Question

If astronauts could travel at v = 0.960c, we on Earth would say it takes (4.20 / 0.960) = 4.67 years to reach Alpha Centauri, 4.38 lightyears away. The astronauts disagree.

(a) How much time passes on the astronauts' clocks?
  years
(b) What is the distance to Alpha Centauri as measured by the astronauts?
  light-years

Answer 1

Given :-

v = 0.960c,

x = 4.38c,

t = 4.67 yr

The traveler's perspective of speed & distance during near-light speed travel can be found by multiplying by the Lorentz factor, given by:

γ = 1/√(1 - v^2/c^2)

γ = 1/√(1 - (0.960c)^2 / c^2) = 3.57

(a)

Traveler time is:
t' = t/γ = 4.67/3.57 = 1.308 years

(b)

Traveler distance is:
x' = x/γ = 4.38/3.57 = 1.2269 light-years