How do the gravitational pulls of planets affect Keplerian orbits?

Kepler’s laws of planetary motion, formulated by the German astronomer Johannes Kepler, describe planetary motion as if each planet were orbiting the Sun in isolation. In reality, these laws are only approximations because they do not account for the gravitational interactions between planets.12

Because planets exert gravitational forces on one another, the total force acting on a planet is not solely due to the Sun. These mutual attractions cause small deviations, or perturbations, from the ideal elliptical orbits that would occur in a simple two-body system.13

Because all planetary masses are very small compared to the mass of the Sun, these perturbations are minor, allowing the motion of a planet to be treated as a slightly perturbed ellipse. Celestial mechanicians use complex perturbation theories to calculate how these gravitational pulls cause the parameters of an orbit—such as its eccentricity, inclination, and orientation—to vary slowly over time. While the "two-body problem" has an exact solution, the interaction of multiple bodies means that predicting precise motions requires numerical solutions or successive approximations.13