This solution is pretty well recognized: Let “t” be the angle around a unit circle, then A=1/2*t gives circular area, and A_t=1/2*e*sin(t) gives the area of a triangle such that the sectorial area can be written: A_s=Sqrt(1-e^2)*(A+A_t). Invert this equation to get the correct time parameter. I doubt that your pals Julian and Neil are the first to have noticed this. Your preferred calculation is very similar to the certificate method I was discussing recently. One area integral is easy to calculate and equals the sectorial area by the addition of a polygon volume. I have already shown *on this list* that the same tactic is capable of defining sectorial area relative to Cartesian area, which is calculated by a relatively simple trigonometric integral. I don’t have my computer with me at the moment, but later I will try to copy your Mathematica code with my alternative approach. Merry Ellipse-Mas, and a Happy New-Circle, —Brad
On Dec 25, 2019, at 6:03 PM, Bill Gosper <billgosper@gmail.com> wrote:
Yes! How could we possibly have gone this long without a universally recognized Kepler(a,b,t) function? —Bill