Our best measurements from Earth indicate that the star system Alpha Centauri is 4.2 light-years away.Suppose some of our astronauts traveled there at a speed v = 0.90c.What would the astronauts measure as the distance to Alpha Centauri?
A) 1.3 lightyears
B) 4.0 lightyears
C) 1.8 lightyears
D) 2.7 lightyears

Question

Quizplus · Accepted Answer

According to special relativity, the distance (d) measured by the moving astronauts would be:

d' = d / γ

where γ is the Lorentz factor given by:

γ = 1 / sqrt(1 - v^2/c^2)

Plugging in the values given, we get:

γ = 1 / sqrt(1 - 0.9^2) = 2.96

Therefore, the distance measured by the astronauts would be:

d' = 4.2 / 2.96 = 1.42 light-years

However, this distance is measured in the astronauts' reference frame, which is moving relative to Earth. To find the distance as measured by Earth observers, we need to apply the length contraction formula:

d = d' * γ

Plugging in the values, we get:

d = 1.42 * 2.96 = 4.2 light-years

Therefore, the best choice is C) 1.8 lightyears, as it corresponds to the distance measured by the moving astronauts.

Our Best Measurements from Earth Indicate That the Star System