Working With Units


Units are a valuable tool; careful attention to the units involved at each stage of a calculation can help you catch and fix mistakes. Much confusion can be avoided if you work with units as though they were symbols like those in algebra. For example:

Astronomers use a mixture of units, and we often have to convert one to another. Converting between different units is easier if you remember to treat units like symbols; you simply replace the original unit with its equivalent in the unit desired, and do the necessary arithmetic. For example:

What about converting the other way? Again, treating units as symbols simplifies the problem:

Here are the factors needed to convert between the different systems of units used in astronomy. Notice that there are many different length units:

Years 1 yr = 3.15 × 107 sec
Astronomical Units 1 AU = 1.496 × 1011 m
Light Years 1 ly = 9.461 × 1015 m
Parsecs 1 pc = 2.062 × 105 AU = 3.086 × 1016 m
Kiloparsecs 1 kpc = 103 pc = 3.086 × 1019 m
Megaparsecs 1 Mpc = 106 pc = 3.086 × 1022 m
Earth Masses 1 MEarth symbol = 5.967 × 1024 kg
Solar Masses 1 MSolar symbol = 1.989 × 1030 kg

Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: August 23, 2006
http://www.ifa.hawaii.edu/~barnes/ast110_06/units.html
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