This project involves the application of molecular dynamics (MD) to a simple two-dimensional planetary system consisting of two planets and a fixed star. The primary focus is to construct a MD code using Newton’s law of universal gravitation as the interaction law and the Verlet algorithm for solving the initial value problem. The project examines the gravitational interaction described by Newton’s laws, focusing on the law of universal gravitation and its application to the planetary system. It further explores the principle of equivalence, the concept of conservative force, and the effective potential energy of the system. The discussion also covers the reduction of a single planet motion to one dimension, which offers insights into the trajectory of the planetary system. Finally, the project outlines the numerical approach using the Verlet algorithm for simulating the motion of the planets. The comprehensive understanding of the gravitational interactions and the computational techniques provide a solid foundation for the study of complex dynamical systems.

The principle of equivalence and its empirical foundation.

After many years of effort, Einstein discovered the general theory of relativity, the extension of special relativity to include the force of gravity. To do this, he extended the four-vector structure of special relativity to more general Riemannian geometries in which space-time is bent under the influence of gravity. The theory has successfully passed all the high precision tests now available. Predictions include the existence of black holes and gravitational waves. Both have now been convincingly observed. In this chapter, the basic concepts behind the theory are described and then illustrated by analysis of the Schwarzschild metric.

The Directive on Damages Actions 104/2014 (the Damages Directive) has laid down a common European framework for the regulation of competition damages actions. It establishes fundamental principles, such as the right to compensation and the joint liability of antitrust infringers for such compensation. However, it explicitly avoids defining causation, thus leaving it to the domestic laws of member states. The only limit set by the EU law is the observance of the principles of equivalence and effectiveness, in line with what was already disposed by the CJEU in Manfredi. However, there are some principles addressing causation that can be found in European law and case law.