Sidereal Birthdays

I had a milestone birthday today — the earth has orbited around the sun 50 times since I was born. Unpacking that statement a bit, I puzzle over what point exactly marks that milestone? The usual notion I suppose would be to say that since I was born way back when at 4:04 PM on 11 April, therefore that time this year would be the milestone point. But that however is with reference to the Gregorian calendar, which keeps the date of the equinoxes more-or-less in the same point in the calendar by inserting leap days every four years except on centuries not divisible by four. Obviously, leap days are discrete insertions into the calendar, which is why the actual date of the vernal equinox varies between the 19th and the 21st of March depending upon the year.

Defining one’s calendar with reference to the equinoxes still isn’t exactly the same thing as the earth being in the same position in its orbit. The year with reference to the equinoxes is called the tropical year, and is 365.242190 days long. The year with reference to the fixed stars is the sidereal year, and is 365.256363 days in length. The latter seems to be what I’m interested in identifying in my milestone, so how do we determine this?

What it seems we want to do is calculate things in heliocentric coordinates, that is, with reference to an observer standing at the middle of the sun. To figure this out, I reached for a venerable piece of astronomy software, XEphem, and did some calculations. The heliocentric longitude of the earth from the sun at the time of my birth was 201:23:09 (degrees-minutes-seconds). Changing the date in the program to April 2013, I then stepped its clock forward and back until the heliocentric longitude was 201:23:09 again. This I find occurred at 7:50 PM on April 10th. Not today at all. Hmm.

All of which is a good reminder that time is a lot more subtle of a concept than many people realize.