The Solving of the Kepler's Problem for Six Planets of Solar System.
Abstract:
In the following methodical article we describe the effort of teenaged schoolers to solve the classical Kepler's problem, taking three Newton's laws and his law of gravity as a base. Traditionally this brunch of physics is not included in school programs, earlier because of the elements of the mathematical analysis needed in the formulation of the question not included in it, and nowadays because the theory of integrating, which are used in solving of this problem consist only in the school program of the XI form, when the astronomy and the mechanics were being already studied. The proposed variant of solving needs neither integrating nor differential equations, appearing during the formulation of the problem. We use the law of the Laplas' vector conservation, that defines elliptic orbits of planets. All physical and mathematical effects used in the search for solution are argued and proved if it is necessary during education process. To reach the shortness in transformations the arguments of functions may be left during writing down. For the same reason vectors always are written in the bold font instead of using arrows (as it used in secondary schools).
