29:120 Introduction to Astrophysics II
Spring 2009
Final Exam ...May 13, 2009

Start each question on a new page. Write legibly. Explain what ideas you are using and what you are trying to do. There are 8 questions.

Una Salus Victis, Nullam Sperare Salutem ...The Aeneid

(1) A star is orbiting in the Galaxy, and its orbit lies in the Galactic plane. The perigalacticon is 4.0 kpc and the apogalacticon is 16.0 kpc.
(a) What is its speed when it crosses the Sun's orbit?
(b) Qualitatively describe the way in which its peculiar velocity would be, well, peculiar.

(2) Describe, using physical terms, why we know that older stars were born when the Galaxy had a different shape, or that they have had their orbits modified.

(3) Use a diagram and equations to explain how 21 cm observations can yield the rotation curve $\Theta(R)$ in the inner part of the Galaxy.

(4) Consider a typical radio galaxy.
(a) Sketch the radio spectrum, and point out and define special characteristics.
(b) Sketch the structure of the radio galaxy.
(c) What is the radiation mechanism responsible for generating the radio waves?

(5) Consider a radio galaxy observed at a frequency of 1.4 GHz. Suppose we can independently estimate the magnetic field to be $2 \times 10^{-5}$ Gauss (2 nanoTesla, if that helps, which it probably doesn't). On what timescale will the electrons responsible for this radiation lose roughly half their energy. How does this timescale compare with the age of the galaxy?

(6) Derive the expression for the scalar curvature $R(t)$ as a function of time in a Friedmann Universe in which $k=0$.

(7) Explain the observational and theoretical arguments of why the real universe cannot be described by a Friedmann Universe model.

(8) What are the dimensions of the Hubble Constant? What is the fundamental physical significance of the value of the Hubble Constant?