In 2047, NASA sends the first spaceship to Alpha Centauri, the closest star outs
ID: 1274181 • Letter: I
Question
In 2047, NASA sends the first spaceship to Alpha Centauri, the closest star outside our solar system (at 4 light-years distance). Assume the spacecraft can go at 80% of the speed of light (relative to Earth). Ignoring the (short) periods of acceleration and deceleration at each end of the trip, explain why the astronauts age by less than what an Earth-based observer would expect for the trip. (How many years would the trip take, according to Earth? How many years according to the astronauts?) How can the astronauts explain the fact that they covered a distance of 4 lightyears in less than 4 years? I.e., how would THEY describe the trip, from their own reference frame?
Explanation / Answer
time according to earth = 4/(.8)= 5 years
but this distance will be contracted for astronauts
L = 4*sqrt(1-.8^2)=2.4
so time = 2.4/0.8 = 3 years for astronauts