- #1

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## Homework Statement

This is not a HW questions but from another thread.

https://www.physicsforums.com/showthread.php?p=4495692&posted=1#post4495692

The statement I made was that if z increases for a source, then it is accelerating away. Or, it could that if z is constant then the sources moves with constant velocity away from an observer.

I just need to know where my logic is breaking down and what direction I can try to find the right answer.

## Homework Equations

I took the equation:

1+z = [itex]\sqrt{\frac{1+v/c}{1-v/c}}[/itex]

## The Attempt at a Solution

So taking d/dt on both sides I end up with:

dz/dt = 1/2 [itex]\frac{1+v/c}{1-v/c}

^{-1/2}[/itex]*[itex]\frac{(1/c dv/dt)*(1-v/c)-(1/c dv/dt)*(1+v/c)}{(1-v/c)

^{2}}[/itex]

Re-writting this:

dz/dt= [itex]\frac{-v* dv/dt}{c

^{2}*(z+1)*(1-v/c)

^{2}}[/itex]

Since the first term is negative (from the minus sign) and v is positive, then a positive dz/dt would require that dv/dt is negative or that the sources acceleration is radially

*inward*when I had suspected outward.

This may be a result of me using the flat-spacetime (Minkowski metric) but I am not sure. Can anyone point me in the right direction.

Please and thank you.