Changing the phases of the moon
probably the first of astronomical phenomena, on which drew the attention of primitive man was changing phases of the moon.It was she who let him learn to keep score days.It is no coincidence, apparently, in many languages, the word "month" has a common root, in tune with the roots of the word "measure" and "Moon", for example, the Latin mensis - month and mensuga - measure, the Greek "mene" - the Moon and "Men "- month, the English moon - the moon and month - a month.And the Russian nation-wide title of the Moon - a month!In the Ukrainian language, these names are identical: "mkyats".
sidereal month. observing the position of the Moon in the sky for a few nights, it is easy to make sure that it moves among the stars from west to east with an average speed of 13 °, 2 per day.Moon angular diameter (as well as the sun) equal about 0 °, 5.We can say, therefore, that for each day of the moon moves eastward at 26 their widths, and in an hour - more than the value of its diameter.Having made a full circle
Configurations and phases of the moon. As you know, the moon, the diameter of which is almost 4, and weight - 81 times less than the Earth orbits our planet at an average distance of 384 000 km.The surface of the moon shone cold, and she reflected sunlight.When you call the moon around the earth, or, as they say, by changing the configuration of the Moon (from the Latin configuro - attach the correct form) - its provisions relative to the Earth and the Sun that part of its surface, which can be seen from our planet, the sun illuminated differently.The result is a periodic variation of the moon phases (Fig.).
Fig.Configuration (1 - conjunction, 3 and 7 - area, 5 - opposition) and moon phase (1 - new moon, 3 the first quarter, 5 - Full Moon 7 last, or third quarter, 2, 4, 6, 8 - intermediatephase)
When the moon is in its motion between the Sun and the Earth (this position is called a conjunction - compound) to Earth to face the unlit side, and then it is absolutely not visible.This is - the new moon.
Appearing then in the evening sky, first as a narrow crescent moon in about 7 days is already visible in the form of a semicircle.This phase is called the first quarter.Even after about 8 days the Moon occupies a position directly opposite the Sun and its side facing the Earth is fully lit them.There comes a full moon, at which time the moon will rise all night at sunset and is visible in the sky.Within 7 days after the full moon comes the last quarter, when the moon is visible again in the form of a semicircle, facing bulge in the other side, and goes after midnight.Recall that at the time of the new moon the Moon's shadow falls on Earth (most often it slips "above" or "below" of our planet), there is a solar eclipse.If the Moon in the full moon immersed in Earth's shadow, there is a lunar eclipse.
synodic month.The amount of time, after which the moon phase is repeated again in the same order, is called synodic month.He is 29.53058812 days.Twelve months make up the synodical 354.36706 days.Thus, the synodic month commensurate with either the clock or the tropical year: it does not consist of a whole number of the day and does not fit evenly in a tropical year.
specified duration of the synodic month is its mean value, which is obtained as follows: count how much time elapsed between the two far from each other eclipses, how many times during this time the Moon has changed its phase, and divide the first value to the second (and choose a few pairsand find the average value).As the Moon moves around the Earth in an elliptical orbit, the linear and angular velocity observed her movements at various points of the orbit are different.In particular, the latter ranges from about 11 ° to 15 ° per day.It is complicated by the movement of the moon and the force of gravity acting on it from the sun, because the magnitude of this force is constantly changing both its numerical value, and the direction it has the greatest value in the new moon, and the smallest - in the full moon.
Fig.Deviation duration of synodical months in 1967-1986 gg.of the average of
Neomeniya. The average time interval between the disappearance of the moon in the rays of the rising sun and its appearance in the evening after sunset, it is 2-3 days.During these days the moon moves (relative to the sun) on the western side of the sky in the east, becoming thus of the morning light in the evening.The first appearance of the moon in the evening sky ( "birth of a new Moon"), ancient Greek astronomers called neomeniey ( "New Moon").From neomenii and was convenient to start track of time in a month.
But, as has just been said, the length of the synodic month may be more than six hours shorter or longer than its average value.Therefore neomeniya may occur as the day before and the day after with respect to the expected average date of appearance of the new moon (Fig.).Deviation from the new moon dates calculated by the average length of the synodic month and is shown in Fig.
