Mercury, not Venus, is the nearest planet to Earth and every other planet solar

It is nicely done, they've proved it by the time they turned the integral into the second Elliptic Integral, but using PyEphem to simulate it numerically is great.

My gut feel from a lifetime of futzing around with rectifiers, A.C. current and the effects of cross terms like the one in

   sqrt(1+αx+βx^2)

where the linear term is driven by the sunward distance to the other planet but the quadratic term is driven directly by the motion of the other planet perpendicular to the sun.

In the full calculation x is going to swing from (say) -0.5 to 0.5 and higher order terms are to matter, but the sunward motion will cancel when you integrate over the orbit, leaving the excess distance from the perpendicular motion to be the important thing.