The study of the Moon's motions has been central to the growth of knowledge not only about the Moon itself but also about fundamentals of celestial mechanics and physics. As the stars appear to move westward because of Earth's daily rotation and its annual motion about the Sun, so the Moon slowly moves eastward, rising later each day and passing through its phases: new, first quarter, full, last quarter, and new again each month. The long-running Chinese,
Chaldean, and Mayan calendars were attempts to reconcile these repetitive but incommensurate movements. From the time of the Babylonian astrologers and the Greek astronomers up to the present, investigators looked for small departures from the motions predicted. The English physicist Isaac Newton used lunar observations in developing his theory of gravitation in the late 17th century, and he was able to show some effects of solar gravity in perturbing the Moon's motion. By the 18th and 19th centuries the mathematical study of lunar movements, both orbital and rotational, was advancing, driven in part by the need for precise tables of the predicted positions of celestial bodies (ephemerides) for navigation. While theory developed with improved observations, many small and puzzling discrepancies continued to appear. It gradually became evident that some arise from irregularities in Earth's rotation rate, others from minor tidal effects on Earth and the Moon.
Space exploration brought a need for greatly increased accuracy, and, at the same time, the availability of fast computers and new observational tools provided the means for attaining it. Analytic treatments—mathematical modeling of the Moon's motions with a series of terms representing the gravitational influence of Earth, the Sun, and the planets—gave way to methods based on direct numerical integration of equations of motion for the Moon. Both methods required significant input based on observation, but use of the latter led to great increases in the accuracy of predictions. At the same time, optical and radio observations vastly improved—retroreflectors placed on the lunar surface by Apollo astronauts allowed laser ranging of the Moon from Earth, and new techniques of radio astronomy, including very long baseline interferometry, permitted observations of celestial radio sources as the Moon occulted them. These observations, having precisions on the order of centimetres, have enabled scientists to measure changes in the Moon's speed caused by terrestrial tidal momentum exchange, have advanced understanding of the theories of relativity, and are leading to improved geophysical knowledge of both the Moon and Earth.
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