the crab nebula is a cloud of glowing gas about 10 light years across, located a
ID: 2245347 • Letter: T
Question
the crab nebula is a cloud of glowing gas about 10 light years across, located about 6500 light years from earth. it is the reminant of a star that underwent a supernova explosion seen on earth in 1054 A.D. energy is released by the crab nebula at a rate of about 5e31 about 10^5 times the rate at which the sun radiates energy. the crab nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. suppose this object rotates once every 0.0317s and this period is increasing by 4.20e-13s for each second of time that elapses.
moment of inertia is 9.61e37
b. theories of supernovae predict that the neuron star in the crab nebula has a mass about 1.4 times that of the sun. modeling the neutron star as a solid uniform sphere, calculate its radius in kilometers.
c. what us the linear speed of a point on the equator of the neuron star? compare to the speed of light.
d. assume taht the neuron star is unifrom and calulcate its density. compare to the density of ordinary rock (3000 kg/m3) and to the density of an atomic nucleus (about 10^7 kg/m3)
Explanation / Answer
A)
Pn=Power Release by the Nebula
=5E31 Watts
T=period=.0317 s
T'=dT/dt=4.20E-31
w=2*pi/T
E=rotational energy
= I*w^2 = 4*pi^2*I*T^(-2)
Ps=Power radiate by the star
=dE/dt=E'=4*pi^2*I*(-2)*T^(-3)*T' = -8...
Ps = -Pn <-------Plug in the expression, solve for I and compute.
B)
I=(2/5)M*r^2, moment of inertia of a solid sphere
solve for R and compute.
I is computed in part A)
M=1.4
C)v=w*r
w=2*pi/T
r from part B
D)Density = mass/volume
mass = 1.4 solar mass
volume=(4/3) pi r^3
r from part B
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