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?

Respuesta :

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

[tex]l = l_0 \sqrt{1-\frac{v^2}{c^2}}[/tex]

Where

[tex]l_0[/tex]= Relative length

v = Velocity of the spaceship

c = Speed of light

Replacing with our values we have that

[tex]l = l_0 \sqrt{1-\frac{v^2}{c^2}}[/tex]

[tex]l = 1.2*10^{11} \sqrt{1-\frac{0.8c^2}{c^2}}[/tex]

[tex]l = 1.2*10^{11} \sqrt{1-0.8^2}[/tex]

[tex]l = 7.2*10^{10}m[/tex]

Therefore the distance between Mars and Venus measured by the Martin is [tex]7.2*10^{10}m[/tex]