Fig.Reject new moon moments in the 1967-1986 biennium.from "high" calculated by the average duration of
synodical month the moon and "low". Terms appear in the evening sky of a narrow crescent of the "new" moon to a large extent determined by the peculiarities and its movement around the Earth.The plane of the Moon's orbit is inclined to the ecliptic plane at an angle i = 5 ° 9.Therefore, the moon is "lifted" above the ecliptic ( "close" to the north pole of the world) for ten of its apparent angular diameters, the "falls" under the ecliptic at the same rate.Twice during the period of 27.2122 days (this period is called dracontic month) the path of the moon in the sky and the ecliptic intersect at points called nodes of the lunar orbit.
node, passing through which the moon is close to the north pole of the world, is called the ascending node, the opposite -niskhodyaschim.The line passing through the center of the earth and connecting the nodes of the lunar orbit is called the line of nodes.As is easy to see by observing the moon and mapping its provisions among the stars on the map of the sky, the lunar nodes are continuously moved toward the moon, t. E. To the west, making a complete revolution of 18.61 years.Each year, the ascending node distance.the vernal equinox is reduced by about 20 °, and at a draconic month -on 1 °, 5.
Let us now see how the effect of the inclination of the lunar orbit plane affects the height of the moon at the top of the climax.If the ascending node is the same ( "almost the same") with the vernal equinox (which is repeated every 18.61 years), the angle of inclination of the plane of the lunar orbit to the celestial equator is ε + i (28 °, 5).During this time, the declination of the moon during the day varies from 27.2 + 28 °, 5 to -28 °, 5 (Fig.).
Fig.Limits of change of declination of the moon during the year 18.61
After 14 days the declination of the Moon is already equal to its lowest value of -28 °, 5, and its height at the top of the climax to the same latitude of 50 ° is only 11 °, 5.This will be the position of the "low" of the moon: it is even in the upper culmination barely visible over the horizon ...
easy to see that this highest position in the sky in the spring reaches the moon at the time of the first quarter of the night, and the lowest - in the last quarter of the morning.Conversely, in the autumn, when the sun is near the point of the autumnal equinox, the ecliptic arc in the evening sky is below the celestial equator, and the Moon's orbit is even lower.Therefore, the moon reaches the specified position of the lowest in the first quarter, while in the last quarter of the morning, it is most appreciated.
Due to the continuous movement of the lunar orbital nodes through 9.3 years near the vernal equinox would already be descending node.The angle of inclination of the lunar orbit plane to the celestial equator will be already ε - i (18 °, 5).At the latitude of 50 ° elevation of the moon at the top of the climax at the maximum 18 °, 5 ° is already 58, 5 (in the spring -in the first quarter, the fall -in the latter), and the lowest, 14 days later - 21 °, 5 (in the spring - in the last quarterautumn - in the first).In the intervening years the lunar orbit nodes pass the arc of the ecliptic, on which there are points of the solstices.This declination of the moon during the month ranges from about + 23 °, -23 ° to 5, 5, as shown in Fig.Accordingly, the change of the moon, and the height of the upper culmination.
Overall visibility of the moon in the evening sky is primarily determined by the position of all of the ecliptic to the horizon: spring moon is always much higher than in autumn (Fig.).
Fig.The position of the new moon in the night sky: a) in the spring, b) in the fall at the same angular distance from the Sun, 1 - to "the top" of the moon, 2-position "bottom" of the moon
This effect, however, is significantly enhanced by the favorable orientation of the lunar orbit plane: the height of the moon at the time of upper culmination of the spring evening sky at φ = 50 ° is from 58 °, 5 to 68 °, 5, whereas in the fall - from 11 °, 5 to 21 °, 5.
angular distance of the ascending node of the lunar orbit from the vernal equinox on January 1, 1900 was equal to 259 °, 18.Using the formula W = 259 °, 18-19 °, 34t, where t - time in years, it is easy to calculate the points of coincidence of these points;1913.4, 1932.0, 1950.6, 1969.2, and 1987.8.Thus, the last "high moon" was observed in the early 1969 city usually, and as is seen from Fig.near these moments declination of the Moon from month to month changes very slowly.Therefore the moon is "high" for about three years, in this case - in the years 1968-1970.Such an event happen again in the 1986-1988 biennium."Low" Luna observed near the middle points 1904.1, 1922.7, 1941.3, 1959.9, 1978.5, 1997.1, etc.
from all the foregoing it follows that the observer can observe the spring narrow crescent moon after the new moon on the day before the fall.This effect is also still depends on the geographical coordinates of the observer.In particular, at a latitude of 32 °, 5 (this ancient Babylon latitude) between the time interval and the conjunction neomeniey varies from 16 min to 30 h to 42 h March to September.At the latitude of 38 ° (latitude of Athens) -from 23 to 69 hours. An experienced Polish astronomer, compiler of the first maps of the visible side of the Moon Hevelius (1611-1687), watching the moon in Gdansk, never seen her no later than 27 hours before the conjunction, no earlier than 40 hours after.
thus be used to construct such a calendar would seem to easily noticeable phenomenon of change of phases of the moon - all the same thing pretty hard ...