Question

The length of a rocket is measured to be 6.0 m by an observer on Earth as it moves with respect to the Earth at a speed of 0.8c. What is the length of the rocket as measured by an astronaut inside the rocket?

Answer 1

For the "outside" observer the length

$$L$$

of a moving rocket is

$$L=L_0\cdot \sqrt{1-v^2/c^2},$$

where

$$L_0$$

- the length measured in the inertial frame by an observer resting relative to the rocket. Thus

$$L_0=\frac{L}{\sqrt{1-v^2/c^2}}=\frac{6}{\sqrt{1-(0.8c)^2/c^2}}=10 \text{ m}.$$