Question

A spacecraft is moving at a speed of 0.630 c relative to the earth. part a what is the ratio of the length of the spacecraft, as viewed through a telescope on earth, to its length when measured after landing on earth? (assume that the spacecraft is moving at a right angle to the line of observation.)

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Answer 1

The length of the spacecraft as viewed through a telescope on Earth can be calculated using the Lorentz transformation formula. The formula takes into account the spacecraft's relative speed to Earth and the Lorentz factor.

Step-by-step explanation:

The length contraction phenomenon is described by the Lorentz transformation formula, which relates the length of an object in one frame of reference to its length in another frame of reference moving at a relativistic speed relative to the first.

In this case, the spacecraft is moving at a speed of 0.630c relative to the Earth. According to the Lorentz transformation formula, the length of the spacecraft as viewed through a telescope on Earth is given by:

L' = L / γ

where L' is the length of the spacecraft as viewed from Earth, L is the actual length of the spacecraft, and γ is the Lorentz factor given by:

γ = 1 / sqrt(1 - v^2 / c^2)

Substituting the values into the formulas, we can calculate the length ratio.