A commenter on reddit points out that the Winter Solstice itself may be pretty arbitrary. Too true!
So, let’s consider another possibility, and calculate from perihelion to perihelion. According to the US Naval Observatory, the last perihelion was at 3pm UTC on January 3, 2010, and the next will be at midnight on January 3, 2011. Turning again to Frink, that would give us a date of April 29, 2010 at around 3pm UTC.
#2010-01-03 15:00 UTC#+((#2011-01-03 00:00 UTC#-#2010-01-03 15:00 UTC#)/pi)->UTC
Any further refinements are appreciated!
Please help us improve our estimation of the point at which the Earth has passed through 1/π-th of its orbit, as measured from Winter Solstice 2009 to Winter Solstice 2010. Based on our current, simplified estimation, this will be on Saturday, April 17, 2010 at 12:02 AM Coordinated Universal Time.
The above calculation is based on a naïve assumption of the Earth’s velocity as a constant. Since Kepler’s Second Law tells us that the orbital velocity of a planet is faster when it is closer to the sun, the date suggested above is undoubtedly imperfect.
Frink is a fantastic tool for performing all manner of interesting calculations and conversions. You might find this Frink formula useful as a starting point for exploration:
#2009-12-21 17:47 UTC#+((#2010-12-21 23:38 UTC#-#2009-12-21 17:47 UTC#)/pi)->UTC
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Welcome to the campaign for a saner Pi Day, http://www.realpiday.org!