Understanding date of astronomical events I have a masters in chemistry but pretty much, a layman in astronomy.
So, can you please explain to a novice like me, about this paragraph taken from the Wikipedia article on Makar Sankranti:

There are two different systems to calculate the Makara Sankranti date: nirayana (without adjusting for precession of equinoxes, tropical) and sayana (with adjustment, sidereal). The January 14 date is based on the nirayana system, while the sayana system typically computes to about December 23, per most Siddhanta texts for Hindu calendars.

Am I correct to understand that when the date was assigned in Hinduism some thousand (?) years back, the winter solistice used to be on 14th/15th January?
Precession of equinoxes means that the North pole of the Earth is changing its direction. This also means, that the dates of the seasons (seen from outside the Solar System (= sidereal)) are changing. Nirayana calculates the date of Makar Sankranti with adding years to the first Makar Sankranti, but sayana calculates the date of Makar Sankranti relative to stars (sidereal).
In a nutshell: nirayana is on the same date as the first event (first Makar Sankranti), but sayana is on the same event as the first Makar Sankranti (winter solstice). Yes, winter solstice was once on the 14 January.