Question

A Martian leaves Mars in a spaceship that is heading to Venus. On the way, the spaceship passes earth with a speed v = 0.80c relative to it. Assume that the three planets do not move relative to each other during the trip. The distance between Mars and Venus is 1.20 × 1011 m, as measured by a person on earth. What does the Martian measure for the distance between Mars and Venus?

Answer 1

To find the relative distance from one point to another it is necessary to apply the Relativity equations.

Under the concept of relativity the distance measured from a spatial object is given by the equation

$l = l_0 \sqrt{1-\frac{v^2}{c^2}}$

Where

$l_0$= Relative length

v = Velocity of the spaceship

c = Speed of light

Replacing with our values we have that

$l = l_0 \sqrt{1-\frac{v^2}{c^2}}$

$l = 1.2*10^{11} \sqrt{1-\frac{0.8c^2}{c^2}}$

$l = 1.2*10^{11} \sqrt{1-0.8^2}$

$l = 7.2*10^{10}m$

Therefore the distance between Mars and Venus measured by the Martin is $7.2*10^{10}m$