Why are Kepler's laws approximate rather than perfectly exact for the solar system?

Kepler’s laws are considered approximate because they are derived from the "two-body problem," which assumes a planet orbits an isolated, fixed Sun under the influence of a single central force. In reality, the solar system is an n-body system where multiple factors prevent perfect adherence to these laws:123

• Mutual Gravitational Perturbations: Planets do not just orbit the Sun; they also exert gravitational forces on one another. These interactions "perturb" the ideal elliptical paths that would occur if a planet were orbiting the Sun alone.2
• Motion of the Sun: Kepler’s laws assume the Sun is a fixed point. In actuality, the Sun itself experiences small accelerations due to the gravitational pull of the planets.2
• Complexity of the n-body Problem: Because every body in the solar system interacts with every other body, there is no exact analytical solution for their motions. While Kepler’s laws are excellent approximations because planetary masses are very small compared to the Sun, they remain incomplete descriptions of the complex gravitational dynamics at play.2

Ultimately, these laws serve as a foundational, highly accurate model, but they do not account for the continuous, subtle gravitational tugs that define true celestial mechanics.2