Physics 110: Homework #9 Solutions

9.1

Orbital velocities: 250 km/s, 275 km/s, 300 km/s, 300 km/s. Masses: , , , . or , , , .

9.2

The rapid revolution of the stars near the center of the Andromeda Galaxy shows that 10 to 100 million solar masses of material lie within the central 1 or 2 parsecs of the galaxy.

9.3

We do not know the intrinsic brightness or luminosity of astronomical objects, so we cannot use their apparent brightness to determine distances. Likewise we do not know the intrinsic sizes of astronomical objects, so we cannot use their angular sizes to determine distances. Much astronomical research is directed toward finding classes of objects (e.g., supernovae, planetary nebulae, bright galaxies, and so on) that can be considered to have the same intrinsic brightness or intrinsic size so that they can be used as distance indicators. Evolution of intrinsic properties could have a significant impact on a tertiary distance indicator. For example, if a class of long-lived astronomical objects tended to grow dimmer as the objects aged, then such objects observed nearby would be intrinsically fainter than such objects viewed at great distances from us. This is because far away objects are being viewed when they're much younger than nearby objects.

9.4

Hubble's Law says that the apparent recessional speed of a galaxy (based on its measured redshift) is proportional to its distance from us. So by measuring a galaxy's redshift, we can determine its distance if we know the constant of proportionality, which is Hubble's constant. Hubble's Law is explained in the following way: The expansion of the Universe carries all galaxies away from one another. The apparent speed of recession increases with the distance between two galaxies. All observers in the Universe see the Universe expanding.

9.5

We know quasars are distant by determining their redshifts from emission lines and using Hubble's Law. Quasars are compact in size because the changes in their brightness as a function of time are fairly rapid, of order a day or so. This suggests that they can't be much larger than a size that corresponds to the distance that light travels in a day, which is about 170 AU. The orbit of Pluto (the outermost planet) is about 40 AU, so the size of a quasar is roughly the size of the solar system.

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