Question

How does Kepler’s law contradict with circular motion?

Answer 1

Circular motion says that all orbits are perfect circles with the orbiting body on the circumference and the primary at the center. However, Kepler identified that orbits are not perfect circles but they are ellipses with the primary at one focus. While the actual shape of the orbit is very close to a circular shape.

Complete answer:
Kepler’s first law states that each planet's orbit about the Sun is an ellipse. The Sun's center is always located at one focus of the orbital ellipse. The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit.
Kepler’s second law states that the imaginary line joining a planet and the Sun sweep equal areas of space during equal time intervals as the planet orbits. That planets do not move with constant speed along their orbits. Rather, their speed varies so that the line joining the centers of the Sun and the planet sweeps out equal parts of an area in equal times. The point of the nearest approach of the planet to the Sun is termed perihelion. The point of greatest separation is aphelion, hence by Kepler's Second Law, a planet is moving fastest when it is at perihelion and slowest at aphelion.
The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.
It is the first law that mainly contradicts the laws of circular motion. In a circular motion, the body always moves in a perfectly circular path. But according to Kepler’s law, the path of the planet is elliptical. Now if we consider the second law then a body moving in a circular path moves with a uniform speed. It is called a uniform circular motion.

Note: If you notice that an imaginary line connecting the sun and a body in a circular motion always covers the equal area in an equal period of time, it is also true for the planet revolving in an elliptical path around the sun. The main difference is that the velocity of the planet is changing with time but the velocity of the body in a uniform circular motion is not changing.