How can I change our units so that Newton's gravitational constant is $G=1$? I'm just wondering if you can change our arbitrary values for , say, the kg, meter, or newton so that G=1 instead of 6.67x10^-11
 A: This is commonly done in general relativity to avoid cluttering up already complicated equations with factors of $G$ and $c$. The system of units is called geometrised units. The table here gives the units for the various physical quantities in these units.
A: Atomic units (https://en.wikipedia.org/wiki/Atomic_units) are used for a similar purpose for quantum mechanical calculations. In this system many quantities such as the reduced Planck's constant $ \hbar $ are equal to one. You can always make whatever units you want.
$$ G = 6.67408×10^{-11} m^3 kg^{-1}s^{-2} $$
So let's just make up some new unit of length called A, and let's say
$$ 1 A^3 = 6.67408×10^{-11} m^3 $$
Now in our new units:
$$ G = 1 A^3 kg^{-1} s^{-2} $$
A: I mean, trivially, yes.  You can do whatever the hell you want.  Let's make a new unit of force called a "Gravinewton" (GN) such that:
$\frac{1 \text{ kg} \cdot 1 \text{ kg}}{(1 \text{ m})^2} \cdot 1 \frac{\text{ m}^3}{\text{kg}\cdot\text{s}^2} = 1 \text{ GN}$
Disclaimer: this will make Newton's second law into $\vec{F} = m\vec{a}\cdot6.67\times10^{-11}$, so, that's a thing.
A: If we take G=1, then masses should be in solar mass and and distances in parsec and time in year.
