Gravitational Force

The gravitational force is between at least two objects.  It:

• Acts along a line connecting the two objects.
• Is proportional to the masses.
• Is inversely proportional to the square of the distance between the centers of the two objects.

It can be modeled in several different ways.  The approximate gravitational force is $$|\vec{F}_{grav}| = mg$$However, there is a much more accurate, albeit complicated, way of determining the forces of gravity.  To determine the force of gravity from one object upon another, you simply use the equation:$$\vec{F}_{grav \space on \space 2 \space by \space 1} = -G\frac{m_1 m_2}{|\vec{r}|^2} \hat{r}$$
$\vec{r} = \vec{r}_2 - \vec{r}_1$ extends from the center of object 1 to object 2.
$G = 6.7 \times 10^-11 \frac{N m^2}{kg^2}$ and is known as the gravitational constant ($G$).

To calculate the magnitude of gravitational field near an object's surface, use the equation:$$g = G\frac{M_E}{R_E^2}$$