In the late 19^th century, George Hill first derived a set of equations that approximately govern the motion of a small mass in a hierarchical 3-body system.

In the 2-D case, Hill's equations become (in non-dimensional terms)

Where the frame is fixed on m₂ and x points away from m₁. d is the distance to m₂ (sqrt(x²+y²)).

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By John Weiss
Rendered Sunday 30 March 2003