Many pulsars radiate radio frequency or other radiation in a periodic manner and are bound to a companion star in what is known as a binary pulsar system. In 2004, a double pulsar system, PSR J0737-3039A and J0737—3039B, was discovered by astronomers at the Jodrell Bank Observatory in the United Kingdom. In this system, both stars are pulsars. The pulsar with the faster rotation period rotates once every 0.023 s, while the other pulsar has a rotation period of 2.8 s. The faster pulsar has a mass 1.337 times that of the Sun, while the slower pulsar has a mass 1.250 times that of the Sun.
a) If each pulsar has a radius of 20.0 km, express the ratio of their rotational kinetic energies. Consider each star to be a uniform sphere with a fixed rotation period.
b) The orbits of the two pulsars about their common center of mass are rather eccentric (highly squashed ellipses), but an estimate of their average translational kinetic energy can be obtained by treating each orbit as circular with a radius equal to the mean distance from the systems center of mass. This radius is equal to 4.23 · 108 m for the larger star, and 4.54 · 108 m for the smaller star. If the orbital period is 2.4 h, calculate the ratio of rotational to translational kinetic energies for each star.
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