Alternian calendar

Solar Sweep
Solar Sweeps are used as a measurement of time on Alternia. They are probably a Troll term for "years". Each solar sweep lasts 26 Earth months (or about 2.16 (repeating) Earth years), meaning six Solar Sweeps are exactly equal to 13 earth years, putting the Trolls at roughly the same age as the Kids.

To convert any number of years to sweeps, multiply it by (6/13). S=(6/13)Y.

To convert any number of sweeps to years multiply by (13/6). Y=(13/6)S. Where Y is Earth years and S is Alternian solar sweeps.

Perigee
A perigee is the moment a body orbiting Alternia is closest to it. Since all perigees mentioned thus far are "bilunar," it seems Alternia's two moons have identical orbits. There seem to be at least twenty-four perigees in a solar sweep, since Karkat's wriggling day occurs on "the 12th bilunar perigee of the 6th dark season's equinox", and there ought to be two equinoxes per solar sweep.

Seasons
So far only 2 types of seasons have been mentioned and it is unknown how many other types of seasons, if any, there are.
 * Dark Seasons: There are at at least six dark seasons in a solar sweep, during which it HS 3905 (remains dusk for most of the day.) The events of Hivebent take place during the dark seasons. It is unknown what or how many other types of seasons there are.
 * Dim Seasons: There are at least 2 dim seasons in a solar sweep. The page of Mindfang's journal Vriska reads is dated to the 14th bilunar perigree of the 2nd dim season's equinox.

Equinox
One of Alternia's equinoxes occurs during the sixth dark season. Assuming full parallelism, this suggests that the other should occur during a sixth light season. It seems that perigees can be counted between equinoxes as well as within a sweep.

Earth Terms
The trolls never use the word "month" except when communicating with the kids, and even then possibly without understanding what it means. They make frequent use of "day" and "week," although notably days are never numbered, not even with respect to perigees. Trollian measures time in hours, as does Karkat when recapping their Sgrub session as having lasted 600 hours, but this may be solely a game phenomenon and not reflective of general troll culture.

Wriggling Day
Wriggling Days are the Troll equivalents of Earth birthdays, occurring once for each Troll each Alternian Solar Sweep. It just so happens that at the beginning of Act 5 Act 1 we see our first Wriggling Day, that of Karkat Vantas, on "the 12th bilunar perigee of the 6th dark season's equinox", making him 6 Solar Sweeps (13 Earth years) old. The other Trolls are presumably all the same age. Trolls apparently view their Wriggling Days as opportunities to lament their insufficiencies. This may be an idiosyncrasy unique to Karkat, though.

12th Perigee's Eve
This holiday is the Troll equivalent to Christmas, possibly with some elements of New Year's Eve. The Trolls and their Lusus may decorate the hive or just stay inside, and the Lusus goes and collects a "behemoth leaving" in the style of a Christmas tree. The "12th" perigee is probably counted in number of perigees from the beginning of a sweep, rather than from the last equinox, since HS 4467 (there is only one 12th Perigee's Eve per solar sweep.)

Trivia

 * At some point, Latula says it's been HS 7163 ("4pprox1m4t3ly H3LLA y34rz") since she has done any fighting. Furthermore, KarkatHS 3503, AradiaHS 4708 and AraneaHS 6831. From the context, it's not clear if it's used as a synonym for sweep or just a colloquial term for a vague amount of time.
 * Terezi also mentions that her hive looks nice in the HS 3958 ("third autumn"), indicating that Earth seasons may be used on Alternia too.