The phase change of the moon
Probably the first of the astronomical phenomena, which primitive man drew attention to, was the phase change of the Moon .She even allowed him to learn how to keep track of the day. And it is no coincidence, apparently, in many languages the word "month" has a common root, consonant with the roots of the words "measure" and "Moon", for example, Latin mensis - month and mensuha - measure, Greek "mane" - Moon and "men "- month, English moon - Moon and month - month. And the Russian national name of the moon is a month! In the Ukrainian language, these names are identical: "μyats".
A sidereal month. Observing the position of the moon in the sky for several evenings, it's easy to make sure that it moves among the stars from west to east with an average speed of 13 °, 2 per day. The angular diameter of the Moon( as well as of the Sun) is approximately 0 °, 5.We can therefore say that for each day the Moon moves to the east by 26 of its widths, and in one hour - by more than its diameter. Having made a full circle on the celestial sphere, the Moon after 27,321661 days returns to the same star. This period of time is called sidereal( ie, stellar: sidus - a star in Latin) month.
Configurations and phases of the moon. As you know, the Moon, whose diameter is almost 4, and the mass - 81 times less than that of the Earth, revolves around our planet at an average distance of 384,000 km. The surface of the Moon is cold and shines with reflected sunlight. When the Moon turns around the Earth or, as is customary, when the configurations of the Moon are changed( from the Latin configuro - I give the correct form) - its positions relative to the Earth and the Sun, that part of its surface that is visible from our planet is illuminated by the Sun unequally. A consequence of this is a periodic change in the phases of the moon( Fig.).
Fig. The configuration( 1 - conjunction, 3 and 7 - quadrature, 5 - confrontation) and the phases of the moon( 1 - new moon, 3-first quarter, 5 - full moon, 7-last, or third quarter; 2, 4, 6, 8 - intermediatephase)
When the Moon moves between the Sun and the Earth( this position is called conjuncture-connection), it is facing the Earth unlit side, and then it is not visible at all. This is the new moon.
After appearing in the evening sky first in the form of a narrow sickle, the 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 to the Sun and its side facing the Earth is fully illuminated by it. The full moon comes, at which time the moon rises when the sun sets and is visible in the sky all night.7 days after the full moon, the last quarter comes, when the Moon is again visible in the form of a semicircle, turned by convexity already in the other direction, and it goes back after midnight. Recall that if at the time of the new moon the shadow of the Moon falls to Earth( more often it slips "above" or "below" our planet), there is a solar eclipse. If the moon in the full moon sinks into the shadow of the Earth, there is a lunar eclipse.
Synodic month. The interval of time after which the phases of the moon are repeated again in the same order is called the synodic month. It is equal to 29,53058812 days. The twelve synodic months are 354.36706 days. Thus, the synodic month is incommensurable with either the day or the tropical year: it does not consist of a whole number of days and does not fit without a residue in the tropical year.
The specified duration of the synodic month is its average, which is obtained as follows: calculate how much time elapsed between two widely separated eclipses, how many times during this time the moon changed its phases, and divide the first value by the second( with several pairs selected andfind an average value).Since the Moon moves around the Earth in an elliptical orbit, the linear and observed angular velocities of its motion at different points of the orbit are different. In particular, this latter varies in the range of about 11 ° to 15 ° per day. The movement of the Moon and the gravitational force acting on it from the side of the Sun is very complicated, because the magnitude of this force is continuously changing both in its numerical value and in direction it is most significant in the new moon and the smallest in the full moon.
Fig. The deviation of the duration of the synodic months in 1967-1986.of the average
I do not know. The average time from the disappearance of the Moon in the rays of the rising sun and its appearance in the evening after sunset, is 2-3 days. During these days, the Moon passes( in relation to the Sun) from the west side of the sky to the east, thus transforming from the morning light into the evening light. The first appearance of the moon in the evening sky( "the birth of a new moon"), the ancient Greek astronomers called neomenia( "new moon").From neo and it was convenient to start the count of time in a month.
