Principles of Astrophysics 342
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.