Physics 209: Take Home Mid-term

Due: Monday, May 8, 1995

Answer 4 out of the 6 questions

Question 1:

What is the explanation favored by most astronomers for Hubble's law, v = H(now) x D? How would you convince my Mom, a college educated nonscience major, that this is the correct explanation? How convincing do you find your argument? Pay careful attention to whether your argument is simply a plausibility argument or not.

Question 2:

How are the velocities of galaxies which are used to define Hubble's Law deduced? How accurate are these determinations? What are the major problems in the determinations of the velocities needed to determine Hubble's Law?

Explain the idea of bootstrapping in the context of distance determinations. Which method for the determination of extra-galactic distances do you believe is the most accurate of the ones in current use? Upon what do you base this belief?

Question 3:

A distant cluster of galaxies has a mass of 10**15 M(Sun) and a radius of 10 million light years. 1 light year = 300,000,000 x 31,000,000 cm [or so] and 1 M(Sun) = 2 x 10**33 grams. Estimate the typical peculiar velocity for a galaxy in this cluster.

How far away must this cluster of galaxies live in order for the Hubble flow velocities to be much larger than this peculiar velocity? Assume that the current value for the Hubble constant is H(now) = 25 (km/s) per million light years ~ 82 (km/s) per million parsecs?

Question 4:

Suppose a galaxy has rotation curve which looks like:



How is the mass distributed in the galaxy? What is the mass of the galaxy?

Question 5:

I have mentioned several interesting properties of the Universe which seem a little bit strange in that they are seemingly special or that their values seem to be very finely tuned. What are these mysteries? What do you believe is the correct explanation for these so-called mysteries? Upon what do you base your beliefs? [Answer this question along philosophical lines.]

Question 6:

For a universe where the Cosmological Constant is larger than 0, schematically sketch how the scale factor, R(t), would evolve with time. Use
-k=1/2[dR(t)/dt]**2-(4 pi/3) G rho(t) R(t)**2 - (CC/3) R(t)**2
For simplicity, assume that the Universe is flat, i.e., k = 0. Be sure to tell me what other assumptions you make.

From your sketch, argue that the age of the universe could be larger or smaller than 1/(Hubble constant) depending upon when you measured the Hubble constant.