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I was just messing around with some simple calculator-calculable things, and I've put together a short formula for the semi-diameter of the Sun:

SD = 16.00' + 0.27'·cos(M·30° + D - 34°)

where M is the month number ("one-based" so that January is M=1), and D is the day number in the month. For example, on March 17, M=3 and D=17 so the calculated Sun SD is 16.08'. Naturally, it's not perfect. It's intended to be fast and generally accurate to better than a tenth of a minute of arc. From a few test cases for coming years, it seems that it's usually accurate to +/- 0.01'. Does anyone have a better approximation, either more accurate with the same work, or maybe slightly less accurate with less work? By the way, the the origin of the 34° here is nothing complicated. Perihelion occurs on about January 4, so you would normally subtract just about 4° from the argument of the cosine, but we usually think of month numbers starting with 1 for January, so that bumps it up to 34°.

-FER