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 Ă— 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]