Astronomy 102 Problem Set #6
due 30 March 2000, 5:00 pm
Please note the correction in problem #1 and #2. Updated March
27.
Problem #1: The pulsar in the crab nebula
spins around its axis 30 times in one second. Using the dynamical equation
of gravity, (Minimum Period2 = 6 x 1011 kg sec^2
/ m^3 x Radius3 / Mass of star) show:
a. A pulsar cannot be a spinning white dwarf. A white dwarf has 0.8
x mass of the sun and the size of earth.
b. A pulsar can be a spinning neutron star. A neutron star has 1.4
x mass of the sun and the size of a mid-size town (less than 20 km radius).
Problem #2: A black hole has a total mass
that is 106 times that of the sun.
a. What is the radius of that black hole (usually referred to as the
black hole event horizon)? Size = 12 x 10^-11 m^3 /(kg x s^2) x Mass
of black hole / c^2. c is the speed of light.
b. Assume that photons with frequency 1.55 x 1018 Hz are
emitted from a distance that is 10 time the radius of the black hole. Using
the gravitational Doppler effect show that the recieved frequency is 1.41
x 1018 Hz. (change in frequency / rest frequency = size of black
hole / distance from black hole.