Why isn’t the vernal equinox the same day and hour every year?
Seasons are defined by the instant the sun passes in a prescribed direction, and calendars and clocks are simply ways of recording it.
The calendar says equinoxes and solstices, but they are not arbitrary whole days designated. Given a year, calculate the moment when the sun's ecliptic longitude crosses 0°, 90°, 180° or 270°.
Guess first
In astronomy, is the vernal equinox a whole day or a moment?
Show answer and explanation
a well-defined moment — Defined by the instant the sun passes in a specified direction.
Then connect experience and science
First define what is a solar term moment
The ecliptic longitude of the sun is equal to four specified angles, which respectively define the two to two degrees.
λ viewing = 0°, 90°, 180°, 270°
First estimate an average time
Select the polynomial in Table 27.A or 27.B by year to get JDE₀.
Y=year/1000 or (year−2000)/1000
Add period changes
Table 27.C in the original book has 24 items, corrected average time. It has limited precision and cannot treat decimal places as accuracy.
JDE=JDE₀+0.00001ΣAcos(B+CT)/Δλ
Then use the sun position to chase the target direction
Refined and repeated calculation of the solar retinoid meridian, and then adjusted the time; TT is output here and is not directly used as the local mobile phone clock.
ΔJDE=58 sin(target yellow meridian − current retinoid meridian)
First select the origin of Y according to the year segment, find JDE₀, and then make period corrections; the refinement branch continues to find the root of the solar ecliptic longitude. The unit of ΔJDE is day, and the target longitudes are 0°, 90°, 180°, and 270° respectively.
give it a try
Let’s first compare the periodic formula and successive refinement of the 1962 summer solstice. Two routes are not exactly the same just because they are both called "summer solstice."
No need to memorize symbols
- JDE
- Earth's current continuous Julian days
- lambda view
- Solar retinoid meridian including FK5, nutation and aberration
- S
- Table 27. 24-term periodic sum of C
Algorithm, accuracy and scope of application
Supplement Chapter 27 Table 27.A/B/C, 1962 Summer Solstice Example 27.a/b and 27.1 iteration. The fine restoration uses the original book of this website to truncate the VSOP87 sun route, and does not claim the complete second-level measured true value of VSOP87. Explicitly retain the periodic formula results when exceeding the refinement verification range, and do not silently switch to modern external ephemeris.
my understanding check
Can the TT output in this lesson be regarded as Beijing time without conversion?
cannot — ΔT/UTC and time zone processing are also required.
The output of the period formula and the refinement method are slightly different, what does it mean?
Model and accuracy are different — The original book gives two calculation routes with different accuracy.
Can empirical polynomials be extrapolated arbitrarily to tens of thousands of years?
cannot — The table's chronological range must be respected.
A solar term is first a solar direction event and then translated into calendar and clock readings.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 27 chapter