A starship navigator measures the distance between the Earth and the Sun. If the ship is moving at a speed of 0.90c, instead of obtaining 93 million miles, the navigator measures a distance (in millions of miles) of
A)41.
B)30.
C)80.
D)215.
E)90.

Question

Quizplus · Accepted Answer

Due to the effects of length contraction in special relativity, the distance measured by an observer moving at a significant fraction of the speed of light (0.90c) will be shorter than the distance measured by a stationary observer. The contracted length L is given by L = L0 * sqrt(1 - v^2/c^2), where L0 is the proper length (93 million miles), v is the velocity (0.90c), and c is the speed of light. Calculating this gives approximately 41 million miles.

A Starship Navigator Measures the Distance Between the Earth and the Sun