Two spaceships travel away from the earth.

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Two spaceships are traveling away from Earth in opposite directions at speeds of 0.75 c each. To determine the rate at which the distance between them changes in the Earth's rest frame, the formula for relative velocity must be applied. Using the formula for two objects moving in opposite directions, the calculated relative speed is 1.5 c. However, this result is incorrect as it does not account for relativistic effects. The correct interpretation involves recognizing that the distance changes at a rate less than 1.5 c due to the principles of relativity.
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They go in opposite directions. In the rest frame of the earth, the speed of each spaceship is 0.75 c.

In the rest frame of the earth, what is the rate at which the distance between the two spaceships changes?

Carl
 
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Surely you should know the formula for this. If, in a given frame, two objects, moving in opposite directions, have speeds, relative to an object motionless in that frame, of v1 and v2 then their speeds, relative to one another in that frame is \frac{v_1+ v_2}{1+ \frac{v_1v_2}{c^2}}.
 
CarlB said:
In the rest frame of the earth, what is the rate at which the distance between the two spaceships changes?
1.5 c, of course.

(Halls answered a different question: What is the rate at which the distance between the ships changes in the rest frame of either ship.)
 
Oops. Thanks, Doc.
 
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