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Cell[CellGroupData[{
Cell["The Restricted Three-Body Problem: Sun-Jupiter & \"X\"", "Title"],

Cell["AP1603", "Subsubtitle"],

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Cell["Introduction", "Section"],

Cell["\<\
Some definitions for Jupiter's orbit. For simplicity, we'll take Jupiter's \
orbit to be a circle, and we'll study only motion on the plane.\
\>", "Text"],

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Cell["Equations of Motion: Sun & Jupiter", "Section"],

Cell["\<\
The equations of motion for a planet describe the time evolution of the \
planet's phase-space location and its initial position.\
\>", "Text"],

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Cell["Earth's Orbit", "Subsection"],

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relatively easy to calculate. The key is finding the appropriate initial \
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Cell["\<\
The orbit is a circle because of our choice of the initial condition.\
\>", "Text"]
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Cell["Longer Integration Times", "Section"],

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Cell["Asteroid Resonances", "Section"],

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Cell["Kirkwood Gaps", "Subsubsection"],

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Kirkwood gaps shown in a histogram of asteroid orbits in the main asteroid \
belts. The gaps labeled \"3:1\", \"5:2\", \"7:3\", \"2:1\" are caused by \
mean-motion resonances between an asteroid and Jupiter. For example, at the \
3:1 resonance, the asteroid completes three orbits for every one orbit of \
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