I Satellite Orbit synchronization

[name123]

Again, this is not what happens or is observed. If a satellite is watching another satellite's clock (or via radio), when they are moving apart each will observe the other's clock to be running slower and when they are approaching each will observe the other's clock to be running faster.

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.

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?

 

[Ibix]

No you I was not asking what a satellites clock shows at the same time as another satellites clock reads 00.01, 00.02 etc. I had tried to explain what I meant in post #82 when I wrote

The satellites in the same chain always look to be in the same place as seen by one of their number, but this comes under what I said in #88 - you can work out what a camera sees. You still cannot back out from that to get "where they really are now" because "where they really are now" depends on what you mean by "now".

 

[Janus]

My surprise with your visualisation in post #55 was that you were envisaging length contraction not just in the x direction, but also in the y direction perpendicular to it. I did not realize there would be length contraction in the y direction also. I was imagining it without length contraction in the y direction, and wondered how if there was no length contraction in the y, such that the satellites either side of the satellite opposite the one whose perspective it is where the same distance from the spaceship as the ones either side of the satellite whose perspective it is, how it could be explained them receiving the light at the same time if they were thought to be in the position you depicted. So a confusion on my part. The answer presumably being that there would be considered to be length contraction in the y. Anyway, as I mentioned I did not realize there would be length contraction in the y direction as it isn't mentioned in the special relativity equations.

The the image is from the frame of the rocket which is just skimming the orbit, going right to left, while the satellites are orbiting in a clockwise direction. His speed is equal to the orbital speed of the satellite he is passing at the moment. ( the bottom most blue dot. ) As measured from his frame, The satellite he is next to at that moment has a relative speed of 0 with respect to himself . The satellite on the opposite of the orbit would have an a velocity of 2v/(1+v^2/c) assuming v is the orbital velocity. (in Newtonian Physics it would be 2v.)
So let's say that the 0ribital velocity as measured from the center of the orbit is 0.6c. Then the spaceship will measure the velocity of the satellite next to it at that moment to have a relative velocity of 0. and the satellite on the opposite side as having a relative velocity of 0.8826c. (this also means that he will measure the respective speed between these satellites and the center of the orbit as being different.)
Now imagine that each of these satellites has a satellite just leading and just trailing it. as long as they are close to each other, the spaceship can consider each group of three satellites as all having close to an equal velocity with respect to him. ( the near group would all have 0 velocity and the far group would all have a velocity of 0.8826. This means that he will measure no length contraction between the nearby satellites and a length contraction of 0.47. Thus he will measure the distance between the further satellites as being less than that for the nearby satellites (even though if you were to ask the satellites themselves they would all give the same answer as to their distance apart).

But what about the satellites 90° away in the orbit? For the ship, these satellites have two velocity components, 0.6 in the x direction due to the relative velocity between the ship and the center of the orbit, and a component in the y direction due to the satellite's orbital velocity. The y velocity component will work out to be .0.48c. For a group of three satellites at this these points of the orbit, the ship would measure a length contraction between them of 0.877. ( there would also be a 0.8 x-axis length contraction, but since each group of three satellites is in a nearly straight line along the y axis, it wouldn't be easily noticeable.)

So relative to the spaceship frame, the satellites have a mixture of various x and y relative velocities and thus a mixture of x and y-axis length contraction affecting the measured distance between them and the distance between adjacent satellites vary as they travel around an orbit.

Three points of importance:

I'm using the "merry-go-round" model rather than the "orbiting due a gravity field" model to avoid having to deal with the extra complications gravity brings.

This isn't what the spaceship would visually perceive at that moment, rather what he would determine were the positions of those satellites at that moment (by taking what he sees, and working backwards while compensating for light travel time, aberration, etc. )

These are not the relative positions between satellites the the satellite the ship is adjacent to would measure. Even though it is at that moment at rest with respect to the spaceship and seeing exactly the same light, it would come to a different conclusion of how the other satellites are positioned relative to itself.

