29:119 Introduction to Astrophysics I
Fall 2008
First Hour Exam ...September 29, 2008

Start each question on a new page. It allows me to make comments and generally keeps me in a better mood. Write legibly. Explain what ideas you are using and what you are trying to do. There are 5 questions. Good luck and no whining.

Walk with Ursus!!!

(1) Stars radiate approximately like blackbodies. Make a sketch showing the spectrum of a star, properly labeling the axes, and giving approximately correct numbers on the abscissa (x axis). Identify and define any wavelengths of particular significance.

(2) Assume that a hydrogen atom has an effective size given by the radius of the Bohr atom in its ground state.

• What is the radiation force exerted by sunlight on a hydrogen atom at a distance of 1 astronomical unit? Assume complete reflection of the incident sunlight.
• How does this force compare with the gravitational force between the Sun and the atom?

(3) A hydrogen atom is at rest in its ground state. It absorbs a photon which was moving in the +x direction, and is excited to the first excited state. What is the subsequent motion of the hydrogen atom (before de-excitation), i.e. does it move? If so, in what direction and with what speed?

(4) A so-called Kuiper Belt Object orbits the Sun on an orbit with a semi-major axis of 35 astronomical units (a.u.) and an eccentricity of $\epsilon=0.35$. What are the values of the perihelion and aphelion distances?

(5) Imagine that the mass of the Milky Way galaxy consists of a large black hole with a mass $M_1$ at the center of the galaxy, and a uniform, spherically-symmetric component (approximating the distribution of masses of the stars) possessing a density $\rho \mbox{ if } r \leq R$, and $0 \mbox{ if } r> R$. Describe, using words and equations, how observations could be used to deduce this picture of the mass distribution.

(6) An exoplanet orbits another star, which has the same stellar properties as the Sun. The planet has a mass 1000 times that of the Earth (or about 3 times that of Jupiter), and orbits at a distance of $4 R_{\odot}$ (solar radii) from the center of the star.

• What is the period of the orbit?
• How far from the center of the star is the center of mass of the system?
• What is the speed at which the star moves, relative to an observer at rest in the center of mass system?