Seasons

Solstices and equinoxes

Goal: compute the four turning points yourself, to the minute.

Definitions that are more precise than you think

These are instants, not days:

Not "the day with equal light and dark"; that is close, but not the definition, and not even quite true (see below).

Compute them

import datetime as dt
from moonfield import sun, time as mtime

def find_event(year, target_longitude):
    """Bisect for the instant the Sun's apparent longitude hits the target."""
    lo = dt.datetime(year, 1, 1, tzinfo=mtime.UTC)
    hi = lo + dt.timedelta(days=366)

    def offset(when):
        lon = sun.apparent_longitude(when)
        return ((lon - target_longitude + 180) % 360) - 180

    # coarse scan for the sign change
    step = dt.timedelta(hours=6)
    when = lo
    while when < hi:
        if offset(when) < 0 <= offset(when + step):
            lo, hi = when, when + step
            break
        when += step

    for _ in range(60):
        mid = lo + (hi - lo) / 2
        if offset(mid) < 0:
            lo = mid
        else:
            hi = mid
    return lo

for name, lon in [("March equinox", 0), ("June solstice", 90),
                  ("September equinox", 180), ("December solstice", 270)]:
    print(f"{name:20s} {find_event(2026, lon):%Y-%m-%d %H:%M} UTC")

Check against a published almanac. You should be within a couple of minutes.

Why the dates drift

The tropical year is 365.2422 days, not 365. That quarter-day is why the events drift about six hours later each year and jump back on leap years, and why the Gregorian calendar exists at all. The 400-year rule (skip the leap year in 1900 and 2100 but not 2000) tracks 365.2422 to within about 27 seconds a year.

The equinox is not equal day and night

"Equinox" means equal night, but equal daylight actually falls a few days earlier in spring and later in autumn. Two reasons, both from module 05:

• Sunrise and sunset are defined by the Sun's upper limb, not its centre
• Refraction lifts the Sun about 0.57° at the horizon

Together these add several minutes of daylight at both ends. Check it:

moonfield sun --date 2026-03-20

Daylight will be slightly over 12 hours. The date of true 12-hour daylight is called the equilux, and it depends on your latitude.

Checkpoint

• I know the four events are defined by solar longitude
• I have computed them and checked against an almanac
• I know why the dates shift year to year
• I can explain why the equinox is not exactly equal day and night

Try it yourself

1. Compute all four for the year you were born
2. Find the equilux date for your latitude
3. Measure the interval between successive March equinoxes; that is the

tropical year, and you just measured it

1. Compare the lengths of the four seasons. They are not equal, why not?

That last one is a good one. The answer involves Kepler's second law.

Next: Module 07, Planets (planned).