Kepler's First Law of Planetary Motion

Johannes Kepler stated in his first law that each planet traces an elliptical orbit, with the Sun at one of its foci.

In the elliptical orbit, a planet is closest to the Sun at the perihelion point A and farthest from the Sun when it is at the aphelion point B. The average distance of the planet from the Sun is equal to the semi-major axis of the ellipse.

At perihelion, the planet's potential energy is lower than at aphelion, since distance r_A is smaller than distance r_B.

Following the energy conservation principle, the total energy of the planet in a closed orbit is conserved. Therefore, the kinetic energy of the planet at perihelion is higher than at aphelion.

Since the kinetic energy equals half times the product of the planet's mass and square of its orbital velocity, the planet moves faster in its orbit when it is closer to the Sun at perihelion and slows down when it is away from the Sun.