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 = 0.95 c.What would the astronauts measure as the distance to Alpha Centauri?
A)4.0 lightyears
B)2.7 lightyears
C)1.9 lightyears
D)1.3 lightyears

Question

Quizplus · Accepted Answer

According to special relativity, length contraction occurs when an object is moving relative to an observer. The equation for length contraction is:

L = L0/γ

where L is the contracted length, L0 is the rest length, and γ is the Lorentz factor, which depends on the relative velocity of the object and the observer.

In this case, the rest distance to Alpha Centauri is 4.2 lightyears. If the astronauts are traveling at 0.95 c, then γ = 1/√(1-(0.95)^2) = 3.2.

Plugging in the values, we get:

L = 4.2/3.2 = 1.3 lightyears

Therefore, the distance to Alpha Centauri as measured by the astronauts would be 1.3 lightyears. The best choice is D.

Our Best Measurements from Earth Indicate That the Star System