Solution (source code)

= Solution

For the two-body approximation with a dominant central mass, <Kepler's laws of planetary motion> are:

* <Kepler's first law>: a bound planetary <orbit> is an <ellipse> with the central attracting body at one focus.
* <Kepler's second law>: the line from that focus to the planet sweeps equal areas in equal times, equivalent to constant <areal velocity>.
* <Kepler's third law>: the squared <orbital period> is proportional to the cube of the <semi-major axis>, $T^2=4\pi^2a^3/(GM)$ when the orbiting mass is negligible.

The first law includes a <circular Kepler orbit> as a special case. The third-law constant is the same for bodies orbiting the same dominant mass.