#AP Physics C: Mechanics - Satellite Motion 🚀

Hey there! Let's get you prepped for the AP Physics C: Mechanics exam with a deep dive into satellite motion. We'll break down everything from circular orbits to escape velocity, making sure you're not just memorizing formulas but truly understanding the concepts. Let's get started!

#Motions in Gravitational Systems

#Central Object Motion

• Key Idea: In a satellite-central object system, the central object is so much more massive that we treat it as stationary. 🪐
• The central object's motion is negligible compared to the satellite's orbit.
• No need to calculate the central object's motion; it's effectively at rest.

#Satellite Orbit Constraints

• Conservation Laws: These are your best friends! They dictate how satellites move.
• Circular Orbits:
  • Total mechanical energy, gravitational potential energy, kinetic energy, and angular momentum are all constant.
  • Think of it as a perfectly balanced system.
• Elliptical Orbits:
  • Total mechanical energy and angular momentum are constant.
  • Gravitational potential energy and kinetic energy vary throughout the orbit.
• Gravitational Potential Energy:
  • Defined as zero when the satellite is infinitely far away.
  • Becomes increasingly negative as the satellite gets closer to the central object.

#Energy in Circular Orbits

• Energy Relationship: The total energy can be expressed using either potential or kinetic energy.
• Kinetic Energy: $K = -\frac{1}{2} U$ (always half the magnitude of potential energy).
• Total Energy: $E_{\text{total}} = \frac{1}{2} U = -\frac{GMm}{2r}$ 🛰️
  • $G$ = gravitational constant
  • $M$ = mass of the central object
  • $m$ = mass of the satellite
  • $r$ = ra...