A spacecraft travels along a straight line from the Earth to the Moon a distance of 3.84 * 10⁸ m.Its speed measured on Earth is 0.70 c.Determine the distance between the Earth and Moon if it were measured by a person on the spacecraft.

Question

Quizplus · Accepted Answer

Let's use the formula for length contraction:

L' = L / γ

where L is the length as measured on Earth, L' is the length as measured on the spacecraft, and γ is the Lorentz factor given by:

γ = 1 / sqrt(1 - v^2/c^2)

where v is the speed of the spacecraft and c is the speed of light.

Plugging in the numbers, we get:

γ = 1 / sqrt(1 - 0.70^2) = 1.71

L' = 3.84 x 10^8 m / 1.71 = 2.24 x 10^8 m

So the distance between the Earth and Moon as measured by a person on the spacecraft is 2.24 x 10^8 m, or 2.7 x 10^8 m (rounded to one significant figure). Therefore, the best choice is C.

A Spacecraft Travels Along a Straight Line from the Earth