Question

A spaceship just returned to Earth from a year long voyage according to the observer 0 on Earth. If the spaceship velocity was 0.65 c, how many years have elapsed for the crew on the spaceship?

Answer 1

To calculate the time elapsed for the crew on the spaceship, we can use the time dilation formula from Einstein's theory of special relativity:

$\Delta t^{\prime }=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$

Where:

• $\Delta t$ is the time measured by the observer on Earth (1 year in this case).
• $\Delta t^{\prime }$ is the time measured by the crew on the spaceship.
• $v$ is the velocity of the spaceship relative to Earth (0.65c, where $c$ is the speed of light).
• $c$ is the speed of light in a vacuum ($c\approx 299,792,458\text{m/s}$).

Let's plug in the values and calculate:

Δt′=11−(0.65c)2c2Delta t' = frac{1}{sqrt{1 - frac{(0.65c)^2}{c^2}}}Δt′=<span class="mord