Jim and John are twins. Jim stays on Earth but John goes on a space ship which travels at 0.2c. If 10 years pass for Jim, how much time does John think have passed on his spaceship?

Solution

John travels at 0.2c, where c is the speed of light. Divide the speed of the spaceship by c so that leaves 0.2. Square this so that leaves 0.04. Subtract this from 1 so that leaves 0.96. Take the square root. That leaves 0.98. Thus if 10 years pass for Jim on Earth, John only thinks 9.8 years have passed on the spaceship.

What if the spaceship were to travel at 0.8c?

Now divide the speed of the spaceship by c so that leaves 0.8. Square this, so that leaves 0.64. Subtract from 1 so that leaves 0.36. Take the square root, so that leaves 0.6. Thus if 10 years pass for Jim on Earth, only 6 years pass for John's spaceship travelling at 0.8c.