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Three Body Dynamics

Delve into the complexities of three-body dynamics, from gravitational assists to numerical solutions, examining test particles and Lagrange points. Discover the motion and stability in the unsolvable 3-body problem.

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Three Body Dynamics

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  1. Three Body Dynamics 4 September 2018

  2. Pluto and Charon Orbits

  3. Cassini trajectory shows gravity assists from Venus, Earth, Jupiter

  4. Tadpole and horseshoe orbits

  5. 3-body Problem • 2-body problem is soluble in closed form (see the lecture from last time). • Since no general solution, resort to numerical solution or limiting cases • If one body is small: restricted 3-body problem • The small (third) body is called a test particle: it does not affect the two larger ones • Assume the 2 larger particles move in circles around their center of mass, CM

  6. Lagrange Points L1 – L5

  7. Motion of test particles in the 3-body Problem

  8. Summary • The 3-body problem is unsolvable • But a modified “energy” is conserved • Find places where test particle velocity vanishes: It can’t cross these “zero-velocity surfaces”. These bound the motion • Lagrange points are where forces vanish. The triangular ‘trojan’ points can be stble. • Key words: horseshoe and tadpole orbits; libration, circulation; resonances

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