Approximate Formula For #Days From V Equinox to A Equinox, Take 2

I was able to compute an expression for the remaining constant in B(e) by expanding the integral for the difference in time as a linear function of the eccentricity near e = 0.

The constant is the derivative of the integral w.r.t. e at e = 0.


The formula gives a good approximation for the time it takes to go from the Vernal Equinox to the Autumnal Equinox if the orbital period, T₀ (tropical year), the eccentricity, e, and the angle, θ, are known. There are higher order terms but the error is about 30 minutes or less.