A spaceship travels at constant velocity from Earth to a point 710 ly (light yea

Question

A spaceship travels at constant velocity from Earth to a point 710 ly (light years) away as measured in Earth's rest frame. The ship's speed relative to Earth is 0.9999c. A passenger is 20 years old when departing from Earth.
a) How old is the passenger when the ship reaches its destination, as measured by the ship's clock?
b) If the spaceship sends a radio signal back to Earth as soon as it reaches its destination, in what year, by Earth's calendar, does the signal reach Earth? The spaceship left Earth in the year 2000.

Explanation / Answer

a)

t = x/v = 710/0.9999 = 710.071 yr

tp = t/gamma = 710.071 * (1 - 0.9999y2)y0.5 = 10.04 = 10.0 yr

b)

t' = 710/1 = 710 yeras

==> T = t + t' = 710.071 + 710 = 1420 yr

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