The Martian clocks (keeping Martian time) on the Mars Weather page also display the L_s (pron. ell-sub-ess) - a way of describing where the planet is in its orbit, and the displacement of the sun in the sky at midday. I noticed the value for this was out by some distance, and after pondering the problem (and the code) for a while, the penny dropped.

Unfortunately, the code was still generating a value that was out by 1/100^th of a degree, which isn't much but it bothered me. It turned out to be due to a rounding issue, so I fixed that. L_s is now displayed to two unrounded decimal places, with the same value shown to three decimal places for those that find this interesting or important. The two-decimal value is the primary because it then matches the value generated by Mar24, a program available from the Goddard Institute for Space Studies, a branch of NASA.

For Earth, L_s advances approximately one degree per day (~0.9863°), but for Mars with its more eccentric orbit, things don't work out quite so neatly. Some Martian months are as short as 46 sols, while others are as long as 67 sols, so months are not determined by dividing the sols per year by 12. A new month begins when the planet reaches an increment of 30° around its orbit. Since L_s determines where in the orbit it is, it is the only viable way of determining what the current month is.