Ch-14 Homework
1

The disk of the Galaxy is about 50 kpc in diameter and 600 pc thick.
(a) Find the volume of the disk in cubic parsecs.
(b) Find the volume (in cubic parsecs) of a sphere 300 pc in radius centered on the Sun.
(c) If supernovae occur randomly throughout the volume of the Galaxy, what is the probability that a given supernova will occur within 300 pc of the Sun? If there are about three supernovae each century in our Galaxy, how often, on average, should we expect to see one within 300 pc of the Sun?

2

According to the Galaxy's rotation curve in , a star 16 kpc from the galactic center has an orbital speed of about 270 km/s. Calculate the mass within that star's orbit.

3 (a) Calculate the Schwarzschild radius of a supermassive black hole of mass 4x106 solar masses, the estimated mass of the black hole at the galactic center. Give your answer in both kilometer and in astronomical units.
(b) What is the angular diameter of such a black hole as seen at a distance of 8 kpc, the distance from the Earth to the galactic center? Give your answer in arcseconds. Observing an object with such a small angular size will be a challenge indeed!
4 The orbital periods of the stars SO-1 and SO-2 shown in are estimated to be 63 and 17 years, respectively.
(a) Assuming that the supermassive black hole in Sagittarius A* has a mass of 4x106 solar masses, determine the semimajor axes of the orbits of these two stars. Give your answers in AU.
(b) Calculate the angular size of each orbit's semimajor axis as seen from Earth, which is 8000 pc from the center of the Galaxy. Explain why extremely high-resolution infrared images are required to observe the motions of these stars.
5 Consider a star that orbits around Sagittarius A* in a circular orbit of radius 1000 AU.
(a) If the star's orbital speed is 1500 km/s, what is its orbital period? Give your answer in years.
(b) Determine the sum of the masses of Sagittarius A* and the star. Give your answer in solar masses. (Your answer is an estimate of the mass of Sagittarius A*, because the mass of a single star is negligibly small by comparison.)