/sci/ - Science & Math

But even if we stopped using the metric system, G would still be necessary. From Newton's second law, [math]\sum\mathbf{F}=m\mathbf{a}[/math] we can see that force has the dimensions [math]\frac{\text{mass}\times\text{length}}{\text{time}^2}[/math]. Note this has nothing to do with our choice of units. Newton and Kepler noticed that gravitational force is proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them. This is way too fucking long to say so we say [math]F_g\propto\frac{m_1m_2}{r^2}[/math]. Notice the right side of this proportionality statement (NOT an equation) doesn't have the correct dimensions. Thus there MUST be a constant of proportionality with dimensions [math][G]=\frac{\text{force}\times\text{time}^2}{\text{mass}\times\text{length}}[/math]. Which is exactly the system we have and how it was taught to me. Notice none of this was dependent on whether we used metric or british units or anything.

tl;dr you're wrong