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165.

Problem 21.11 (RHK)

To circle the Earth in low orbit a satellite must have a speed of Suppose that two such satellites orbit the Earth in opposite directions. We have to find (a) their relative speed as they pass using the classical Galilean transformation equation; (b) the fractional error that is made because of not using the correct relativistic transformation equation.

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(a)

According to classical Galilean transformation equations as the two satellites are moving with equal speed, v, in opposite directions, their relative speed will be the arithmetic sum

(b)

According to the relativistic velocity addition their relative speed is given by the equation

Therefore, the fractional error in using the Galilean velocity addition is