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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on some parts of the world, “winter solstice” is a completely different thing. next.
Surely a good way would be to take the point from perihelion after which the area subscribed by a chord from the sun to the earth has covered 1/pi the area enclosed by the earth’s entire elliptical orbit?
An imaginary line connecting the sun and a planet sweeps out equal areas in equal times as the planet moves through its orbit. A consequence of this is that a planet moves fastest when closest to the Sun. Newton will have something to say about this.
So from this we only need to calculate 1/pi the number of days in the year from perihelion or winter solstice.
It seems more practical to find something interesting about the day that is 365.25/6.28 days prior to March 14 and calling that the starting point.
One difficulty that I have with the whole proposal is that no matter how we calculate this, even down to the millisecond, we are not getting “real” pi unless we want to say that real pi occurs sometime between time A and time B. After all, any time we give will still be a rational number of time units, which pi transcends.
I suggest we turn our efforts to something more practical … such as constructing a pi:1 Martini to celebrate the day.
It isn’t as fun as (1/pi) but 2*pi is 360 degrees. So the 1/2 point through the year would “truly” be pi day. (Choose whatever starting point you wish but I like your winter solstice idea. What is 1 man’s pi day would be another’s 2*pi day.)