Answer to Question #192443 in Physics for Harry

Question

You decide to travel to a star 62 light-years from Earth at a speed that tells you the distance is only 25 lightyears. How many years would it take you to make the trip?

Answer 1

The equation for the contracted distance:

$$L=L_0\sqrt{1-\frac{v^2}{c^2}}.$$

Express the velocity $v$:

$$v=c\sqrt{1-\frac{L^2}{L_0^2}}.$$

The time required to pass distance $L$ at speed $v$:

$$t=\frac Lv=\frac{L}{c\sqrt{1-(L/L_0)^2}}=861.545·10^6\text{ s},\\\space\\ t=27^\text y 3^\text m26^\text d.$$