# Units for Kepler's 3rd Law

## Homework Statement

Kepler's 3rd law can be written as ##p^2=a^3##
If p, the period, is given in years, what are the units for a?

n/a

## The Attempt at a Solution

The answer is AU. Is there a proof for this or is this merely a definition? Thank you.

Let's consider the Earth.

If we choose the "year" for period, then the value of ## a ## also have to be ## 1 ## with some unit and the only thing is ## 1 \text{AU}. ## You may think that this is the definition for ## \text{AU}. ##

BTW, be careful about dimensions of each side. ## (\text{Year})^2 \neq (\text{AU})^3, ## and so usually we write the law as ## p^2 \propto a^3. ##

S.G. Janssens