29:62 GENERAL ASTRONOMY
Fifth Homework Set...Due March 24, 1999

Show calculations and give reasons for your answers. A couple of additional sentences of clarification and explanation may convince the grader you know what you are doing.

As always, I have your best interests in mind. You will notice that there are three more problems than usual. This is because I realize that during Spring break you will either (a) be bored to tears with your old High School friends back home, with whom you no longer have anything in common, or (b) in serious danger of withering your skin with solar ultraviolet radiation at some beach. In either case, you need something to keep you occupied and indoors. These will help you.

1. Detailed calculations show that much of the energy of the core collapse in a supernova explosion comes off in the form of neutrinos, rather than in the blast wave which produces the visible radiation. Explain in about a paragraph why this happens.
2. Calculate the density of a neutron gas at which the Fermi energy equals the rest mass energy of a neutron. The rest mass energy is defined as the energy which would be obtained by converting the mass of the particle entirely to energy.
3. What would be the radius of a sphere of neutrons which had the density calculated above and a mass equal to that of the sun? Would this object resemble any of the astronomical objects described in class so far this semester?
4. The famous radio spectral line of neutral hydrogen has a wavelength of 21 centimeters. What is the radio frequency in Megahertz (MHz)?
5. A picture or ``image'' or an extragalactic radio source is shown on the bottom of p 564 of your textbook. What was the size of the radio telescope which made this image? Hint: Think about how the resolution of an image made with a radio telescope is related to the characteristics of its beam. Based on your answer, state what kind of radio telescope it was. Describe what your reasoning is in this problem rather than just plugging in numbers.
6. A pulsar has a rotational period of 0.50 seconds. What is its rotational kinetic energy?
7. Approximate the Sun by a sphere of uniform density. Assume, for the sake of argument, that as it slows down, it converts rotational kinetic energy into luminous energy. What would the slowdown rate of the Sun have to be to account for its present luminosity? Is such a rate consistent with other information we have about the Sun?
8. The spectrum of a radio source (in Janskys) may be described as follows. At frequencies below 200 MHz the flux density is zero. At 200 MHz the flux density is 5.0 Janskys. At higher frequencies the flux density (plotted as a function of frequency) declines linearly and goes to zero at 900 MHz. The distance to the source is 500 parsecs. What is the total luminosity at radio wavelengths?

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