An alien spaceship traveling at 0.520c toward the Earth launches a landing craft

Question

An alien spaceship traveling at 0.520c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.780c relative to the mother ship (as measured by aliens on the mother ship). As measured on the Earth, the spaceship is 0.250 ly from the Earth when the landing craft is launched. (a) What speed do the Earth-based observers measure for the approaching landing craft? (b) What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens (mother ship)? (c) What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? (d*) What travel time is required for the landing craft to reach the Earth as measured by Earth-based observers? (e*) what travel time is required for the landing craft to reach the Earth as measured by those on the landing craft?

Explanation / Answer

a)
ux = (0.520c + 0.780c)/(1+(0.520)(0.780))
= 0.925c

b)
L = Lp/y
L = (0.250)sqrt(1-(0.520)^2)
= 0.213 Ly

c) t = 0.213 Ly / (0.520c + 0.780c)
= 0.164 yr

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