Gravitational Force and Orbital Motion
This page introduces fundamental concepts in celestial mechanics for Terminale students. It covers gravitational force, acceleration, and the gravitational field, providing essential formulas for the Spécialité physique-chimie Terminale course.
The gravitational force is explained using Newton's second law, relating it to mass and acceleration. The gravitational field is defined as the force per unit mass, expressed as a vector pointing towards the center of the attracting body.
Definition: The gravitational force F = GMm/r² u, where G is the gravitational constant, M and m are the masses of the attracting and attracted bodies, r is the distance between them, and u is a unit vector.
For circular orbits, the page derives the formula for satellite velocity:
Formula: v = √GM/r, where v is the orbital velocity, G is the gravitational constant, M is the mass of the central body, and r is the orbital radius.
The orbital period T is then related to the radius r and the central body's mass M:
Formula: T = 2πr√r/GM, a crucial equation in the Mouvement dans un champ de gravitation Terminale syllabus.
Highlight: This page lays the groundwork for understanding orbital mechanics, essential for solving problems related to satellite motion and planetary orbits in the Programme physique-chimie Terminale.