Moon Sign Calculator

The Moon sign is the 30-degree zodiac sector containing the Moon's ecliptic longitude at the birth instant, converted to Universal Time. The Moon is by far the fastest-moving body in a chart, averaging 13.176 degrees per day and completing a tropical circuit in 27.32 days, so it changes sign roughly every 2.3 days and shifts about half a degree per hour. Birth time and time zone therefore matter more for this placement than for any other. This calculator builds a Julian Day from the calendar date and UTC offset, then evaluates an abridged lunar series: a mean longitude plus the largest periodic corrections, led by the equation of the center at 6.289 degrees, the evection at 1.274 degrees, the variation at 0.658 degrees and the annual equation at 0.186 degrees, together with several smaller terms. Truncating the series there gives accuracy on the order of ten arcminutes, which is sufficient except within a few hours of a sign ingress. It also reports lunar phase from the synodic month of 29.53059 days measured against a reference new moon. Two practical cautions apply: the UTC offset must be entered as it actually stood on the birth date, including any daylight saving then in force, and a full theory such as ELP-2000 uses thousands of terms rather than the dozen used here.

Lunar motion is the hardest classical problem in celestial mechanics, and each correction term in this calculation marks a historical discovery. Hipparchus, working in the second century BCE, established the lengths of the lunar months and the equation of the center. Ptolemy identified the evection in the second century CE while trying to reconcile eclipse observations with lunar positions at quadrature. Tycho Brahe found the variation and the annual equation in the late sixteenth century from his sustained observing programme at Uraniborg. Isaac Newton attacked the problem gravitationally in the Principia in 1687 without fully solving it; Euler, Clairaut and d'Alembert took it up during the eighteenth century, and Charles-Eugene Delaunay published an analytical theory in the 1860s running to hundreds of terms. Ernest W. Brown's tables, completed in 1919, supplied lunar positions for national almanacs until 1984, when the ELP-2000 semi-analytical theory of Michelle Chapront-Touze and Jean Chapront replaced them, later joined by JPL numerical ephemerides. On the interpretive side, the Moon has signified the body, the mother, habit and emotional temperament since Hellenistic doctrine, and the Moon sign gained prominence in popular astrology as readers pressed past newspaper Sun-sign columns toward complete natal charts.