Posted: Aug 05, 2016 6:59 am
Like Thommo, I'm struggling a little to understand your question. Maybe this will help; apologies if it doesn’t in fact address your question.
An example of something travelling at a very high speed that we observe at a great distance might be a star surrounded by a halo of matter ejected in an earlier event, which then goes supernova. The first thing we observe will be the flash from the supernova itself; then, after a little while, the light will reach the halo, and for a short period of time we can observe an illuminated ring surrounding the star. The delay between the initial flash and the brightening of the halo represents the time taken for the light to travel, and because we know how fast light travels, we can calculate how far away the supernova is by measuring that delay.
Of course we know that we’re not observing these events in real time: if the supernova is, say, 100,000 light years away, then these events actually occurred 100,000 years ago; but that doesn’t matter for our purposes, because the only thing that matters is the time that elapses between the initial flash and the appearance of the illuminated ring.
That only works, strictly, if the travel that we are observing is at right angles to our line of sight. We have to be very careful where that is not the case. For instance (and this is an example brought up a few months ago by another poster), consider a jet of matter that has been ejected by an active galactic nucleus, is travelling at close to the speed of light at a small angle to our line of sight (it will just miss us if it carries on unabated), and is emitting light as it goes. If we observe the light that arrives on Earth at two different points in time, A and B, and estimate the distance across the sky between the two places at which the light was emitted (assuming we know from other methods how far away the jet is from us), we can get wildly inaccurate results for the jet’s transverse motion if we don’t make an adjustment for the radial motion. We have to take into account that the light that we observe at A was emitted much further away than the light we observe at B, and it has therefore taken longer to travel the transverse distance across the sky than the delay between times A and B.
An example of something travelling at a very high speed that we observe at a great distance might be a star surrounded by a halo of matter ejected in an earlier event, which then goes supernova. The first thing we observe will be the flash from the supernova itself; then, after a little while, the light will reach the halo, and for a short period of time we can observe an illuminated ring surrounding the star. The delay between the initial flash and the brightening of the halo represents the time taken for the light to travel, and because we know how fast light travels, we can calculate how far away the supernova is by measuring that delay.
Of course we know that we’re not observing these events in real time: if the supernova is, say, 100,000 light years away, then these events actually occurred 100,000 years ago; but that doesn’t matter for our purposes, because the only thing that matters is the time that elapses between the initial flash and the appearance of the illuminated ring.
That only works, strictly, if the travel that we are observing is at right angles to our line of sight. We have to be very careful where that is not the case. For instance (and this is an example brought up a few months ago by another poster), consider a jet of matter that has been ejected by an active galactic nucleus, is travelling at close to the speed of light at a small angle to our line of sight (it will just miss us if it carries on unabated), and is emitting light as it goes. If we observe the light that arrives on Earth at two different points in time, A and B, and estimate the distance across the sky between the two places at which the light was emitted (assuming we know from other methods how far away the jet is from us), we can get wildly inaccurate results for the jet’s transverse motion if we don’t make an adjustment for the radial motion. We have to take into account that the light that we observe at A was emitted much further away than the light we observe at B, and it has therefore taken longer to travel the transverse distance across the sky than the delay between times A and B.