Newtonian mechanics and Kepler's laws of planetary motion do not necessarily contradict each other but rather complement each other. In fact, Kepler's laws can be derived from Newtonian mechanics under certain assumptions.
Kepler's laws, formulated by Johannes Kepler in the early 17th century, describe the motion of planets around the Sun based on empirical observations. They are as follows:
Kepler's First Law (Law of Orbits): Planets move in elliptical orbits, with the Sun at one of the foci of the ellipse.
Kepler's Second Law (Law of Areas): A line segment joining a planet to the Sun sweeps out equal areas in equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther away.
Kepler's Third Law (Law of Harmonies): The square of the orbital period of a planet is proportional to the cube of its semi-major axis (the average distance between the planet and the Sun raised to the power of 3/2).
Newtonian mechanics, developed by Sir Isaac Newton in the late 17th century, provides a more fundamental explanation for the motion of celestial bodies, including planets. It encompasses Newton's laws of motion and the law of universal gravitation. According to Newton's laws, any two objects with mass exert an attractive force on each other, and the strength of this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
By applying Newton's laws of motion and the law of universal gravitation, one can mathematically derive Kepler's laws as approximate solutions for the motion of planets under the influence of the Sun's gravitational force. This derivation assumes that the planets have negligible mass compared to the Sun, and that there are no significant gravitational interactions between the planets themselves.
So, rather than contradicting each other, Newtonian mechanics provides a more comprehensive framework that explains the underlying principles behind Kepler's laws and extends them to describe the motion of all objects in the universe, not just planets.