A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from Earth, how far is the star as measured from the moving spaceship?
A) 2.7 ly
B) 1.9 ly
C) 1.6 ly
D) 1.2 ly
E) 0.96 ly

Question

Quizplus · Accepted Answer

The correct answer is E.The distance from the spaceship to the star is 1.6 ly as measured from Earth. The spaceship is moving toward the star at a speed of 0.80 c. The distance from the spaceship to the star as measured from the moving spaceship is given by the following equation:$$d' = d/\gamma$$where:* d' is the distance from the spaceship to the star as measured from the moving spaceship* d is the distance from the spaceship to the star as measured from Earth* γ is the Lorentz factorThe Lorentz factor is given by the following equation:$$\gamma = 1/\sqrt{1 - v^2/c^2}$$where:* v is the speed of the spaceship* c is the speed of lightSubstituting the given values into the equations, we get:$$d' = 1.6 ly / 1.667 = 0.96 ly$$

A Spaceship Is Observed from the Earth to Be Moving