Problem Solving


1		Given that the Sun moves in a circular orbit of radius 8.5 kiloparsecs around the center of the Milky Way and that its orbital speed is 220 kilometers per second, work out how long it takes the Sun to complete one orbit of the galaxy. NOTE: 1 kiloparsec is about 3 x 10¹⁶ kilometers, and 1 year is about 3 x 10⁷ seconds.



2		Gas is observed to be orbiting in a circle at 200 km/s about a dark central mass. If the gas's orbit has a radius of 1 parsec, how much mass must be present to hold it in orbit?



3		Suppose the mass in problem 2 were packed into a sphere whose radius is 20 AU. Would it be a black hole?



4		According to figure 9.24, the Milky Way's rotation speed is about 230 km-S^-1 at a distance of about 16 kiloparsecs from its center. Use the method discussed in the box on page 289 to find the mass of the Milky Way implied by these values. Hint: These values correspond to a distance of about 3.3 x 10⁹ AU and an orbital period of about 4.3 x 10⁸ yrs.

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