Some Non-SI Units
While most scientific measurements use SI Units (meters, [kilo]grams, seconds) with various Metric Prefixes there are several historical units that commonly arise in astronomy that are still used. Some of these also take metric prefixes, for instance kiloparsecs (kpc) and megaparsecs (Mpc) occur frequently.

The tables below provide equivalences for some of the more common units you may encounter in this course.

Unit Symbol Metric Equivalent Used for
Angstrom 10-10m Atomic physics; Spectroscopy
Earth Radius 6.378 x 106m Planetology
Solar Radius 6.96 x 108m Stellar astronomy
Astronomical Unit AU 1.496 x 1011m Solar system astronomy
Lightyear ly 9.46 x 1015m Interstellar & intergalactic astronomy
Parsec pc 3.09 x 1016m Interstellar & intergalactic astronomy
In the context of cosmology, very large distances (and velocities) are also measured in terms of redshift. This is not actually a unit, but is a dimensionless measurement. In terms of velocity, it can be related to the ratio of velocity to the speed of light. It can then be related to a distance (or to a time) through certain assumptions about the expansion of the universe. The exact relationship is complex, and the numbers involved are constantly changing due to new measurements and models, so suffice it to say here that if a distance is measured in terms of redshift it is many megaparsecs.
Unit Symbol Metric Equivalent Used for
Earth Mass 5.98 x 1024kg Planetology
Solar Mass 1.99 x 1030kg Stellar and galactic astronomy

Unit Symbol Metric Equivalent Used for
Solar Luminosity 3.90 x 1026Watts Stellar and galactic astronomy

Luminosities are also measured in terms of absolute magnitude. This is not a unit of measurement per se, but is related to ratios of luminosity in a non-linear way which many people find confusing (especially since there is a related measure known as apparent magnitude to deal with as well). Suffice it to say here that a smaller magnitude means a brighter star.
Chris Dolan at the University of Wisconsin - Madison Astronomy Department has a JavaScript Astrophysical Calculator that includes astrophysical constants and planetary data that you may find useful if you need to do any calculations with these numbers. Note: The units are implemented as constants, so if you want to enter 4 astronomical units, you would have to punch 4 x AU. You must have JavaScript enabled on your browser for the calculater to work.

Scott Smith