Two spaceships travel away from the earth.

[CarlB]

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

 

[HallsofIvy]

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 $$\frac{v_1+ v_2}{1+ \frac{v_1v_2}{c^2}}$$.

 

[Doc Al]

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.)

 

[HallsofIvy]

Oops. Thanks, Doc.