Johannes Kepler was the first to analyze the law relating to motion of the planets. He was the first person to find out that the planets’ orbits are elliptical and not circular as was the belief of the people in the past. He also found out that the sun is located at a focus and not at the centre point of the orbits. It was previously believed that the planet’s orbital speed is not constant and that the planet’s speed depends much on the sun’s distance from the planet. Kepler also discovered a relationship that is universal for all properties relating to planets that orbit round the sun.
Due to gravitational disturbances, Mercury, a planet that is the smallest in the solar system has a very eccentric orbit. Smallest eccentricities are found in the case of Neptune and Venus. Mars’ eccentricity is the greatest. There are dwarf planets, space debris, asteroids and comets which have elliptical orbits. A comet however in a hyperbolic or parabolic orbit is not bound gravitationally to any star. Of course, no comet till date has a specifically hyperbolic orbit.
While orbiting of two objects take place, they meet at periapsis which is the point the two objects come close to each other while apoapsis is where they get farther off from each other. While the planet gets closer to the periapsis point, it increases in its velocity and when it reaches the apoapsis point, the velocity decreases.