Trajectoire d'un satellite artificiel en chute autour de la terre

TL;DR

This paper develops a mathematical model to determine the trajectory of a satellite falling towards Earth, accounting for air resistance and varying air density with altitude.

Contribution

It introduces a comprehensive mathematical approach incorporating air friction and density variation to predict satellite trajectories during descent.

Findings

Derived equations linking trajectory, speed, and air density.

Analyzed the impact of initial conditions on satellite descent.

Validated the model with zero initial velocity scenario.

Abstract

The project consists to determine, mathematically, the trajectory that will take an artificial satellite to fight against the air resistance. During our work, we had to consider that our satellite will crash to the surface of our planet. We started our study by understanding the system of forces that are acting between our satellite and the earth. In this work, we had to study the second law of Newton by taking knowledge of the air friction, the speed of the satellite which helped us to find the equation that relates the trajectory of the satellite itself, its speed and the density of the air depending on the altitude. Finally, we had to find a mathematic relation that links the density with the altitude and then we had to put it into our movement equation. In order to verify our model, we'll see what happens if we give a zero velocity to the satellite.