Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 17: Galaxies

Problems

1
A Cepheid variable in a nearby galaxy looks 106 times fainter than an identical Cepheid (in the Milky Way) 1000 parsecs away. How far away is the nearby galaxy?
2
What would be the angular diameter of the Milky Way as seen by an alien astronomer in the Virgo Cluster at a distance of 18 Mpc?
3
A galaxy has a recession velocity of 19,250 kilometers per second. What is its distance in megaparsecs?
4
A quasar's spectrum shows a shift in spectral lines (??/?) of 0.158. Use the Doppler-shift formula to determine what recession velocity this shift indicates, and then use the Hubble law to determine the distance to the quasar in Mpc if H = 70 km/sec/Mpc. Be sure to calculate the recession velocity in kilometers per second.
5
A radio galaxy shows lobes that extend 1.5 megaparsecs away from the galaxy on each side. If the accelerated electrons in the lobe travel at nearly the speed of light, how long will it take them to travel to the edge of the lobe?
6
A nearby radio galaxy 50 megaparsecs from the Earth has a 1 billion solar mass black hole at its center. If the diameter of this black hole is twice its Schwarzschild radius, calculate the angular size of the black hole as seen from Earth. Convert the angular size from degrees to arc seconds (3600 arc seconds per degree). Can we directly image the black hole as a dark spot in the accretion disk? Compare your result with 1 × 10-5 arc seconds, which is about the best resolution currently possible with the radio astronomy technique of very long baseline interferometry.
7
What is the minimum size of a quasar that shows variations in brightness over a period of 36 hours? Express your answer in kilometers.
8
Estimate from figure 17.33 the ratio of the diameter of the local group to the diameter of the Milky Way (100,000 light-years across). Compare this with the ratio of the diameter of the Milky Way to the diameter of the Solar System (including the Oort cloud, the Solar System's diameter is about 200,000 AU).
9
A galaxy cluster has a total mass of 1015 M.. If the cluster contains 100 galaxies, each with typical masses of 1011 M., and 10 times as much mass in hot X-ray gas as in galaxies, how much dark matter is contained in the cluster? What percentage of the total mass is this?
10
NGC 3200 has a rotation speed of 200 kilometers per second at 5 kiloparsecs from its center, and 210 kilometers per second at 50 kiloparsecs. What is its mass within each distance, and what makes up most of the mass in each region?
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