Question

A nova is a sudden brief brightening of a star. An astronomer on Earth sees two novas occurring at the same time. Both novas are the same distance from Earth, 2.5x10^3 lightyears, but they are in exactly opposite directions. An observer on a spacecraft traveling 0.2c in the direction of one of the novas sees the same two novas. For the observer on the spacecraft how much time separates the two novas?

Answer 1

The position of the two novas are

and

According to Earth's observer, the two novas occur at the same time

By Lorentz transformation, the time in the spacecraft frame is

where

The difference in time of the two novas in the spacecraft's frame is

Using

Substituting values

Using 1ly/c=1y

The two novas are separated by 1021 years.