Question

While a planet P rotates in a circle about its sun, a moon M rotates in a circle about the planet, and both motions are in a plane. Let's call the distance between M and P one {\it lunar unit}. Suppose the distance of P from the sun is 3.5×103 lunar units; the planet makes one revolution about the sun every 9 years, and the moon makes one rotation about the planet every 0.25 years. Choosing coordinates centered at the sun, so that, at time t=0 the planet is at (3.5×103, 0), and the moon is at (3.5×103, 1), then the location of the moon at time t, where t is measured in years, is x(t)=? y(t)=?

Answer 1

aka Circular restricted three-body problem