I Satellite Orbit synchronization

[PeterDonis]

what about the rest frame of a satellite at a given point of time? The positions of the other satellites at that point of time according to the satellite in that rest frame at that point of time.

That's what @Janus has been describing for you. But the satellite is only at rest in this frame for that instant of time, so it doesn't work as "the satellite's perspective" globally.

 

[name123]

Huh? Frames of reference are not things that you can be "in".

My fault. What I meant was when it was at rest with respect to the spaceship. I was not clear why at that point they would come to a different conclusion about the positions and clock speeds of the other satellites.

 

[name123]

That's what @Janus has been describing for you. But the satellite is only at rest in this frame for that instant of time, so it doesn't work as "the satellite's perspective" globally.

No I realize that, but I am just considering their relative perspectives at that point in time, and curious as to why they would be different.

 

[Ibix]

My fault. What I meant was when it was at rest with respect to the spaceship. I was not clear why at that point they would come to a different conclusion about the positions and clock speeds of the other satellites.

Because clock rates aren't something you can define at an instant in time. Take a photo of two clocks. Can you tell if they both tick at the same rate from that snapshot? No - one could have stopped, even. You need to look at two separate times, and then the ship and the satellite aren't co-moving for at least one of those.

 

[Dale]

Unless you're happy for the satellite to use the sphere-centred inertial frame (in which it is moving).

Which is a perfectly valid choice too. In fact, the GPS system uses essentially this approach.

 

[name123]

Because clock rates aren't something you can define at an instant in time. Take a photo of two clocks. Can you tell if they both tick at the same rate from that snapshot? No - one could have stopped, even. You need to look at two separate times, and then the ship and the satellite aren't co-moving for at least one of those.

So you could not simply know the positions given say the frame of reference of an observer in the centre of the sphere, and then use the equations to calculate it for a point in time for another frame of reference?

 

[Dale]

So you could not simply know the positions given say the frame of reference of an observer in the centre of the sphere, and then use the equations to calculate it for a point in time for another frame of reference?

That is the purpose of the transformation equations, like those I posted above. That is what you need to do to make your question be a well-defined question. (Either that or change the question to remove the undefined "in the satellite's frame")

 

[Ibix]

So you could not simply know the positions given say the frame of reference of an observer in the centre of the sphere, and then use the equations to calculate it for a point in time for another frame of reference?

Of course you can. But you haven't described that frame. You want "the satellite's reference frame", but there are an infinite number of coordinate systems that fit that description and no obvious criterion to prefer one over another. The only attempt you made to pick one (chaining together local inertial rest frames) doesn't work.

 

[name123]

Of course. But you haven't described that frame. You want "the satellite's reference frame", but there are an infinite number of coordinate systems that fit that description and no obvious criterion to pick one over another.

So consider a spaceship skimming past as described by Janus in post #55. There is a point where the satellite is at rest relative to the passing spaceship. So if you knew the positions from the frame of reference of an observer in the centre of the sphere, you could use the equations to calculate the positions of the satellites and their time dilation etc., for the frame of reference in which the passing spaceship is at rest with it at that point of time. A reason for favouring that inertial frame of reference for the satellite would be that it would be the one where the satellite is at that point of time. My question is why the answer regarding the description for that frame of reference at that point in time would not be the same for that satellite as the passing spaceship, or would it be?

 

[Ibix]

So consider a spaceship skimming past as described by Janus in post #55. There is a point where the satellite is at rest to the passing spaceship. So if you knew the positions from the frame of reference of an observer in the centre of the sphere, why could you not use those equations to calculate to calculate the positions of the satellites and there time dilation etc., for the frame of reference in which the passing spaceship is at rest with it at that point of time. A reason for favouring that inertial frame of reference for the satellite would be that it would be one where it is at rest at that point of time.

That's just a Lorentz transform. But the satellite is only instantaneously at rest in this frame so, as noted by @PeterDonis in #101, myself in #104, and by @Janus on the previous page, it doesn't really describe the satellite's perspective even instantaneously.

Edit: and you most definitely cannot chain two of these frames together. The simultaneity planes overlap, which is the same class of mistake as taking a street map, photocopying two pages, and taping the photocopies together without noticing that the maps overlap. Then asking if the streets really don't join up in the middle of the town.

 

[name123]

That's just a Lorentz transform. But the satellite is only instantaneously at rest in this frame so, as noted by @PeterDonis in #101, myself in #104, and by @Janus on the previous page, it doesn't really describe the satellite's perspective even instantaneously.

Why does it not describe it for that point of time?

 

[PeterDonis]

Why does it not describe it for that point of time?

Because there is no such thing as a frame for a single point of time. Frames of reference cover regions of spacetime--space and time.

