AST 307 · Introductory Astronomy Fall 2003

AST 307
Homework #9
Due Friday Nov 14

1. A typical white dwarf has a mass about equal to that of the sun and a radius about equal to that of the earth. Use these numbers to calculate the density of a typical white dwarf in kg/m^3. A typical neutron star has a mass about twice that of the sun and a radius of about 10 km. Use these numbers to calculate the density of a typical neutron star. Compare this number to the density inside of a proton, which has a radius of about 10^-15 m.

2. Use the numbers in problem 1 to calculate the escape speed from the surface of a white dwarf and the escape speed from the surface of a neutron star. What fraction of the speed of light are these numbers?

3. I observed a planetary nebula which has the shape of a thin shell of ionized gas with an angular diameter of 1 arcminute. When looking at its center, I see an emission line which is split by the Doppler shift into two peaks separated by 0.01% of the normal wavelength of that line. From this I conclude that I am seeing emission from the front and back sides of an expanding shell.
a) What is the expansion velocity of the planetary nebula shell?
(That is, what is the speed of gas on the surface of the shell moving away from the center of the shell?)
b) I found an old photograph of the planetary nebula which shows that 100 years ago its angular diameter was only 58 arcseconds. Assuming that the shell is expanding at a constant speed, how old is the shell?
(That is, how long ago was it that the diameter was zero?)
c) What is the current diameter of the shell in kilometers?
What is that in AU?
d) Knowing that an object of size 1 AU at a distance of 1 pc subtends an angle in the sky of 1 arcsecond (which is one way of stating the definition of the parsec), figure out how far away the planetary nebula must be.

11 November 2003
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
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