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Earth and Planet X are in the same inertial frame of reference. In the Earth-Planet X...

Earth and Planet X are in the same inertial frame of reference. In the Earth-Planet X reference frame the distance between Earth and Planet X is 12 ly (light years). A spaceship travels at a constant speed from Earth to Planet X. In the reference frame of the spaceship, it takes 15 years to reach Planet X. What is the speed of the spaceship relative to Earth(as a fraction of the speed of light)?

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Answer #1

Let be the velocity of the spaceship relative to the Earth-Planet X reference frame. If is the distance between earth and the planet X in the earth-planetX reference frame, then by length contraction this distance will be observed as by the spaceship.

The spaceship will cover the distance in time with velocity

Squaring on both the sides

Using and

We get

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