A pulsar is a rapidly rotating neutron star that emits a radio beam the way a li

Question

A pulsar is a rapidly rotating neutron star that emits a radio beam the way a lighthouse emits a light beam. We receive a radio pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. Suppose a pulsar has a period of rotation of T = 0.0488 s that is increasing at the rate of 5.26 x 10-8 s/y.

A pulsar is a rapidly rotating neutron star that emits a radio beam the way a lighthouse emits a light beam. We receive a radio pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. Suppose a pulsar has a period of rotation of T = 0.0488 s that is increasing at the rate of 5.26 x 10-8 s/y. What is the pulsar's angular acceleration ? If is constant, how many years from now will the pulsar stop rotating? Suppose the pulsar originated in a supernova explosion seen 549 years ago. Assuming constant , find the initial T.

Explanation / Answer

T1 = 0.0638s => f1 = 1/T1 = 15.67398 Hz
w1 = 2pi*f1 = 98.48253 rad/s

T2 = 0.06380342s (7 sig figs required?)
=> f2 = 15.67314 Hz => w2 = 98.47725 Hz

(a) ALPHA = (w2 - w1) / 1y = -5.27887*10^-3 rad/s/y

(b) time to stop is -u / ALPHA = -98.48253 / -5.27887*10^-3 = 18656 years

(c) After 845 years, speed decrease is 5.27887*10^-3 * 845 = 4.4606... rad/s
so initial speed was w = 98.4825... + 4.4606... = 102.943177 rad/s
so initial period was T = 2pi / 102.943... = 0.06103547 s

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