homework and exercises - Astronomical Constant in Astronomical units?

I'm doing a computer simulation of the solar system and I'm having trouble working with big numbers (implementation specific problem). So what would be the Newtonian gravitational constant $G$ in relation with the Earth mass instead of kilograms and astronomical units instead of meters?

Answer

This is a typical "unit conversion" problem. Write $G$ in SI units:

$$G=6.6738\times10^{-11} \frac{\text{m}^3}{\text{kg}\cdot\text{s}^2}.$$

Now find out how many kilograms are in an Earth mass, and how many meters are in an astronomical unit. Also consider converting seconds to some other more convenient measure of time so that $G$ comes close to unity. (Thanks, Davidmh.)

All of this should help you convert units. See this page for further help.