- #1
Jufro
- 92
- 8
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}{c2*(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.