Section 2: Introduction to Kepler's laws and the Dynamics of Spaceflight

• Orbital Kinematics:
  • The n-body problem
  • The 2-body problem
• Kepler's First Law, Conic Sections
  • Circular and Elliptical Orbits

• Kepler's Second Law
  • The "Swept-Area Integral"
  • Swept-Area Working Charts for a Unit Ellipse
  • Orbital Angular Momentum
• Kepler's Third Law
  • Velocity vector and Angular velocity
  • Orbital Period Law
  • Escape Velocity
• Appendix I: Deriving Kepler's Law from the Swept Area Integral
• Appendix II: Numerical Solutions of Kepler's Equation

• Orbital Dynamics: The Vis-Viva Equation
  • Gravitational Potential Energy
  • Kinetic Energy
  • Total Orbital Energy
  • Proof of the Vis-Viva Equation
  • Vis Viva Equation for all of the Conic Sections
  • Appendices to Section 2.3
    • Alternate Proof of Vis-Viva Equation for Elliptical Orbit
    • Proof of Vis Viva Equation for Hyperbolic Orbit

Addendum to Sections 1-3: ............... (pdf)

• The Open Conic Sections
  • What Happens to Elliptical orbit as A-->"infinity"
    • The Cartisian Form of the Parabola Equation
    • The Polar Form of the Parabola Equation
• The Equation of a Hyperbola
  • Polar Form of Hyperbola Equation
  • Asymptotic Behavior of Hyperbolic Trajectory
• Summary of the Conic sections
  • Eccentricities
  • Polar Forms
  • Vis-Viva Equations

Lecture4 Notes: .................. (pdf )