Question

why is it preferred to write field strength as (Gm/r^3)*r*?

Answer 1

\vec{F} = Gm/r^2 \^{r} but \^{r} = \vec{r}/r
\therefore \vec{F} = Gm/r^2 \vec{r}/r
so \vec{F} = Gm/r^3 \vec{r}

Answer 2

I think its because Gm/r^2 does not give a vector direction so it is only a scalar quantity. (Gm/r^3)*r* gives you both the magnitude and direction. I suspect that it will become more important when the fields are no longer spherical

Answer 3

Thanks guys. Seems like it started to make sense when I added vectors. Cosine and sine are both calculated with r in the numerator and resulted in r^3 in denominator.