For getting winter-time the True Anomaly must be 90 degrees from the vernal point.
For getting the true anomaly it must be got the Excentric Anomaly and for getting this it
must be got the Normal Anomaly.
The Normal Anomaly is an angle, growing linear with the time
after the equinox and is not zero at the equinox time. But it is not exactly 360 degrees per year,
because the year is not exactly 365.25 days. This is compensated by the leap days (not perfectly exact after 1000 years),
but this is a calendar date and not a continuous time. And so the Normal Anomaly must be taken from a table
of ephemeries and substracted all multiple of 360 degrees. From this the True Anomaly can be calculated.
Now the earth orbit ellipse, with the sun in one focus is turned in the ecliptic around the sun
for approx. 101 degrees from vernal point. This is the lenght of the perihelion, the angle of the major semi axis.
This must be added to the angle of the True Anomaly and this is thereafter the position of the earth in
heliocentric ecliptical coordinates.
For getting winter-begin, it must be chosen the True Anomaly so, that it together with the
lenght of perihelion has 90 degrees after the vernal point, because that is 90 degrees in the equator plane.
The True Anomaly has than approx. -11 degrees or better 349 degrees in the year before. And thereafter the
calculation must be made backward to get the Normal Anomaly and to this you must add the Normal Anomaly of all
the years since the exinox. From there you get the Calendar Date and Time out of the procedure unterneath.