Gravitational Perturbations

and the Prediction of New Planets

Computing the orbit of the Earth as an ellipse around the center of mass for the Earth-Sun system assumes that they are the only two masses in the Universe. In reality, the Universal Law of Gravitation implies that the Earth interacts gravitationally not only with the Sun, but with every other mass in the Universe: the Moon, the other planets, asteroids and comets, the distant stars.

The Two-Body Approximation

The Sun is so massive compared with every other object in the Solar System, Objects outside the Solar System such as stars are so distant that the distance squared factor in the denominator renders their gravitational interactions with the planets negligible.

Gravitational Perturbations

If we account carefully for all known gravitational perturbations on the motion of observed planets and the motion of the planet still deviates from the prediction, there are two options:

Newton's Law of Gravitation requires modification, There is a previously undetected mass that is perturbing the orbits of the observed planets.

The Discovery of the New Planet Neptune

This precise prediction of the new planet and its location was striking confirmation of the power of Newton's theory of gravitation. (Although in truth it must be said that both Leverrier and Adams made an incorrect assumption in their calculations concerning the radius of the new planet's orbit. Fortunately, the error largely cancelled out of the calculations and had little effect on their final results.)

The Accidental Discovery of Pluto

Effects Beyond Newtonian Perturbations