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2. The Crab pulsar radiates at a luminosity of 1 × 1031 W and has a period of 0.033 s. (a) If the luminosity is a direct result of the loss of rotational energy of the pulsar, de- termine the rate at which its period is increasing (dP/dt) in s/yr. How many years will it take for the period to double its present value? NOTE: the moment of inertia for a solid sphere is I = MR², where M = 1.4M and R = 1.1 × 104 m for the Crab pulsar; the angular frequency is w = 2π/P. (b) Calculate the density of the neutron star by assuming the pulsar rotates close to break-up velocity (i.e. where the centripetal acceleration is close or equal to the gravitational acceleration).

2. The Crab pulsar radiates at a luminosity of 1 × 1031 W and has a period of 0.033 s. (a) If the luminosity is a direct result of the loss of rotational energy of the pulsar, de- termine the rate at which its period is increasing (dP/dt) in s/yr. How many years will it take for the period to double its present value? NOTE: the moment of inertia for a solid sphere is I = MR², where M = 1.4M and R = 1.1 × 104 m for the Crab pulsar; the angular frequency is w = 2π/P. (b) Calculate the density of the neutron star by assuming the pulsar rotates close to break-up velocity (i.e. where the centripetal acceleration is close or equal to the gravitational acceleration).

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2. The Crab pulsar radiates at a luminosity of $1 \times 10^{31} \mathrm{~W}$ and has a period of 0.033 s .
(a) If the luminosity is a direct result of the loss of rotational energy of the pulsar, determine the rate at which its period is increasing $(\mathrm{dP} / \mathrm{dt})$ in $\mathrm{s} / \mathrm{yr}$. How many years will it take for the period to double its present value? NOTE: the moment of inertia for a solid sphere is $I=\frac{2}{5} M R^2$, where $M=1.4 M_{\odot}$ and $R=1.1 \times 10^4 \mathrm{~m}$ for the Crab pulsar; the angular frequency is $\omega=2 \pi / P$.
(b) Calculate the density of the neutron star by assuming the pulsar rotates close to break-up velocity (i.e. where the centripetal acceleration is close or equal to the gravitational acceleration).

2. The Crab pulsar radiates at a luminosity of 1 × 1031 W and has a period of 0.033 s. (a) If the luminosity is a direct result of the loss of rotational energy of the pulsar, de- termine the rate at which its period is increasing (dP/dt) in s/yr. How many years will it take for the period to double its present value? NOTE: the moment of inertia for a solid sphere is I = MR², where M = 1.4M and R = 1.1 × 104 m for the Crab pulsar; the angular frequency is w = 2π/P. (b) Calculate the density of the neutron star by assuming the pulsar rotates close to break-up velocity (i.e. where the centripetal acceleration is close or equal to the gravitational acceleration).
Transcribed Image Text:2. The Crab pulsar radiates at a luminosity of 1 × 1031 W and has a period of 0.033 s. (a) If the luminosity is a direct result of the loss of rotational energy of the pulsar, de- termine the rate at which its period is increasing (dP/dt) in s/yr. How many years will it take for the period to double its present value? NOTE: the moment of inertia for a solid sphere is I = MR², where M = 1.4M and R = 1.1 × 104 m for the Crab pulsar; the angular frequency is w = 2π/P. (b) Calculate the density of the neutron star by assuming the pulsar rotates close to break-up velocity (i.e. where the centripetal acceleration is close or equal to the gravitational acceleration).
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