The equation is called, quite mystically, the Equation of Time, or EOT and is written thus:
E = 9.87sin(2B) – 7.53cos(B) – 1.5sin(B).
On the commentary track, Cohen talks about the EOT, and what the “Futurama” writers did to tinker with it for sci-fi reasons. He said:
“[T]he equation of time. Look it up on the internet, quite interesting. It is the equation for correcting the time given by a sundial. So you know what day of the year it is, you can correct to the right time using that equation. Although we added one extra term to what is about to be written here as the ‘doom field.’ So that one with the delta, the greek letter at the end, that very last part we added. But the rest is the time equation.”
To quote the website Sus Design, the equation of time is “a formula used in the process of converting between solar time and clock time to compensate for the earth’s elliptical orbit around the sun and its axial tilt.” Because the Earth doesn’t rotate in a perfectly round pattern, and because it is tilted on its access, sundials will not be wholly accurate throughout the year. To account for the solar drift, as it were, the EOT can be applied to give one a good idea as to how it would need to be adjusted throughout the year.
Indeed, only in mid-April, mid-June, and right at the end of August would a sundial not need to be adjusted from a central standard. In early February and early November, a sundial will need to be adjusted as much as 15 minutes in either direction.