Satellites

A satellite on a circular orbit is always falling toward the planet, but moves sideways so fast that it keeps missing it. Gravity points to the centre and is the centripetal force.

Gravity points to the centre; the velocity runs along the orbit.

Set the pull equal to the centripetal force:

$$\frac{GMm}{r^2} = \frac{mv^2}{r} \quad\Rightarrow\quad v = \sqrt{\frac{GM}{r}}$$

The satellite's mass cancels. A lower orbit is faster.