering the tides.

 

[DrClaude]

The orbiting satellite is continuously accelerating. Therefore, there is no equivalence between orbiting a non-rotating planet and hovering over a rotating planet.

 

[ScientificMind]

A completely non rotating planet would be a rare thing though not an impossibility.
In the usual case of a planet which IS rotating there there will be some particular altitude at which it is possible for a satellite to be in geosynchronous orbit around the equator.
The exact altitude will depend on the gravity of the planet and the mass and velocity of the satellite, in other words it's angular momentum.

If the planet is not rotating it has NO angular momentum or velocity, so to match the planet the satellite also must have and orbit with zero angular momentum.
So a geosynchronous orbit would be at ground level!
If you launch it into space it will orbit alright, but it can't be geosynchronous orbit.

Does that mean that there is an objective and absolute version of what is spinning/rotating/orbiting and what is not spinning/rotating/orbiting that is the same regardless of where or how you look at it?

 

[DrClaude]

Does that mean that there is an objective and absolute version of what is spinning/rotating/orbiting and what is not spinning/rotating/orbiting that is the same regardless of where or how you look at it?

Yes.

 

[Ken G]

Does that mean that there is an objective and absolute version of what is spinning/rotating/orbiting and what is not spinning/rotating/orbiting that is the same regardless of where or how you look at it?

It sounds to me like what you are asking about is something known as "Mach's principle." I'm not a GR expert, but it is my impression that there remains considerable debate about just what Mach's principle should be regarded to be, and whether or not GR respects that principle. What is clear is that Mach was asking similar questions to what you are asking, and that Einstein was in part inspired by these kinds of questions to come up with GR in the first place.

The answer that Mach would have given is, the difference between a rotating planet and a co-orbiting satellite, and a non-rotating planet and a non-orbiting satellite, is just one thing: the behavior of the rest of the universe. So Mach felt this must mean that the behavior of the rest of the universe is important for an orbiting satellite. The way this would work in GR is, the dynamical history of the whole universe, from the Big Bang right onward, is necessary to know in order to understand the spacetime of the satellite+planet system. So a universe with nothing in it but a planet and a satellite would have an ill-posed solution to your question, but our universe has a well-posed answer, because it does have a dynamical history that is capable of differentiating those two situations. In fact, we might argue that if the entire universe comprised of two planets with different rotation rates, and the whole rest of the universe has a similar history as ours but was comprised entirely of dark matter, we might be able to postulate the existence of that dark matter just from looking at satellites in orbit around those two planets. The only alternative would seem to be some kind of ether, but with no dynamical constraints to tell us what the ether should do.

So your question is similar to asking, in a universe comprising of just two planets, in a long-period circular orbit around each other, one planet which we would regard in a Newtonian sense as not rotating, and the other rotating in synch with its orbit, what determines which one should really be regarded as rotating? People will quickly bring up experiments involving coriolis forces and so on, but that begs the question, because then the question becomes, what determines which planet experiences coriolis forces? Inevitably, you will at some point need to look at the history of that system, so whether one regards that as a history of an entire coupled universe, as in Mach's viewpoint, or if you think you can just look at the rotational histories of those two objects, you will need to connect to that history in order to make sense of questions like how much coriolis force should each planet experience. I'd say that's the crux of Mach's principle-- the spacetime environment of any system must have a dynamical history, and that is where lies the answer to your question.

 

[ScientificMind]

It sounds to me like what you are asking about is something known as "Mach's principle." I'm not a GR expert, but it is my impression that there remains considerable debate about just what Mach's principle should be regarded to be, and whether or not GR respects that principle. What is clear is that Mach was asking similar questions to what you are asking, and that Einstein was in part inspired by these kinds of questions to come up with GR in the first place.

The answer that Mach would have given is, the difference between a rotating planet and a co-orbiting satellite, and a non-rotating planet and a non-orbiting satellite, is just one thing: the behavior of the rest of the universe. So Mach felt this must mean that the behavior of the rest of the universe is important for an orbiting satellite. The way this would work in GR is, the dynamical history of the whole universe, from the Big Bang right onward, is necessary to know in order to understand the spacetime of the satellite+planet system. So a universe with nothing in it but a planet and a satellite would have an ill-posed solution to your question, but our universe has a well-posed answer, because it does have a dynamical history that is capable of differentiating those two situations. In fact, we might argue that if the entire universe comprised of two planets with different rotation rates, and the whole rest of the universe has a similar history as ours but was comprised entirely of dark matter, we might be able to postulate the existence of that dark matter just from looking at satellites in orbit around those two planets. The only alternative would seem to be some kind of ether, but with no dynamical constraints to tell us what the ether should do.

So your question is similar to asking, in a universe comprising of just two planets, in a long-period circular orbit around each other, one planet which we would regard in a Newtonian sense as not rotating, and the other rotating in synch with its orbit, what determines which one should really be regarded as rotating? People will quickly bring up experiments involving coriolis forces and so on, but that begs the question, because then the question becomes, what determines which planet experiences coriolis forces? Inevitably, you will at some point need to look at the history of that system, so whether one regards that as a history of an entire coupled universe, as in Mach's viewpoint, or if you think you can just look at the rotational histories of those two objects, you will need to connect to that history in order to make sense of questions like how much coriolis force should each planet experience. I'd say that's the crux of Mach's principle-- the spacetime environment of any system must have a dynamical history, and that is where lies the answer to your question.

Thank you so much. That is exactly what I was asking. I can't tell you how much of a relief it is to know that other people have thought about this before and that it wasn't just a huge misunderstanding on my part. I've actually been confused about this since I first learned about how orbit works about two years ago, but only recently remembered to ask since I started using PF(plus I'm not even sure if I fully understood my own confusion until I learned more about relativity somewhat recently). Anyway, this was very interesting, and I will almost undoubtedly look into Mach's Principle more on my own. Again, thank you