 

[Ibix]

Why does it not describe it for that point of time?

You may wish to look at the edit to #110, which I think I made after you read it.

 

[name123]

Because there is no such thing as a frame for a single point of time. Frames of reference cover regions of spacetime--space and time.

But things can go in and out of rest with respect to that frame of reference can they not? And while they are at rest, can that frame of reference not be used for them?

 

[name123]

You may wish to look at the edit to #110, which I think I made after you read it.

Thanks I saw it (since you drew my attention to it), but did not totally understand it. I would not be trying to do any approximation, it would simply be that given the symmetry, like with the photos, the same thing could be done throughout the orbit, and the result would presumably be the same.

 

[PeterDonis]

But things can go in and out of rest with respect to that frame of reference can they not? And while they are at rest, can that frame of reference not be used for them?

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.

 

[Janus]

I apologise. I had assumed you were considering them to have been the same at the point the A series satellite was in the same frame of reference as the passing spaceship. I was assuming it would have been in the same frame of reference at that point of time (even if not for any period of time). The point of time that its velocity was equal to the passing spaceships and in the same direction. Was I mistaken?

Actually from you answer in post #93, I can tell that I was. What I am not clear on is why when it is in the same rest frame it comes to a different conclusion from the spaceship in the same rest frame.

I apologise. I had assumed you were considering them to have been the same at the point the A series satellite was in the same frame of reference as the passing spaceship. I was assuming it would have been in the same frame of reference at that point of time (even if not for any period of time). The point of time that its velocity was equal to the passing spaceships and in the same direction. Was I mistaken?

Actually from you answer in post #93, I can tell that I was. What I am not clear on is why when it is in the same rest frame it comes to a different conclusion from the spaceship in the same rest frame, regarding the other satellite positions at that point.

Inertial frame vs. non-inertial frame. The rocket ship is at rest with respect to an inertial frame and always remains so. The only frame that the satellite can be considered always at rest with respect to is an non-inertial one. Put another way, even though there is a instant where according to the ship, it and the satellite have exactly the same velocity, the satellite is still changing its velocity at that moment relative to the inertial frame the ship is at rest with respect to.

Let's consider an analogy. You have a ball suspended by a string at some height above the ground. From below, you toss an identical ball upwards,so that it just becomes equal with the height of the first ball at the top of its trajectory. At that instant, both balls are side by side and both have 0 velocity with respect to the ground.
However, the first ball is not changing its velocity at that moment, but the tossed ball is. The first ball is always feeling the full pull of gravity (if the ball were hollow, a test mass inside would settle towards the bottom of the ball), yet the tossed ball is in free-fall and would not. (a test mass inside the ball would show no tendency to settle in any preferred spot inside the ball while in the air).

The point being that there is a fundamental difference between these two balls even while side by side and motionless with respect to each other.
There is also a fundamental difference between what observers maintaining inertial motion vs those who are not will measure. It's not really intuitive as to why this is the case, but it is none the less true. I think this is part of your difficulty. Your intuition is telling you one thing, but relativity is saying something else.

For example, intuition wants to tell us that "now" is the same for everybody, But SR says that "now" for someone moving relative to you isn't always going to be "now" for you.

 

[russ_watters]

You seem to have mistakenly thought that I was discussing an A series satellite looking at B series satellite, but I was discussing an A series satellite looking at an A series satellite, as I thought I made clear in the post you were quoting from. At that point I was thinking that the orbits of the A series satellites would appear elliptical as it seems Janus also thought in post #55. But apparently that was wrong. According to Dale in post #79 at least.

Indeed I did. Buuuut, now I'm confused, because this seems too basic to be causing confusion: Of course the series A satellites see each other's clocks to be ticking at the same rate! They are keeping station!

The elliptical orbit/length contraction thing was for an external spaceship moving past them. It does not affect how they see eachvother.

If you had thought I was discussing an A series satellite looking at a B series satellite, then I would have thought that the one in front and the one behind appeared the same throughout the orbit, neither seeming to approaching or going away. Are you disagreeing with that?

Huh? Aren't they orbiting in opposite directions? Or did you make a typo?

 

[PeterDonis]

given the symmetry, like with the photos, the same thing could be done throughout the orbit

No, it can't. Once more: you cannot construct a valid "satellite's perspective" by somehow combining the individual inertial frames in which the satellite is momentarily at rest at individual points on its orbit. This cannot be done. You have been told this repeatedly, yet you persist in trying to do it. Which means, again, that this thread is going nowhere and is on the point of being closed.

 

[Ibix]

But things can go in and out of rest with respect to that frame of reference can they not? And while they are at rest, can that frame of reference not be used for them?

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.

 

[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.