Gravitation

Newton's Universal Law of Gravity states that for any two objects with masses $m_1$ and $m_2$, there is an attractive gravitational force between them with magnitude $F = \frac{Gm_{1}m_{2}}{r^2}$ where r is the distance between their centers and G is the gravitational constant $6.6743 \times 10^{-11} Nm^2 / kg^2$.

An object in the orbit of earth has one applied force $F_{g} = \frac{GM_{E}m}{r^2}$.

If $F_g = F_c = \frac{mv^2}{r}$, the object will orbit.

$$\frac{GM_{E}m}{r^2} = \frac{mv^2}{r} \to v^2 = \frac{GM_{E}}{r}$$ $$\therefore v_{\text{orbital}} = \sqrt{ G \frac{M_{E}}{r} }$$