As already noted, due to the fact that the satellite is in an non-inertial frame (due to its circular motion) and the spaceship is in an inertial frame, the two will come to different conclusions despite the fact that they are momentarily at rest with respect to each other at that moment.
For example, for the spaceship, a clock sitting at the center of the orbit will run slow by a factor of 0.8, but for the satellite, the center clock runs fast by a factor of 1.25.

 

[Dale]

I am not quite clear on what the different symbols mean

Sorry, I should have been clear. The capital letters are coordinates in the ship's inertial frame. The lower case letters are coordinates in some possible examples of the satellite's frame. Don't take these specific transforms too seriously, I was just throwing together examples, not recommending either of them. You need to sit down and decide what specific of all possible transforms you wish to consider when you use the phrase "the satellite's perspective" or "the satellite's frame".

but are you suggesting that if one of those transformations were chosen, that you could tell from pictures taken from one of the satellites (imagine none contain clocks, and so no clock can be pictured), that you could tell where it was in its orbit?

No, I was giving an example of how the reference frames are arbitrary and some may not result in circular orbits. I was not making any claims about pictures or observations, I am still trying to get you to define what you mean by "the satellite's frame". In the first transform the orbits are circular and in the second they are elliptical.

This is why you cannot just automatically say that they are elliptical, you need to actually write down the transform and check. The observations will be the same in either case, but depending on the details of your transform the same observations will result from different shapes.

 

[Janus]

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.

My image is for what the spaceship, in an inertial frame and traveling at the same velocity as an A series satellite, would determine what the relative positions of the A series satellites as having, not what an A series satellite would determine.

 

[name123]

The satellites in the same chain always look to be in the same place as seen by one of their number, but this comes under what I said in #88 - you can work out what a camera sees. You still cannot back out from that to get "where they really are now" because "where they really are now" depends on what you mean by "now".

Ok, so by pictures or film footage they always look the same. So if the sphere did have markings, and you knew the size of the sphere and the size of the satellites and the altitude the satellites were orbiting at according to an observer in the centre of the sphere: Is it being said that this information would not be enough for an observer on one of the satellites to calculate the doppler effect, and thus not to account for that in the observations? Or is it perhaps that it would be possible to even accounting for the doppler effect but that would not provide the information as to where they "really" are in relation to you the observer?

 

[name123]

My image is for what the spaceship, in an inertial frame and traveling at the same velocity as an A series satellite, would determine what the relative positions of the A series satellites as having, not what an A series satellite would determine.

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.

 

[jbriggs444]

in relation to you the observer?

An observer does not uniquely define a reference frame. For flat space-time and inertial observers, there is an obvious way to define an associated reference frame. But there observers do not qualify.

at the point the A series satellite was in the same frame of reference as the passing spaceship.

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

 

[Ibix]

Ok, so by pictures or film footage they always look the same. So if the sphere did have markings, and you knew the size of the sphere and the size of the satellites and the altitude the satellites were orbiting at according to an observer in the centre of the sphere: Is it being said that this information would not be enough for an observer on one of the satellites to calculate the doppler effect, and thus not to account for that in the observations?

That specifies the ephemerae of the satellites' orbits in the sphere-centred inertial frame. You can use this information to derive the positions of the satellites in that frame, yes. But that is not the rest frame of any satellite; you still haven't specified that, and until you do you cannot say how the satellite interprets things. Unless you're happy for the satellite to use the sphere-centred inertial frame (in which it is moving).

Or is it perhaps that it would be possible to even accounting for the doppler effect but that would not provide the information as to where they "really" are in relation to you the observer?

There are an infinite number of ways of accounting for the Doppler, depending on which choice of coordinates you make. As has been said about forty times now!

 

[name123]

That specifies the ephemerae of the satellites' orbits in the sphere-centred inertial frame. You can use this information to derive the positions of the satellites in that frame, yes. But that is not the rest frame of any satellite; you still haven't specified that, and until you do you cannot say how the satellite interprets things. Unless you're happy for the satellite to use the sphere-centred inertial frame (in which it is moving).
There are an infinite number of ways of accounting for the Doppler, depending on which choice of coordinates you make. As has been said about forty times now!

Well 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.

 

[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.