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Three Body Dynamics. 4 September 2018. Pluto and Charon Orbits. Cassini trajectory shows gravity assists from Venus, Earth, Jupiter. Tadpole and horseshoe orbits. 3-body Problem. 2-body problem is soluble in closed form (see the lecture from last time).
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Three Body Dynamics 4 September 2018
Cassini trajectory shows gravity assists from Venus, Earth, Jupiter
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
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