Gravitational Field and Satellite Motion
This page introduces the fundamental concepts of movement in a gravitational field within the context of satellite motion. It establishes the framework for understanding celestial mechanics at the high school level.
The page begins by defining the reference frame as geocentric or heliocentric, assumed to be Galilean. It then applies Newton's Second Law to a satellite's motion, considering only the gravitational force.
Definition: The gravitational force is given by F = G × m × M / r², where G is the gravitational constant, m is the mass of the satellite, M is the mass of the attracting body, and r is the distance between their centers.
The acceleration of the satellite is broken down into tangential and normal components using the Frenet frame.
Highlight: The acceleration vector is shown to be radial and centripetal, a crucial concept in understanding orbital motion.
The page concludes by deriving the expression for centripetal acceleration in terms of velocity and radius, setting the stage for further analysis of orbital dynamics.
Vocabulary: Centripetal acceleration refers to the component of acceleration directed towards the center of curvature of the orbit.