AST 307 · Introductory Astronomy Fall 2003

AST 307
Homework #8
Due Friday October 31

1. In this problem you will estimate the time it takes for gravity to pull a molecular cloud together to form a star. Assume a fragment of a molecular cloud has a mass of 1 solar mass and a diameter of 0.1 parsec.

a) Assume the only force acting on a hydrogen molecule in the cloud is the gravitational attraction of the other molecules. Newton showed that the force on an object on the outer edge of a spherical cloud is the same as it would be if all of the mass of the cloud were concentrated at the center. Use this fact and Newton's law of gravity to calculate the acceleration of a hydrogen molecule on the outer edge of the cloud.
b) Assume that as the cloud collapses, the hydrogen molecule you considered in part a falls toward the center with a constant acceleration equal to what you calculated. Calculate the time it will take it to reach the center.
c) Name at least one invalid assumption we have made in this calculation, and say in what way that error affected our calculation.
If this problem was too easy for you, you might try to make a more valid calculation of the time for a molecular cloud to fall together.

2. a) If two stars have equal luminosities, but star A is 10 times as distant as star B, how do their fluxes compare? (quantitatively)
b) How do the magnitudes of the two stars in part a compare?
c) If two stars have the same luminosities, but star C appears 16 times brighter than star D, how do their distances compare? (quantitatively)
d) If we knew that the two stars in part c were main-sequence stars, how might we have inferred that they have the same luminosities?
What you did in parts c and d was to use the standard candle method to measure distances. We will use it much more when talking about galaxies.

3. Describe two ways that astronomers can observe interstellar molecules.

29 October 2003
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
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