Two spaceships travel at a speed of 10.9 km/s relative to the Earth in a directi

Question

Two spaceships travel at a speed of 10.9 km/s relative to the Earth in a direction awayfrom the Earth along a line joining the Earth and Sun. The two spaceships are incommunication with one another and, according to their determinations, their clocks aresynchronized. According to observers at rest with respect to the Earth-Sun system, however,the clocks appear to differ by 7.40 ns. What is the distance d separating the two ships asdetermined by observers at rest in the solar system? Thorough answer please Two spaceships travel at a speed of 10.9 km/s relative to the Earth in a direction awayfrom the Earth along a line joining the Earth and Sun. The two spaceships are incommunication with one another and, according to their determinations, their clocks aresynchronized. According to observers at rest with respect to the Earth-Sun system, however,the clocks appear to differ by 7.40 ns. What is the distance d separating the two ships asdetermined by observers at rest in the solar system? Thorough answer please Thorough answer please

Explanation / Answer

t1 = (t1 – x1v/c2), t2 = (t2 – x2v/c2)

where = (1-v2/c2)1/2

t2 - t1 = ((t2 – t1) –(x2 – x1)v/c2)

According to their determinations, their clocks are synchronized

So, t2 - t1 = 0

Given t2 – t1 = 7.40 ns and v = 10.9 km/s

So, x2 – x1 = (t2 – t1)c2/v = 1.92×10-4 m

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