Lunar cycle

“ It had been discovered that the lunar year was eleven days shorter than the solar year; so that, if a new moon occurred upon any given day of any solar year, on the same day of the next solar year the moon would be eleven days old, on the same day of the second year twenty-two days old, etc. Examination showed that the new moon would again occur upon the same day of the solar year in the course of nineteen years. Hence the lunar cycle consists of nineteen years. The other ancient cycles are unimportant for our present purpose ”

“ Just as is the equinox by the movement of precession, but at a much greater rate (see remarks on precession elsewhere) . The moon’s axis completes its revolution in about 19 years, while the earth requires 26,000 years. This is called the lunar cycle. At the time in the lunar cycle when the ascending node of the moon’s orbit is in range with the vernal equinox the moon has her greatest range of declination—about 57° from extreme north to extreme south. She is then 23° north, the amount that the ecliptic is from the equator and 5° more, the amount that the moon’s orbit is above the ecliptic. ”

“ When the remainder is 0, the proposed year is of course the last or 19th of the cycle. It ought to be remarked that the new moons, determined in this manner, may differ from the astronomical new moons sometimes as much as two days. The reason is that the sum of the solar and lunar inequalities, which are compensated in the whole period, may amount in certain cases to 10°, and thereby cause the new moon to arrive on the second day before or after its mean time. ”

“ It would be seen to pass through its phases, just as does our satellite, once in a lunar day or a terrestrial month, and during that cycle of phases, since 29 of our days would be occupied by it, the axial rotation would bring all the 162 features of its surface configuration into view so many times in succession. But the greatest beauty of this noble moon would be seen during the lunar night, in considering which we shall again allude to it; for when it is full-moon to the earth it is new-earth to the moon. At lunar midnight this globe of ours is fully illuminated ”

“ The difficulty of reconciling lunar with solar time is one of the standing puzzles which has taxed the ingenuity of men who are emerging from barbarism. Now an octennial cycle is the shortest period at the end of which sun and moon really mark time together after overlapping, so to say, throughout the whole of the interval. ”

“ On pages 51 to 58 of the Dresden Codex is found a remarkable lunar calendar covering 405 lunations or nearly 33 years. The lunar revolutions are arranged in groups of five or six, the former calculated at 148 days and the latter at 177 or 178 days. These are the necessary intervals between eclipses. The total amounts to 11,960 days which exactly contains the tzolkin and therefore forms a cycle. It is a remarkable fact that 405 lunar revolutions amount, according to modern calculations, to 11,959.888 or only O.112 of a day less than the Mayan lunar calendar. ”

“ One hundred and thirty-five lunar months of 30 and 29 days complete 3986 days, .63 days less than 135 synodical revolutions of the moon. This error which amounts to more than one day when repeated once, necessitates the addition of an extra day in the lunar calendar every other third, which was done in the manuscript in the first and last third, making the total recorded by the lunar calendar 11,960, two days more than the eclipse calendar, and .11 days more than 405 synodical revolutions of the moon. This period of 11,960 days may have been used as a cycle, the zero day of which is 12 Lamat. ”

“ And for that cause Saturn, having a wider orbit, is borne round it in a longer time, Jupiter a shorter, and Mars still less; while Venus takes nine months, Mercury 80 days, on the hypotheses of Copernicus; the Moon going round the Earth with respect to the Sun in 29 days, 12 hours, 44 minutes. We have asserted that the Earth moves circularly about its centre, completing a day by an entire revolution with respect to the Sun. The Moon revolves in a monthly course around the Earth, and, repeating a conjunction with the Sun after a former synodic conjunction, constitutes the month or Lunar day. ”

“ But upon the Moon there is no dawn, and the darkness of night envelops the orb until the appearance of the edge of the Sun’s disc above the horizon, then his dazzling rays illumine the summits and loftiest peaks of the lunar mountains whilst yet their sides and bases are wrapped in deep gloom. Since the pace of the Sun across the lunar heavens is 28 times slower than it is with us, there is continuous sunshine on the Moon for 304 hours, and this long day—equal to about a fortnight of our time—is succeeded by a night of similar duration. ”

“ This small rocky world, which tells us a story full of impacts, orbits the Earth in 27.32 days. It is called the sidereal period. As the Earth revolves around the Sun, the time between two identical lunar phases is known as the synodic period, and it lasts 29.53 days.
Perhaps, you may notice the shape or shapes of the Moon that we see are always the same way. That is because the Moon always shows the same face to Earth, so we always see the same half of it. ”

“ Since the succession of day and night depends on the revolution of a planet on its own axis, and it takes the moon twenty-nine and a half days to perform this revolution, so that the sun shall go from the meridian of any place and return to the same meridian again, of course the lunar day occupies this long period. So protracted an exposure to the sun's rays, especially in the equatorial regions of the moon, must occasion an excessive accumulation of heat; and so long an absence of the sun must occasion a corresponding degree of cold. ”

“ Then, too, regarding the moon as a timekeeper, we must not forget the service that it renders in furnishing a division of time intermediate between the day—which is measured by the earth’s rotation—and the year, which is defined by the earth’s orbital revolution. Notwithstanding the survival of lunar reckoning in our religious services, we, in our time and country, scarcely need a moon to mark our months ”

“ It might seem, that, since the moon rotates on her axis in about twenty-seven days, the lunar day ought to be twenty-seven days long, instead of twenty-nine. There is, however, a solar, as well as a sidereal, day at the moon, as on the earth; and the solar day at the moon is longer than the sidereal day, for the same reason as on the earth. During the solar day the moon must make both a synodical rotation and a synodical revolution. ”

