Astronomers often detect stars that are rotating extremely rapidly,known as neut

Question

Astronomers often detect stars that are rotating extremely rapidly,known as neutron stars. They are believed to have been formed fromthe collapse of a larger star under its own gravitationalattraction. Suppose a star is the same size as the Sun (radius6.96E8 m), but two times as heavy, and it rotates 1 revolutionevery 10 days. If it were to undergo gravitational collapse to aneutron star of radius 10 km, how many revolutions per second wouldit spin? Assume the star is a uniform sphere at all times.

Explanation / Answer

According to Kepler's third law (T^2/r^3) = (T1^2/r1^3) or T1^2 = (T^2/r^3) * r1^3 or T1 = (r1/r)^(3/2) * T r1 = 10 km = 10 * 10^3 m r = 6.96 * 10^8 m T = 1 rev/10 days = 1 * (1/10 * 24 * 60 * 60) rev/sec = 1.15 *10^-6 rev/s

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