# Gravitational Systems

In this section of the site you can find material developed by our research group on the classical theory of gravitation. The material is aimed at teachers and students of high school and early university years and to the whole community of researchers and scholars who want to deepen the topic.

As is known, the Newtonian theory of gravitation is often neglected in the course of studies due to some peculiar criticalities, among which we can mention:

• poor (or nonexistent) knowledge on the part of students of the peculiar characteristics of the motion of the planets of the solar system observed in the night sky;

• lack of understanding of Newton’s idea-force and that the causes of the motion of the projectiles can be unified with those of the motion of the planets;

• poor mathematical pre-knowledge that allows to characterize, using the second law of dynamics and the hypothesis of universal gravitation, the possible orbits of a planet around the sun and to verify the validity of Kepler’s laws (the two-body problem );

We mainly faced the problem of how to overcome the lack of mathematical knowledge for the study of planetary motions.The developed material tries to adapt to the previous mathematical knowledge of different student audiences. Our intentions are to lead students to understand the structure of the model and its explanatory power of the observed phenomena and to be able to independently face explicit calculations at least in simple cases.

To this end, the study of planetary systems is proposed with the use of simplified forms of numerical analysis that can be easily transferred into computational methods of calculation. Both the spreadsheet and object-oriented software are intuitive tools that allow students to approach both the theoretical characteristics and the computational aspects of the evolution equations.

### Two-body Problem

### Three-body Problem

### Video

Keplerian Orbits

The Law of Circular Hodograph

Weak Pertubation

Strong Perturbation

Gravitational Slingshot

Brownian Motion