Problem — Lorentz factor at 0.6c

Problem

A spaceship travels at $v = 0{,}6\,c$ relative to Earth. Calculate the Lorentz factor $\gamma$.

Solution

Given. $v = 0{,}6\,c \Rightarrow \dfrac{v^2}{c^2} = 0{,}36$.

Lorentz factor.

$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} = \frac{1}{\sqrt{1 - 0{,}36}} = \frac{1}{\sqrt{0{,}64}} = \frac{1}{0{,}8}$

$\ev{\gamma \approx 1{,}25}$

At $0{,}6\,c$ relativistic effects are already at the 25% level: times and lengths differ noticeably from their non-relativistic values.

Links

Topics: Special relativity Concepts: Time dilation Skills: Symbolic setup