Gravitational force

At the end of the 17th century, Newton understood that the movement of the planets, in the same way as the movement of the Moon, is caused by the force of gravitation and that this same force is also responsible for the “weight” of objects on Earth (the apple).

Two objects of masses $M_1$ and $M_2$ attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

$$F = \frac {G \times M_1 \times M_2} {D^2}$$

$G$ is a constant equal to $6.67428 \times 10^{-11} \space m^3kg^{-1}s^{-2}$

Kepler’s laws, which govern the motions of planets in the Solar System, can be deduced directly from this expression.

When more than two bodies are present, each one is subjected to the force of attraction of the others and it becomes very hard to determine the movements of the bodies.

Even the three-body problem is very complicated.

Thus, the theory of the movement of the Moon in the presence of the Earth and the Sun, is a life’s work, that of astronomer Charles-Eugène Delaunay, whose results are still today the reference for calculations now performed on computers.