Calculus › Section K · Conics, parametric equations, and polar coordinates › Topic K.6
Polar equations of conics and Kepler's laws
Put a conic's focus at the pole and its polar equation shrinks to one small fraction involving eccentricity. That is exactly the frame in which nature writes orbits, which is how these equations lead straight to Kepler's laws of planetary motion.
In this topic
- Why put the focus at the pole
- One definition, three curves
- Deriving the polar equation
- Worked example: reading a polar conic
- Eccentricity in both languages
- Worked example: a hyperbola
- Kepler's first and second laws
- Kepler's third law and orbits today
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP