Moving mirrors

[geordief]

Suppose we have two mirrors in a gravity free vacuum.

Both are shaped identically and ,why not circular  and extremely thin.(and rigid)

 

They are very close to each other (separation is zero for practical purposes)

 

Mirror A emits a signal (any practical kind that would work in a vacuum) from its cog in the direction of Mirror B's cog.

The signal is reflected back and forth between the two mirrors cross  from that point onwards

 

The 2 mirrors move apart as a consequence. (the signal carries energy)

 

Is there a mathematical /physical description of this increasing separation over time as a function of the speed of the signal  ?

Is this a very complex problem ?

Can it be answered in as simple a way as possible so that I can understand what is involved?

Even better ,has it been brought up before somewhere?

Edited March 31, 2018 by geordief

[studiot]

Here are some thoughts to kick off your analysis.

 

Initially the mirrors (call them A and B) are co moving, so it does not matter which mirror frame you choose to work in.

At the instant mirror A emits a photon, momentum balance requires it to start moving away from mirror B and the photon starts travelling towards B.

From this point on frame A and Frame B are not the same.

 

So the first decision is, which frame do you wish to work in?

[geordief]

Mirror B's and I would want to know  the "state of play" after it had twice  received the signal.

I would also be interested in other stages of the scenario(would that be termed after x re-ransmissions?) and in the limit.