Undergrad Satellite Orbit synchronization

[name123]

No.

Of course objects can be at rest in a frame at some times and not others. Of course you can describe the motion of any object in any frame you like.

But what you mean by "the satellite's perspective" is a frame in which the satellite is always at rest. And there is no inertial frame in which that's true. The fact that the satellite is at rest for an instant in some inertial frame does not mean that frame is "the satellite's perspective" for that instant. There is no such thing; the concept makes no sense.

As I've said before, you are confusing yourself by focusing on frames instead of physical invariants. We are getting to the point where this thread is going nowhere and is on the point of being closed, because, despite repeated attempts to help you, you persist in this confusion.

I am not considering a frame in which the satellite is always at rest. I accept that you are correct that there is not such frame.

Are you also saying that there do not exist frames of reference, in which things can go in and out of rest from, and which, while those things are at rest with them, could be used for how things would appear to those things temporarily at rest with them?

 

[Ibix]

Of course the series A satellites see each other's clocks to be ticking at the same rate! They are keeping station!

Note that this is literally seeing (as in post #88). Interpretation of that fact is frame dependent.

 

[Ibix]

I am not considering a frame in which the satellite is always at rest. I accept that you are correct that there is not such frame.

There are infinitely many such frames. The problem is that none of them look like a bunch of instantaneous inertial frames chained together.

 

[name123]

A frame of reference let's you draw a map of spacetime. With a normal geographic map, you can use any map at any time, whether you are facing in the same direction as the mapmaker was, or are hanging sideways out of the window of an aeroplane that's pulling a barrel roll. It's just that the relationship between your perspective and the map is complicated and time-varying in that case.

Similarly you can use any frame at any time. Most frames won't have any simple relation to "your perspective". And you were asking about the satellite's perspective, which an inertial frame is not.

But I have asked about the satellite's perspective at the point it is at rest with a certain frame of reference. Whether the calculations which indicate how things will "really" be for something at rest with that frame of reference at a point in time can be used for how it would "really" be for the satellite at rest with that frame of reference at the point of time in question. What I am not clear is whether people are claiming that the satellite in question would be exceptional and that the equations would not indicate how it would be for the satellite at rest in that frame of reference at that point of time. That there is some type of "well how long has it been there" criteria that needs to be passed, before the equations can be considered reliable.

 

[PeterDonis]

I am not considering a frame in which the satellite is always at rest.

Then virtually all of the discussion in this thread has been based on a misunderstanding, since it seemed clear to me (and I suspect to the others who have been responding) that the "satellite perspective" you were looking for was a frame in which the satellite was always at rest.

I accept that you are correct that there is not such frame.

Then you are confused, because nobody has said any such thing. It is perfectly possible to construct a non-inertial frame in which the satellite is always at rest. But such a frame must be non-inertial. And, as several of us have told you, there is no way to construct such a frame by combining the inertial frames in which the satellite is momentarily at rest at various points in its orbit.

Are you also saying that there do not exist frames of reference, in which things can go in and out of rest from, and which, while those things are at rest with them, could be used for how things would appear to those things temporarily at rest with them?

I'm saying that there are only two well-defined meanings that I'm aware of for "how things would appear", and what you are describing does not correspond to either of them.

One meaning is "coordinate times and positions in a frame in which the satellite is always at rest".

The other meaning is "the literal content of light signals reaching the satellite, as a function of time on the satellite's clock".

I have asked about the satellite's perspective at the point it is at rest with a certain frame of reference.

Once more: there is no such thing if it does not mean one of the two things I described above, which it seems it does not.

 

[Ibix]

the satellite's perspective at the point it is at rest with a certain frame of reference.

There are infinitely many coordinate systems fitting this description. You haven't picked one. If you pick one, you will have defined all your answers. If you pick another you will have defined all your answers in a different way.

Time for me to bow out of this thread. I'm just repeating myself.

 

[PeterDonis]

Time for me to bow out of this thread. I'm just repeating myself.

At this point we all are. Thread closed.