Our best measurements from Earth indicate that the star system Alpha Centauri is 4.2 lightyears away.Suppose some of our astronauts traveled there at a speed v = 0.80c.What would the astronauts measure as the distance to Alpha Centauri?
A)3.1 lightyears
B)7.0 lightyears
C)8.8 lightyears
D)2.5 lightyears
E)2.7 lightyears

Question

Our best measurements from Earth indicate that the star system Alpha Centauri is 4.2 lightyears away.Suppose some of our astronauts traveled there at a speed v = 0.80c.What would the astronauts measure as the distance to Alpha Centauri?
A)3.1 lightyears
B)7.0 lightyears
C)8.8 lightyears
D)2.5 lightyears
E)​2.7 lightyears

Quizplus · Accepted Answer

Due to the effects of length contraction in special relativity, the distance measured by astronauts moving at a significant fraction of the speed of light (in this case, 0.80c) would be shorter than the distance measured by observers at rest relative to the stars. The formula for length contraction is L = L0 * sqrt(1 - v^2/c^2), where L0 is the rest length (4.2 lightyears), v is the velocity of the astronauts (0.80c), and c is the speed of light. Plugging in the values, we get L = 4.2 * sqrt(1 - (0.80)^2) = 4.2 * sqrt(1 - 0.64) = 4.2 * sqrt(0.36) = 4.2 * 0.6 = 2.52 lightyears, which rounds to 2.5 lightyears.

Our Best Measurements from Earth Indicate That the Star System