“ The west to east motion is steady and continuous, but, owing to the Sun’s attractive force, the Moon is made to swerve from its path, giving rise to irregularities of its motion called PERTURBATIONS. The most important of these is the annual equation, discovered by Tycho Brahé—a yearly effect produced by the Sun’s disturbing influence as the Earth approaches or recedes from him in her orbit; another irregularity, called the evection, is a change in the eccentricity of the lunar orbit, by which the mean longitude of the Moon is increased or diminished. ”

“ Now it is found that when at birth the Moon is increasing in light, that is, going towards the full, and above the horizon, or conversely, decreasing in light and below the horizon, the period from birth to inception is less than ten lunar months by a quantity determined by the Moon’s distance from the horizon. But when the Moon at birth is found to be decreasing and above the horizon, or increasing and below the horizon, the period of time from birth to inception is found to be more than ten lunar months by a quantity determined by the Moon’s distance from the horizon. ”

“ Gazing upon the lunar globe, in which I could distinguish with the naked eye the ancient seas and geographical outlines, I bethought myself that it was still perhaps inhabited by beings organised differently from ourselves who can live in an extremely rarefied atmosphere; but what struck me even more forcibly was its rapid revolution round the Earth, at the rate of 1,000 yards at each beat of the clock, making 38 miles a minute, 2,280 an hour, 53,800 a day, or 1,500,000 miles for each lunar month. ”

“ Assuming the moon to have been once in a fluid state, it is demonstrable that the attraction of the earth would accumulate a mass of matter, like a tidal elevation, in the direction of a line joining the centres of the two 32 bodies: and as a consequence, the real shape of the moon must be an ellipsoid, or somewhat egg-shaped body, the major axis of which is directed towards the earth. That some such phenomenon has obtained is evident from the coincidence of the times of orbital revolution and axial rotation of the lunar sphere. ”

“ Just as the growth and dwindling of plants became associated with the moon’s wax and wane, so changes of weather became associated with changes of the moon, while, by astrologer’s logic, it did not matter whether the moon’s change were real, at new and full, or imaginary, at the intermediate quarters. That educated people to whom exact weather records are accessible should still find satisfaction in the fanciful lunar rule, is an interesting case of intellectual survival. ”

“ Evidence is wanting of the existence of an atmosphere surrounding the Moon; no clouds or exhalations can be perceived, and no water is believed to exist on the lunar surface. Consequently there are no oceans, seas, rivers, or lakes; no fertile plains or forest-clad mountains, such as are found upon the Earth. Indeed, all the conditions essential for the support and maintenance of organic life by which we are surrounded appear to be nonexistent on the Moon. Our satellite has no seasons; its axial rotation is so slow that one lunar day is equal in length to fourteen of our days ”

“ In other words, if a race of beings resembling ourselves, or resembling any of our contemporaries in terrestrial life, ever existed upon the moon, they must long since have perished. That such beings may have existed, is possible, particularly if it be true, as generally believed, that the moon once had a comparatively dense atmosphere and water upon its surface, which have now, in the process of cooling of the lunar globe, been withdrawn into its interior. ”

“ And taking into account the whole effect of them, we may conclude that our view of the moon’s surface, instead of being confined to one half, is extended really to about four-sevenths of the whole area of the lunar globe. The remaining three-sevenths must for ever remain a terra incognita to the habitants of this earth, unless, indeed, from some catastrophe which it would be wild fancy to anticipate, a period of rotation should be given to the moon different from that which it at present possesses. ”

“ For the first phenomenon (accelerated ingress) the choice of stations is not good; but for the other phenomena (retarded ingress, accelerated egress, retarded egress) there appears to be no difficulty.—With regard to the Numerical Lunar Theory: Respecting the discordance of Annual Equation, I suspend my judgment. I have now discussed the theory completely; and in going into details of secular changes, I am at this time engaged on that which is the foundation of all, namely, the change of excentricity of the Solar Orbit, and its result in producing Lunar Acceleration. ”

“ The rotation of the moon upon her axis—the lunar day—has become, as we have seen, equal to her revolution around the earth. An epoch may likewise eventually be reached in the history of our own planet, when the length of the terrestrial day has been so slowed down by tidal friction that it will be equal to the year. Then will the earth revolve around the central orb, with one side plunged in eternal night and the other in eternal sunshine. ”

“ The moon is so near, that the excess of matter at the earth’s equator occasions periodic variations in her longitude, and also that remarkable inequality in her latitude, already mentioned as a nutation in the lunar orbit, which diminishes its inclination to the ecliptic when the moon’s ascending node coincides with the equinox of spring, and augments it when that node coincides with the equinox of autumn. ”

“ The moon is the more powerful of the two perturbing bodies, hence the main tides are due to the moon; and its chief action is to cause a pair of low waves or oceanic humps, of gigantic area, to travel round the earth once in a lunar day, i.e. in about 24 hours and 50 minutes. The sun makes a similar but still lower pair of low elevations to travel round once in a solar day of 24 hours. ”

“ Although the Church, in finding the new moon, and from it the 14th day, uses neither the true nor the mean motion of the moon, but measures only according to the order of a cycle, it is nevertheless undeniable that the mean full moons found from astronomical tables are of the greatest use in determining the cycle which is to be preferred ... ”

“ The zodiacal light also, which in our English latitude and climate is but rarely seen and in more favourable 161 climes appears only when the sun itself is hidden beneath the horizon, would upon the moon be seen as a constant accompaniment to the luminary throughout his daily course across the lunar sky. The other planets would appear generally as they do to us on earth, but, never being lost in daylight, their courses among the stars could be traced with scarcely any interruption. ”