Makar Sankranti is not Uttarayan
Uttarayan means when the sun starts moving northward. In theory, Uttarayan is and starts from the winter solstice. In reality, Uttarayan happens on 21st / 22nd December whereas Makar Sankranti, which is celebrated in India on 14th/15th January is the day when the Sun enters the Capricorn constellation.
However, there was a time when both the winter solstice and Makar Sankranti occurred together. This was around the time the Siddhanta texts of astronomy were written, in around 400 AD. At that time it was noted that the Sun entered Makar Rashi (the zodiac of Capricorn) on the same day as the winter solstice. Therefore, Makar Sankranti (the day when Sun enters Makar Rashi – the zodiac of Capricorn) was marked as start of Uttarayan.
However, due to precession of the axes, slowly the two events drifted apart. Precession of axes happens at ~1° per 72 years. This equals ~1 day per 72 years. At present, there is a difference of 24 days between 21st December and 14th January.
So the question is ‘ how many years did it take to shift winter solstice by 24 days?’ As motion of precession takes 25,700 years to take full round (or 365 days). So number of years taken to shift 24 days would be approx.( 25700/365)×24=1689 years
Therefore the winter solstice must have taken place on makar sankranti approximately 1689 years (i e in 411 AD) ago. Then, uttarayan would have then coincided with makar sankranti.