Therefore, the gravitational force

**that the Earth exerts on the Moon is perpendicular to Moon's velocity**

*F*_{g}**, so it is a centripetal force**

*v***, making the trajectory of the Moon bend:**

*F*_{c}$$ F_{g}=F_{c} \\

\frac{GMm}{r^2}=\frac{mv^2}{r} $$ where

*G*is Newton's constant,

*M*is Earth's mass,

*m*is Moon's mass and

*r*is the radius of the orbit.

This implies that the kinetic energy of the Moon is

$$

K=\frac{1}{2}mv^2=\frac{GMm}{2r}

$$ which is smaller than the absolute value of the potential energy

$$

U=-\frac{GMm}{r}

$$ So the mechanical energy of the Moon is

$$

E=-\frac{GMm}{2r}

$$

We know that at the time of its formation, the Moon sat much closer to the Earth, a mere 22,500 km away, compared with the 402,336 km between the Earth and the Moon today. So the Moon is getting further away from Earth, now at the rate of 3.78 cm per year. Nevertheless, according to the last equation, a larger

*r*means that the Moon has more energy every year. Is its energy non conserved? Who is giving energy to the Moon?