The Law of Gravity

The force ${\bf F}$ between two point objects of masses $m$ and $M$, separated by a distance $r$ has a magnitude

$$F ~=~ G {Mm\over r^2}$$ (1.1)

The force is attractive and points along the line between the two objects. This gravitational force is very fundamental. It can't be explained in terms of other forces such as the forces between charged particles. It doesn't matter what the material is made up of, old pillows, blueberries, lungfish, you name it, as long as the mass is the same, the force is the same. This has been thoroughly tested.

The symbol $G$ is a constant known as the gravitaional constant. It was first determined a long time ago , 1798, by Lord Cavendish. It was quite impressive how he managed to do it.

Essentially he took two small masses and hung them from a very thin quartz fiber. The fiber exerts a tiny torque if twisted away from its equilibrium position. So it makes a very sensitive force meter. He then took two larged masses a put them close to the hanging ones, measuring the twist of the fiber. He did this by attaching a little mirror to the fiber and shining a beam of light at it. It then bounces off the mirror to a wall quite far away. Measuring the displacement of the dot on the wall, you can calculate the force between to two masses. Knowing their distance and their masses, you have enough information to calculate $G$. Cavendish did a jolly good job and even today, $G$ is only known to about three decimal places! Its value is

$$G ~=~ 6.67 \times 10^{-11} {N m^2\over kg^2}$$ (1.2)