# Astronomy 300: Homework Assignment #6

Due: Friday April 4

1. Order-of-magnitude estimate.

Use the information on Page 181 of Croswell to calculate, approximately, the density of stars in the giant sphere surrounding the Sun. Express your answer both in stars/l.y.3 and stars/pc3. From this number estimate the average distance between stars in the Solar Neighborhood. [Hint: to do this it might help to imagine that every star is at the center of a cube in space with the same distance to the next star. Consider, perhaps, a 3x3x3 volume of such cubes]. How does the average distance between stars compare to the distance between the Sun and the Alpha Centauri system?

Orbital periods of visual binary stars

2. Consider a nearby binary at 10 pc distance. The stars are found to be in a circular orbit with angular separation of 1 arc sec. If the combined mass of the system is m1+m2 = 1 MSUN, then what orbital period would it have? (Hint: first determine the physical separation, by reference to a 1pc-1AU-1arcsec triangle.)

3. For a distance of 100 pc, what orbital period would be implied by this same angular separation?

4. C&O, Chapter 7, Problem 7.4 Part (a.) Only. Hint: First determine the stars' distance in pc. Given an angular separation in arc sec. (7.61"), determine the physical separation, as above.

5. C&O, Chapter 7, Problem 7.4 Part (b.) Note you may wish to consult class notes regarding Sirius A & B.

6. Suppose a new planet was found orbiting a 10 solar mass star in a 1 AU orbit. What would be the period of this planet?

7. FIRST: Without consulting your book or references, draw a standard H-R diagram, and label the axes, including numerical values for both axes. (OK to guess here) Indicate the location of: Main Sequence, White Dwarfs, Red Giants.

SECOND: Check a reference and make some adjustments to your graph if needed. (OK to draw a new graph)

THIRD: Suppose someone says to you "Yellow stars are intrinsically brighter than red stars." Use your graph (and Wein's Law) to argue for or against this opinion. Draw one or two lines on the graph to make your point.

8. Spectroscopic Parallax: Problem 8.16 in C&O.

9. What do a star's U, V and W components tell us about the star? If a star has relatively large absolute values of U, V and W, what would you conclude about the star's age, and why?

10. By the early 1900's, it had become clear that the Sun could not be powered by chemical reactions because the energy released from them is so small that the Sun would have expended its energy long ago.

Assume, instead, that the Sun is powered by nuclear reactions, and that 10% of the Sun's mass is available. If the Sun's nuclear reactions have an efficiency of converting mass to energy of about 1%, then estimate the lifetime of the Sun, in years, clearly stating in words the reasoning behind your approach.

Is this consistant with the present age of the Sun?