# Astronomy 300: Homework Assignment #5

Due: Friday. March 7

Scale Model

1. Show all your steps in detail.

A.) Suppose you want to construct a scale model of the Milky Way and Andromeda galaxies using two frisbees. How far apart should you place the two frisbees? Would they both fit in the classroom? How about a large lecture hall? A stadium?

B.) The light we receive from the Andromeda galaxy left it approximately 2.4 million years ago. Assuming that Andromeda is moving directly toward the Milky Way, and using the information given by Croswell in Ch. 1, estimate how much closer the Milky Way is to us *now* than it was when that light left. What fraction of the total distance is this? In the scale model above, how much closer would the two frisbees now be?

2. The rest wavelength of the H α Alpha line of hydrogen is at λ 0= 656.28 nm. Suppose you observe this line in the spectrum of the Andromeda galaxy but find that it is at λ= 656.02 nm. What can you conclude about the relative motion of the Milky Way and the Andromeda galaxy? Are they moving together or apart? At what speed?

3. At this rate, about how long might it be until the two galaxies collide? Express your answer in seconds and in years. Can you think of any reason the two galaxies might not collide, at least not on the "next pass"? Explain. (Feel free to compare your results with p.8 of Croswell)

4. C&O Problem 5.1 (Barnard's star)

5. Hydrogen atom & Quantum Physics

6. In what ways is the Bohr Model similar to the solar system, and in what ways is it different? List as many as you can think of. A.) Compute the energy of the photon that would be emitted if an electron dropped from the n=6 to n=3 level.
B.) What wavelength would this photon have?
C.) Which "series" is this photon part of?

7. C&O Problem 5.14 (White Dwarfs)

8. Rotation of galaxies

Suppose you observe the H α line (rest wavelength = 656.3 nm) from an edge-on spiral galaxy. You find that at the center of the galaxy the line is at 656.5 nm. At a distance 50,000 ly from the center, the H α line is at 656.0 nm and 657.0 nm on the left and right sides, respectively.

A.) Is the galaxy moving toward or away from the Milky Way? How fast?

B.) How fast is the galaxy rotating?

9. The double star Albireo consists of two components, A and B, separated by about 35 arcseconds. Both stars have parallaxes of 0.0085 arcseconds.

How far from the Sun is this binary star system?
Assuming the two stars are at exactly the same distance from the Sun, compute the physical separation between Albireo A and B in AU.

10. Kepler's 3rd Law is very useful for binary star calculations. Its general expression, derived by Newton is given in C&O , Eq. 2.37. A simpler form can be used if semimajor axis is measured in AU and Period in Years:

P2 = a3/(M1+M2)

Prove these expressions are equivalent by looking up the values of G, the AU and the Solar Mass given in your textbook, (all in MKS units), to show that:

2/G = 1 yr2 MSUN /AU3