Keplerian planetary orbits in multidimensional Euclidian spaces

Abstract

Newton's laws of motion are three physical laws that together, laid the foundation for classical three dimensional mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. Kepler's laws of planetary motion are also three scientific laws describing the motion of planets around the Sun. Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a non uniform field of force by small steps. Even though neither the force was known nor its relation to motion, he could determine the differential equations of motion from observation. This is one of the most important achievements in the history of physics. In this paper, we will see that these laws are a consequence of Newton’s second law even in multidimensional Euclidian spaces.

Keywords: Central vector field; Differential equation.