Chapter Two: The Astronomical Foundations of Liqiu — The Sun Reaches 135° Ecliptic Longitude

I. 135° Ecliptic Longitude: Liqiu's Astronomical Coordinate

Liqiu has a precise astronomical definition — the moment when the sun reaches 135° ecliptic longitude. To understand this, we must first understand what "ecliptic longitude" means.

The ecliptic is the great circle formed by the intersection of the plane of Earth's orbit around the sun with the celestial sphere — the apparent path of the sun against the background of fixed stars as seen from Earth over the course of a year. Though the ancients observed from a geocentric perspective, they equally recognized that the sun traverses the ecliptic in one complete circuit during the year. Dividing this ecliptic into 360 degrees yields the "ecliptic longitude" coordinate. Taking the vernal equinox as 0°, each 15° of solar travel corresponds to one solar term. Vernal equinox 0°, Clear and Bright 15°, Grain Rain 30°, Start of Summer 45° — and so on, such that Liqiu corresponds precisely to 135°.

Why 135°$9 Because from the vernal equinox (0°) to Liqiu (135°), the sun has traveled a full 135 degrees — the span of exactly nine solar terms (135 ÷ 15 = 9). This means that from the midpoint of spring to the beginning of autumn, the Way of Heaven has traversed more than three-quarters of a quadrant. The number 135° itself is quite suggestive: it is precisely 45° beyond the summer solstice (90°). The summer solstice is the apex of yang, the longest day; after the solstice, the sun's direct point begins to move southward, daylight begins to shorten, and yang qi begins its decline from fullness. By Liqiu (135°), the sun has slid a full 45° southward from the solsticial summit — an astronomical portrait of yang qi's decline and yin qi's growth reaching a critical threshold.

II. One of the Four Establishments: Astronomical Markers of Seasonal Transition

Liqiu is one of the "Four Establishments." As noted earlier, the earliest solar term system consisted only of the "Two Equinoxes and Two Solstices" — the vernal and autumnal equinoxes, and the summer and winter solstices. These four are the easiest to determine through astronomical observation: two equinoctial points (equal day and night) and two solsticial points (longest and shortest shadow). The "Four Establishments" — Lichun, Lixia, Liqiu, Lidong — were added later on the foundation of the equinoxes and solstices to mark the beginnings of the four seasons.

The special position of the Four Establishments among the Twenty-Four Solar Terms merits deep reflection. Lichun falls between the winter solstice and vernal equinox; Lixia between the vernal equinox and summer solstice; Liqiu between the summer solstice and autumnal equinox; Lidong between the autumnal equinox and winter solstice. Each lies precisely at the midpoint between a solstice and an equinox. In Liqiu's case, it sits at the exact midpoint between the summer solstice (90°) and the autumnal equinox (180°) — that is, 135°.

The choice of this position reflects the ancients' profound dialectical wisdom. The summer solstice is the extreme of yang; yet when things reach their extreme they must reverse, and after yang's apex, yin qi is already born. The autumnal equinox is the balance of day and night, yin and yang in equilibrium. Where, then, is the midpoint on the journey from "yang extreme" to "yin-yang equilibrium"$10 Precisely at Liqiu. In the eyes of the ancients, Liqiu is the turning point where yang qi, having peaked at the summer solstice, begins its discernible decline, yet has not yet reached equipoise with yin. In other words, Liqiu marks not an astronomical extremum, but the "establishment of a trend" — the establishment of decline, the establishment of convergence. This is subtler than mere observation of extremes, and demands greater wisdom.

III. Stars and Liqiu: Celestial Coordinates in the "Monthly Ordinances"

Beyond ecliptic degrees, the ancients also verified seasonal transitions by observing the positions of stellar lodges. The Liji (Book of Rites), "Yueling" ("Monthly Ordinances"), records precise celestial coordinates for the month of Early Autumn (the month containing Liqiu):

"In the month of Early Autumn, the sun is in the lodge Yi (Wing); at dusk, the Establishing Star (Jianxing) culminates; at dawn, the lodge Bi (Net) culminates."

These three statements specify the positions of the sun, the star culminating at dusk in the southern sky, and the star culminating at dawn. "The sun is in Yi" — the sun has moved into the lodge Yi (one of the seven lodges of the southern Vermilion Bird). "At dusk, Jianxing culminates" — at dusk, the Establishing Star (near the Dipper) occupies the meridian in the southern sky. "At dawn, Bi culminates" — at dawn, the lodge Bi (one of the seven lodges of the western White Tiger) occupies the southern meridian.

What is thought-provoking is that the lodge culminating at dawn is "Bi" — and Bi belongs to the western White Tiger group. In the Five Phases system, the west belongs to Metal, and autumn corresponds to Metal. That a western lodge holds the meridian at dawn is a celestial sign that the qi of autumnal Metal is rising. Stars above, season below, the Metal virtue of the Five Phases — all once again form an exquisite correspondence. This is no coincidence, but yet another proof of the ancients' "unified Heaven-and-Humanity" cosmology: they were convinced that the movements of celestial bodies, the sequence of earthly seasons, and the virtues of all things are different manifestations of a single cosmic principle.

IV. Why Was Determining Liqiu So Difficult$11

Here lies a question worth pondering: compared to the summer solstice (shortest shadow), winter solstice (longest shadow), or the equinoxes (equal day and night) — solar terms with clear astronomical extrema or equilibria — why was Liqiu particularly difficult to determine$12

The answer is that Liqiu has no intuitive, extreme astronomical marker. It is neither a shadow extremum nor a day-night equilibrium, but an "ordinary" midpoint on the sun's trajectory (135° ecliptic longitude). To fix this point, the ancients must already have possessed considerable astronomical calculation ability — they first had to precisely determine the equinoxes and solstices, then, on that foundation, use subtle changes in shadow length and long-term records of solar motion to extrapolate this intermediate node.

This precisely reflects the maturation of the solar term system. From "Two Equinoxes and Two Solstices" to "Four Establishments" to the complete Twenty-Four Solar Terms marks a leap from "observing extrema" to "precise calculation." A solar term like Liqiu could be established only because the ancients had become able to divide the year's solar motion into precisely twenty-four equal parts. Behind this lay generations of unbroken gnomon shadow measurement, stellar records, and calendrical computation — the concrete embodiment, in astronomical practice, of the "reverence" in "respectfully bestowing the seasons."

At a deeper level, the difficulty of determining Liqiu corresponds to its philosophical subtlety. Liqiu marks an "invisible turning" — the weather is still hot, all things still flourish, yet the direction of heaven and earth's qi has quietly reversed. Such an "invisible turning" can only be captured through precise astronomical calculation, and can only be confirmed through profound faith in the Way of Heaven. Liqiu thus becomes the perfect juncture of the ancients' astronomical wisdom and philosophical conviction.