Another factor that affects where we see the sun on a given day is that we want a whole number of days in the year, like 365, not 365.256363004, which is closer to the time the sun really takes to come back to the same position as last year.
If not corrected, this problem would give us a calendar that continually shifts the seasons. The beginning of each season would move until the month we call July had winter weather! The Leap Year system was developed to counteract these effects on the calendar and keep the seasons beginning on the same days each year. Now, the sun appears to move eastward for 3 years, then leap year has the effect of pulling it back to nearly the same position as 4 years prior. (The slight difference is due to precession.)
This will have a big effect on determining the star of your birth. Assume the sun is perfectly aligned (not just “nearby”) to a given star on January 1 at 12 noon. By next January noon, the sun has not quite made it back to that star. It still has to travel for another 6 hours, 9.1626 minutes. So it is not there until 6:09+ pm. The next year, at 6 pm it is not all the way back, it has another 6 hours, 9.1626 minutes to travel and now it is after midnight on January 2. That star is now the Star of Your Birth for January 2. When leap year comes, it will bring the star back to being the star for the first again.
Thus the leap year cycle is a 4-year cycle, and you should know if your date of interest occurs on a Leap year, 1 year after, 2, or 3 years after. If the last 2 digits of your year are divisible by 4, then it is a leap year. Century years must be divisible by 400. 2000 was a leap year, but not 1900 or 2100. But see the page on finding your star for the dates January 1 to February 28. These dates actually go with the year before for this purpose.