HW #7 Solutions
•Question 5   (1 point) If the sun is 5 billion years old, how many times has it orbited the galaxy? Assume a circular orbit for the sun around the center of the galaxy, and look up in the text its orbital speed and distance from the galactic center.
 a.5 times b.5 billion times c.200 times d.20 times   e.5000 times
•Approach this problem like a time, rate, distance problem to figure out an orbital period, then see how many go into 5 billion years.  If the orbital speed is 220 km/s, and the oribital radius is 8.5 kpc, we can get the period (time): time = speed/distance and we must convert.  8.5 kpc = 8500 pc x 3.1 x 10 13 meters/pc = 2.6x1017 km.  So time = 2πx2.6x1017 km/220 km/s = 7.5x1015 s.  What is that in years?  There are about 31 million seconds per year, so this period is 7.5x1015/3.1x107 = 2.4x108 years, or about 240 million years.  5 billion divided by 240 million is 5x109/2.4x108 = 20.8.
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• Question 6   (1 point) If all the mass in our galaxy were centrally concentrated, we'd expect velocities to fall with increasing distance according to Kepler's laws. This is not seen in the disks of spiral galaxies. Galactic rotation curves appear "flat" with increasing distance. This must be due to
 a.The gravitational influence of massive globular clusters in the halo.   b.The difficulty in measuring velocities of stars in the galactic disk because of all the gas and dust.   c.The fact that Kepler's laws do not apply over the 25 kpc size of the Milky Way galaxy because the effect of gravity travels only at the speed of light.   d.The Spiral density wave traveling at a different speed than the stars in the disk.   e.The gravitaional influence of "dark matter" in the halo.