ASTR 2010 Modern Cosmology Spring 2002
HOMEWORK #4: out on Fri Apr 5; due in class Fri Apr 19

Student NAME:

Question #1 (20%) - non-math
The Hubble law predicts that the Andromeda galaxy should be moving away from the Milky Way with the recession velocity of about 50 km/s. Observations show that the Andromeda galaxy is actually moving towards us with the velocity of about 275 km/s, in a drastic disagreement with the Hubble law. Can this observation be used to rule out the Big Bang theory? Explain.

 

 

 

 

 

 

 

Question #2 (20%) - non-math
Two astronomers, Jack and Jill, decided to measure the mass of the Andromeda galaxy. Jack simply estimated the total mass in stars that he could see with his telescope. Jill however used the appropriately modified version of the third law of Kepler to measure the mass of Andromeda based on orbits of Andromeda satellites (dwarf galaxies that orbit Andromeda in much the same way as Earth orbits the Sun). To their surprise, they find that their results disagree strongly. Who found the larger value for the mass of Andromeda and why? Whose number is the correct one?

 

 

 

 

 

 

 

Question #3 (20%) - non-math
We know observationally that there are galaxies and quasars at very large cosmological redshifts, the record holder is a quasar at a redshift of about 6. However, not only expansion of the universe can cause a redshift -- a strong gravitational field in the vicinity of a black hole also causes a redshift. For example, the last stable orbit around the black hole has a redshift of about 0.3. Give an argument why astronomers nevertheless think that quasars are at cosmological distances -- why cannot a quasar be just a small but very bright blob of hot gas sitting very close to (but still outside of) the horizon of a black hole? Remember that we do not know the size of a quasar, i.e. you cannot use the size as an argument.

 

 

 

 

 

 

 

 

Question #4 (20%) - non-math
Astronomer Z is very unhappy with the Big Bang theory -- he really does not like a universe which has a beginning. But we know observationally that the universe expands. So, Z invented a model in which the universe exists forever, but still expands. Can we use the Olber paradox (see H&H, pp. 319-320) to rule out his model? Please explain.

 

 

 

 

 

 

 

 

Question #5 (20%) - non-math
Astronomer X developed another model of the universe in which the universe was so hot and dense during some early epoch that nuclear reactions during that epoch created enough oxygen atoms to fit the existing observations of the oxygen abundance in the universe. Give a strong argument against such a cosmological model.

 

 

 

 

 

 

 

Question #6 (20%) - math
Imagine that you built a time machine and went into the past. But something broke down, and you actually went much much further than you had planned -- billions of years back in time, before the Earth or the Sun even existed. You found yourself hanging in the empty space and felt pretty uncomfortable. Thus you decided to have a glass of cold water. To cool the water quickly, you poured it into a closed container and put it outside of your time capsule, exposed to the empty space. To your great amazement, the water started to boil. Estimate the minimum possible value of the cosmological redshift z at which you ended up (water boils at 373 degrees Kelvin). [Hint: see H&H, p. 355 for variation of CMB]

 

 

 

 

 

 

 

Note: The total score from 6 questions adds up to 120%. This means that in order to get the full credit, you need to answer completely 5 out of 6 questions of your choosing. You may also try to do all 6 questions so that if you get only partial credit for some of the questions, you can still get 100% of the score. If you score is more than 100%, it will be truncated to 100% (you cannot get more than 100% even if you do all 6 questions correctly).