Homework 12. Shape & Mass of the Milky Way

NOTE: too many people are turning in their homework late; this make it very difficult to grade and return homework on time. Starting with this assignment, I will deduct a full letter grade for any homework turned in after Monday's lecture.

1. Sketch face-on and edge-on views of the Milky Way galaxy. Use red to represent Population II, and blue to represent Population I. In your sketch, be sure to include the main components of the galaxy (central bulge, disk, halo, globular clusters), and mark the Sun's position.

2. The graph at right is a simplified version of Figure 15-11 from the book. It shows the orbital velocities of gas clouds in the disk of the Milky Way; the horizontal axis is the radius of each cloud's orbit, and the vertical axis is the cloud's orbital velocity. If we assume that each cloud is on circular orbits, we can use the generalized form of Kepler's third law to measure the mass of the Milky Way within the radius of each cloud's orbit.

Begin by picking one of the points plotted in this graph, and draw a circle around it. From the graph, measure the radius (R) and the velocity (V) for this point. Write these values down below.

To use Kepler's third law, you must first calculate the orbital period (P) in years. The period is the orbit's circumference, C = 2R, divided by the velocity V. But you need to convert V from units of km/sec (kilometers per second) to kpc/yr (kiloparsecs per year). Now 1 km/sec is almost exactly 10^-9 kpc/yr, so all you have to do is multiply V by 10^-9. Below, calculate the orbital period P:

	C = 2R = ____________________________________________ kpc
	V = ________________________________________________ kpc/yr
	P = C ÷ V = ____________________________________________ yr

Likewise, you will need to express the orbital radius R in Astronomical Units (AU). Now 1 kpc = 2.06 × 10⁸ AU, so all you have to do is multiply R by this factor:

Finally, calculate R³ ÷ P², which is the mass within the orbit in units of solar masses (M):

M = R3 ÷ P2 = ________________________________________________ M