M2 · Central forces & orbits
A 28-module path through m2 · central forces & orbits, in study order from foundations to the frontier.
Modules
- Central Force Fundamentals
- The Two-Body Problem and Reduced Mass
- Angular Momentum Conservation in Central Fields
- Reduction to the Radial Equation
- The Effective Potential
- Classification of Orbits by Energy
- The Orbit Equation and Binet's Equation
- The Kepler Problem
- Conic-Section Orbits
- Kepler's First Law: Elliptical Orbits
- Kepler's Second Law: Equal Areas
- Kepler's Third Law: Period-Semimajor Relation
- Orbital Elements and Parameterization
- Kepler's Equation and Time of Flight
- The Laplace-Runge-Lenz Vector
- Hidden Symmetry and Orbit Closure
- Bertrand's Theorem
- Stability of Circular Orbits
- Apsidal Angles and Orbital Precession
- Perturbations and Perihelion Precession
- Virial Theorem for Central Forces
- Scattering in a Central Potential
- The Differential Cross-Section
- Rutherford Scattering
- Total Cross-Section and Scattering Limits
- Rainbow and Glory Scattering
- Gravitational Potential Energy and Escape Velocity
- The Shell Theorem and Spherical Mass Distributions