A spaceship travels from one planet to another (assume, for this problem, that t

Question

A spaceship travels from one planet to another (assume, for this problem, that the planets are in the same reference frame - at rest with respect to each other.) An observer on one of the planets measures the distance between the planets as 3 light years, and the time that the spaceship takes to go from one planet to the other as 4.5 years. a. How fast is the spaceship traveling in the planets' frame? b. How fast is the spaceship traveling in the spaceship's frame? c. How fast are the planets traveling in the spaceship's frame? d. How far apart are the planets in the spaceship's frame? e How long does the trip take in the spaceship's frame?

Explanation / Answer

One Light year is the distance travelled by light in one year.

a) Total distance between the planets , do= 3 light years = 3 years* c

speed of spaceship in planet's frame, v = distace/time = 3 years*c/4.5 years = 0.667c

b) speed of spaceship in spaceship's frame = 0

c) speed of planets in spaceship's frame, v = 0.667c

d) Distance travelled by spaceship in spaceship's frame, d= (1- v2/c2)1/2 * do = (1 - 0.6672)0.5 *3 = 2.24 light years

e) Time taken to complete the trip in spaceship's frame = d/v = 2.24/0.667 =3.35 years

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