# 11: Conservative two-body Central Forces

- Page ID
- 9620

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- 11.1: Introduction to Conservative two-body Central Forces
- Conservative, central, two-body central forces are important in physics because of the pivotal role that Coulomb and gravitational forces play in nature. Therefore this chapter focusses on the physics of systems involving conservative two-body central forces.

- 11.2: Equivalent one-body Representation for two-body motion
- The equations for relative motion of two bodies interacting via two-body central forces can be represented by an equivalent one-body problem simplifying the mathematics.

- 11.3: Angular Momentum
- Angular momentum is an important conserved quantity.

- 11.4: Equations of Motion
- Equations of motion.

- 11.5: Differential Orbit Equation
- Differential orbit equation. Binet coordinate transformation.

- 11.6: Hamiltonian
- Hamiltonian for conserved two-body central forces.

- 11.7: General Features of the Orbit Solutions
- General features of the orbit solutions for two-body forces.

- 11.8: Inverse-square, two-body, central force
- Inverse-square, two-body, central force. Eccentricity vector.

- 11.9: Isotropic, linear, two-body, central force
- Isotropic, linear, two-body, central force. Symmetry tensor.

- 11.10: Closed-orbit Stability
- Closed-orbit stability. Bertrands theorem.

- 11.11: The Three-Body Problem
- The three body problem. Planar approximation and the restricted three-body approximation.

- 11.12: Two-body Scattering
- Two-body scattering cross-sections. Rutherford scattering.

- 11.13: Two-body kinematics
- Two-body kinematics. Velocities, angles, kinetic energies, solid angles, optimum detection of the scattered two bodies.

Thumbnail: Two bodies with a major difference in mass orbiting a common barycenter internal to one body (similar to the Earth–Moon system). (Public Domain; Zhatt).