Kepler’s Laws from Comoment Maps

1 Introduction
2 Foundations ▶
- 2.1 Phase Space
- 2.2 Energy and Conserved Vectors
3 Dynamics ▶
- 3.1 The Vector Field
4 Conserved Quantities ▶
- 4.1 Constancy Along Solutions
- 4.2 Algebraic Relations
5 Poisson Brackets and Comoment Maps ▶
- 5.1 Canonical Bracket
- 5.2 Rotation Observables
6 Hidden \(\mathfrak {so}(4)\) Symmetry ▶
- 6.1 Fixed Negative-Energy Surface
7 Orbit Geometry and Kepler’s First Law ▼
- 7.1 Geometric Parameters
- 7.2 Orbit Equation
8 Kepler’s Second Law ▶
- 8.1 Areal Quantities
9 Periods and Kepler’s Third Law ▶
- 9.1 Periods
10 Kepler’s Laws: Combined Statement
Dependency graph

7 Orbit Geometry and Kepler’s First Law

From the conserved quantities we now read off the geometry of the orbit.

7.1 Geometric Parameters
7.2 Orbit Equation