Spring 2003

__HOMEWORK ASSIGNMENT #5 Due Thursday March 13, 2003
4:30PM__

C&O refers to the textbook *An Introduction to Modern Astrophysics,
* by B.W. Carroll & D.A. Ostlie

- C&O, page 482, problem 12.14
- Spectroscopic observation of a star, of known mass 1.15 solar masses, shows a sinusoidal variation of Doppler shift with time, with a period of 2.06 years corresponding to a maximum speed of approach or recession of 52 m/s. What is the minimum mass of the accompanying planet and the radius of its orbit? (Hints: Use Kepler's third law to calculate the semi-major axis length of the planet's orbit from the planet's orbital period and the mass of the star. Then think of the star and planet moving about the center of mass to relate the planet's mass to the mass of the star and the orbital speeds of the planet and the star.) Assume circular orbits.
- Imagine that you are observing a planetary system very much like our Solar System from a distance of 5 pc. What angular separation between a planet in a Earth-like orbit and the central star would you observe? Likewise what is the angular separation between a planet in a Jupiter-like orbit and the central star. Next calculate the astrometric wobble of the central star in this planetary system, first assuming that the only planet is Earth-like and then assuming that the only planet is Jupiter-like. Assume that the "phase factor" is unity (in other words determine the maximum value of the effect in each case) and circular planetary orbits.

Please send any comments to Jack Hughes, jph@physics.rutgers.edu.

Revised March 7, 2003