Astronomy 102 Problem Set #5
due 23 March 2000, 5:00 pm
Problem #1: When a massive star explodes as
a supernova, it emits neutrinos. In February of 1987 a supernova was detected
in the night sky, in the direction of the large magelanic cloud, a satellite
of our own milky way galaxy. It was later revealed to be 169,000 Light
years away. That same night 8 neutrinos from that supernova were detected
in detectors of total surface area 100 m^2.
a. Assuming that 1 in every 1014 neutrinos passing through
the detector were detected, how many neutrinos passed per every square
meter of the detector?
b. Assuming that neutrinos emerged from the supernova in all possible
directions, how many neutrinos were emitted?
c. Assume that every neutrino came from a weak-force interaction of
the form: Proton --> Neutron + Anti Electron + Neutrino+energy. Assume
that 0.1% of the proton mass was converted into energy. How much energy
was emitted in the supernova? Note that this is a very crude approximation
of the supernova energy output.
Problem #2: A white dwarf star has
mass equal to 0.8 solar masses, and radius similar to that of earth.
a. What is the density of the white dwarf star?
b. What is the distance between adjacent electrons in that star? Assume
that it has the same number of electrons as are in the sun, find the volume
per electron, and from that get the cubic root.
c. Using the uncertainty principle find out the momentum of such an
electron. Compare with the momentum of an electron in a regular earthly
solid (10^30 electrons per cubic meter). How much larger is the momentum
in that case?
d. Assuming that the quantum pressure is related to the momentum explain
how solar mass stars evolve into a white dwarf. Concentrate on what happens
to the core.
Problem #3: The pulsar in the crab nebula
spins around its axis 30 times in one second. Using the dynamical equation
of gravity, (Kepler's third law, class March 21, 2000, Minimum Period2
= 3 x 10-11 x Radius3 x 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).