Question

The radius of Earth is 6370 km in the Earth reference frame. The cosmic ray is moving at 0.880Co relative to Earth.

a. In the reference frame of a cosmic ray how wide does Earth seem along the flight direction?
b. In the reference frame of a cosmic ray how wide does Earth seem perpendicular to the flight direction?
Express your answer with the appropriate units.

Answer 1

Answer:

6052114.67492 m

$12.742\times 10^{6}\ m$

Explanation:

v = Velocity of cosmic ray = 0.88c

c = Speed of light = $3\times 10^8\ m/s$

d = Width of Earth = Diameter of Earth = $12.742\times 10^{6}\ m$

When the cosmic ray is moving towards Earth then in the frame of the cosmic ray the width of the Earth appears smaller than the original

This happens due to length contraction

Length contraction is given by

$d_e=d\sqrt{1-\frac{v^2}{c^2}}\\\Rightarrow d_e=12.742\times 10^{6}\sqrt{1-\frac{0.88^2c^2}{c^2}}\\\Rightarrow d_e=6052114.67492\ m$

The Earth's width is 6052114.67492 m

Contraction only occurs in the cosmic ray's frame of reference in the direction of the ray. But in perpendicular direction the width remains unchanged.

Hence, the width is $12.742\times 10^{6}\ m$