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| Active Galaxies and Quasars |
1. About 760 light years, using the Small-Angle Formula Calculator.
2. The radius of the Sun is 6.96 x 105 km. Taking this as a characteristic size for a normal star in a binary containing a black hole of five solar masses, we find from the table of black hole sizes that the ratio of the radii for the normal star and the black hole is
The ring in the Hubble image of NGC 4261 is about 400 LY ~ 3.8 x 1015 km in radius. The billion solar mass black hole has a radius of about 3 x 109 km. Thus, the ring is about
times larger than the black hole. Since the black hole is a million times smaller than the torus, it could not be seen in the Hubble image, even if it were not obscured.
3. There are 3600 seconds in an hour, so in that time light travels 3600 s x 300,000 km/s = 1.08 x 109 km = 7.2 AU.
4. In a week there are
Since light travels at about 3 x 105 km/s, the distance in a light week is
which is about 1200 AU.
5. From the small angle formula, the linear distance d corresponding to 0.05 arc seconds at a distance of 18.4 Mpc is
from which d = 4.46 pc = 1.4 x 1014 km for the minimum diameter region the HST could resolve at the distance of M87. But a billion solar mass black hole has a Schwarzschild diameter of less than 1010 kilometers, which is orders of magnitude smaller than the best resolution of the HST. The solution may also be obtained with the Small-Angle Formula Calculator.
6. Using the Small-Angle Formula Calculator, as in the preceding exercise, 0.05 arc seconds at a distance of 2.9 Mpc corresponds to a size of about 0.7 pc = 2.1 x 1013 km, which is much larger than the expected diameter of a billion solar mass black hole (less than 1010 kilometers).