Classical approach to the many-body problem of astronomy
The perturbing forces of the Sun on the Moon at two places in its orbit. The blue arrows represent the direction and magnitude of the gravitational force on the Earth. Applying this to both the Earth's and the Moon's position does not disturb the positions relative to each other. When it is subtracted from the force on the Moon (black arrows), what is left is the perturbing force (red arrows) on the Moon relative to the Earth. Because the perturbing force is different in direction and magnitude on opposite sides of the orbit, it produces a change in the shape of the orbit.
In astronomy, perturbation is the complex motion of a massive body subjected to forces other than the gravitational attraction of a single other massivebody.[1] The other forces can include a third (fourth, fifth, etc.) body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body.[2]