Question

In an attempt to reduce the extraordinary long travel times for voyaging to distant stars, some people have suggested traveling close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000kg rocket to move so fast that you age only 20 years during the round trip.
How fast must the rocket travel relative to earth?

Answer 1

You can calculate velocity V by simple formula;
velocity=distance/time
\[V=\frac{ 430\times2\times9.4607\times10^{15} }{ 20\times365\times24\times60\times60 }\]
where, 1 light year=9.4607*10^15meters
and since its a round trip hence 430 multiplied by 2.
then use the formula,
\[u _{x}'=\frac{ u _{x} -V}{ 1-\frac{ u _{x}V }{ c ^{2} } }\]