Order of Magnitude

We often deal with a variety of large and small numbers. It is not always important to know a certain number to great accuracy, but only roughly. For example, if you budget for a week of groceries, you probably don't need to know ahead of time whether the bill will be $49.96 or $52.31. Knowing that groceries will be somewhere in the ``neighborhood'' of 50 bucks is close enough.

Here are some astronomical examples:

The radius of the Sun (s), Jupiter (j), and Earth (e):

$$R_s = 695,700 km \approx 700,000 km$$

$$R_j = 71,400 km \approx 70,000 km$$

$$R_e = 6,378 km \approx 7,000 km$$

So, Jupiter is about 10 times the size of the Earth (actually 11.2 times); the Sun is about 10 times the size of Jupiter (actually 9.7 times); and the Sun is about 100 times the size of the Earth (actually 109 times). These are order of magnitude estimates. They are not ``exactly'' right, but usually close enough for purposes of discussion, unless more exact values are required for some formal calculation (like sending a rocket to the Moon).