# How to calculate distance of earth when observer in space ship which travel with speed of light

Suppose we have two observer one is on earth and other is in space ship. If we launch the space craft and a light ray at the same time from earth, after 1 minute, what will be total distance travelled by the light rays which launch from earth?

The observer from earth calculates it to be $$60\times300000$$ km. But because of speed of light the time is slow for the observer in the space craft, suppose observer from space craft spends 55 second however at the same time the observer from earth spend 60 second. But then how observer from space craft count the distance as he spend 55 second? For him, the total distance was $$55\times300000$$ km. But at same time observer from earth count it $$60\times300000$$ km. Is it not a paradox.

But because of speed of light the time is slow for observer who is in space craft

No.

The whole point of relativity is that everyone's local clocks and rulers do not change according to them.

So the person in the ship still measures 60 seconds, and agrees with the person on the ground.

The two observers will not agree on what the other person's clock is saying, but that has no effect on measurements you make with your clock.

• the person in the ship will not measure 60 seconds because of lenght contraction! – Wolphram jonny Nov 6 '18 at 21:18
• The OP clearly states its 55 seconds. Do you think the length contraction will be different than the time dilation? – Maury Markowitz Nov 6 '18 at 21:54
• I do not understand your question, they are different things – Wolphram jonny Nov 6 '18 at 21:55
• I think you do not understand relativity but pretend you do – Wolphram jonny Nov 6 '18 at 21:58
• make a minkowski diagram and see by yourself how wrong is your answer – Wolphram jonny Nov 6 '18 at 21:59

Let us say that it takes a minute for the light, as measured by the person on earth, to reach a detector 1 minute light away. The person in the ship will experience lenght contraction, so to him it took less time for the light to travel to the planet. In addition, assume that both persons waive their hands when the light get to the detector. The observer on earth will notice a lack of synchrony between the time time light gets to the detector and the time the person in the ship waves his hand. He will see that the person in the ship waves his hand before the light gets to the detector, because the two observers disagree on the simultaneity of the events