# Relativistic kinematics: when will a photon and spaceship meet?

Hello to everyone! I cane across this problem and since I have no training in SR I can't solve it on my own, That is why I would very mutch apprecitate any help I could get.

The problem:
A photon and a spaceship simultaneously start at planet A and the travel in paralal towards planet B. The spaceship travels at speed c/n where n>1. The distance between A and B is d. When the photon reaches planet B it gets reflected back to A by a mirror.

The Question:
At what time will the rochet and the spaceship meet since started from planet A?
The clock to measure time is inside the rocket it's self.

Attemting a solution (propably wrong)
The clock is on the spaceship, therefore we are looking at the system from the spaceships frame of reference.
Lorentz-contraction occours :
d' = d √1-(v^2/c^2)

The maximum distance the photon can travel is 2d ; from A to B then back. (the spaceship could move with extreemly slow speeds, almost standing.)
The maximum distance the spaceship can make, is d ; from A to B (because the photon turns around at B making this point theoretically the farthest point where they can meet.)

If I calculate the the time needed for the photon to travel that distance taking into account the Lorentz-contraction, and then subtract the time needed for the rocket to travel the max distance, i get the time of meeting?
Photon: t= 2d'/c
Spaceship: t=d'/(c/n)
Therefore: t=2d'/c - d'/(c/n) Is this correct?
Thank you.

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TSny
Homework Helper
Gold Member
Hello CybrSpace and welcome to PF!

I don't believe your analysis is correct. I suggest you draw a couple of sketches of the situation in the frame of reference of the ship.

For your first sketch, draw the locations of the ship, photon, and planets at the instant the photon leaves planet A. Indicate the distance d' on the picture.

Then draw a sketch showing the locations of these objects at the instant the photon arrives at planet B. Since you are drawing the picture in the frame of reference of the ship, keep in mind which objects change their position in the two drawings and which objects don't move. Indicate the distance of the photon from the ship and the distance of the photon from the original position of planet B in your second picture. Try to relate these two distances to d'.

Orodruin
Staff Emeritus
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Gold Member
2018 Award
In the rest frame of the space ship, B is moving and you have to take this into account. I would suggest first finding the time required in the rest frame of A and B and then relating this to the time on the space ship.