AST 307 · Introductory Astronomy Fall 2003

AST 307
Homework #6
Due Friday October 17

1. Consider a part of an interstellar molecular cloud, which is going to form a star. Assume this cloud fragment has a diameter of 0.2 light-years, a mass of 1 solar mass, and is rotating at a rate of one revolution per million years. (These are reasonable numbers for the cloud that formed the solar system.)
a) What is the rotational speed of the outer edge of this cloud fragment?
b) Assume the cloud fragment is pulled together by gravity until it has a diameter of 100 AU, the size of the solar nebula, and that angular momentum is conserved, or equivalently that Kepler's 2nd law is obeyed. What is the rotational speed and period of the outer edge of the cloud fragment once it is this small?
c) So far we have been following problem 2 on page 402. But can this happen? What is the orbital speed, according to Newton's version of Kepler's 3rd law, 50 AU from a 1 solar mass star? What is the escape speed there?
d) Gravity cannot accelerate something up to a speed greater than escape speed, but it seems that it would have had to in order to form the solar system. This is a problem that has puzzled astronomers for a long time. Can you suggest a possible solution to the problem?

2. Before the cloud fragment in problem 1 was pulled together, what was its density, which is defined as its mass divided by its volume?
Assume the cloud fragment is spherical.
a) Express your answer in grams per cubic centimeter (the density of liquid water).
b) How many hydrogen molecules per cubic centimeter is that?

3. The luminosity of the Sun (the amount of light power it emits) is given in your book.
a) From that number and the distance of the Earth from the Sun, calculate the solar constant, which is defined as the solar light power hitting a square meter at the Earth.
b) Compare the solar constant to the amount of light power hitting an area of one square meter at a distance of 1 meter from a 100 Watt light bulb.

4. Your body generates heat from the food you eat at a rate of about 100 Watts. Calculate the power you generate per kilogram of mass to the power that the Sun generates per kilogram of its mass. If you don't want to use your mass, you can use mine, 66 kg.

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