Time Dilation

Time Dilation Equation §

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

Practice §

A new spacecraft, the Cougar Zoomer 3000, can travel at a 99% of the speed of light. The distance to Vega, the constellation Lyra, is 25.3 ly away. Tiki Barber travels to Vega on the spacecraft while his twin brother Rhone Barber stays on Earth.

1. How long does the trip take from the point of view of Ronde?

$$\begin{array}{rlr}\frac{25.3\text{ ly}}{\Delta t}& =0.99c& \\ \frac{25.3\text{ ly}}{0.99c}& =\Delta t& =25.5\text{ years}\end{array}$$

2. How much has Tiki aged when he arrives at Vega?

$$\begin{array}{rl}25.5\text{ y}& =\frac{\Delta t_i}{\sqrt{1-\frac{(.99c{)}^2}{c^2}}}\\ \Delta t& =3.59\text{ years}\end{array}$$

Length Contraction §

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