But, as just said, the duration of the synodic month can be more than six hours shorter or longer than its mean. Therefore, neoteny can occur both a day earlier and a day later relative to the average expected date for the appearance of a new moon( Fig.).The deviation of the dates of the new moon from the synodic month calculated by the average duration is shown in Fig.
Fig. Deviation of the moments of new moon in 1967-1986.from the calculated for the average duration of the synodic month
, the moon is "high" and "low". The visibility conditions in the evening sky of the narrow crescent of the "new" Moon are to a large extent determined by the features of its movement around the Earth. The plane of the Moon's orbit is inclined to the ecliptic plane at an angle of i = 5 ° 9.Consequently, the moon then "rises" above the ecliptic( "approaching" to the north pole of the world) by ten of its apparent angular diameters, then "falls" under the ecliptic by the same amount. Twice over a period of 27,2122 days( this time interval is called a draconic month), the moon's path in the sky intersects with the ecliptic at points called nodes of the lunar orbit.
The node, passing through which the Moon approaches the North Pole of the world, is called the ascending node, the opposite one-the outgoing one. The line passing through the center of the Earth and connecting the nodes of the lunar orbit is called the knot line. As can be easily verified by observing the Moon and comparing its positions among the stars on a map of the starry sky, the lunar nodes continuously move toward the Moon, ie, to the west, making a full turn in 18.61 years. Annually the distance of the ascending node from.the point of the vernal equinox decreases by approximately 20 °, and in one draconic month, by 1 °, 5 °.
Let's see now how the effect of the inclination of the plane of the lunar orbit affects the height of the Moon in the upper culmination. If the ascending node coincides( "almost coincides") with the point of the vernal equinox( and this repeats every 18.61 years), then the inclination angle of the plane of the lunar orbit to the celestial equator is ε + i( 28 °, 5).During this period, the declination of the moon for 27.2 days varies from + 28 °, 5 to -28 °, 5( Fig.).
Fig. Limits of the variation of the declination of the moon for 18.61 years
After 14 days, the declination of the moon is already equal to its lowest value -28 °, 5, and its height in the upper culmination for the same latitude of 50 ° is only 11 °, 5 °.Such is the position of the "low" Moon: even in the upper culmination it is hardly visible above the horizon. ..
It is easy to understand that in the spring of this highest position in the sky, the Moon reaches at the time of the first quarter in the evening, and the lowest in the last quarter in the morning. Conversely, in the autumn, when the Sun is near the point of the autumnal equinox, the arc of the ecliptic in the evening sky is below the celestial equator, and the orbit of the Moon is even lower. Therefore, the Moon reaches this lowest position in the first quarter, whereas in the last quarter of the morning it is the highest.
Due to the continuous movement of the nodes of the lunar orbit in 9.3 years near the point of the vernal equinox, there will already be a descending node. The angle of inclination of the plane of the lunar orbit to the celestial equator will already be ε -i( 18 °, 5).At a latitude of 50 °, the height of the Moon in the upper culmination at the largest 18 °, 5 is already 58 °, 5( in the spring - in the first quarter, in the autumn - in the latter), the lowest, 14 days later - 21 °, 5( in the spring - in the last quarter, in the fall - in the first).In the intervening years, the nodes of the lunar orbit pass through the arcs of the ecliptic, on which the solstices are located. At the same time, the declination of the moon during the month ranges from + 23 °, 5 to -23 °, 5, as shown in Fig. Accordingly, the height of the Moon in the upper culmination also changes.
In general, the conditions for the visibility of the moon in the evening sky are primarily determined by the position of the ecliptic relative to the horizon: in the spring, the Moon is always much higher than in the autumn( Fig.).
Fig. The position of the young moon in the evening sky: a) in the spring, b) in the autumn with the same angular distance from the Sun, 1 - the position of the "upper" Moon, 2- the position of the "lower" Moon
This effect, however, is greatly enhanced by the favorable orientation of the plane of the lunar orbit: the height of the moon at the time of the upper culmination in the spring evening sky at φ = 50 ° is 58 °, 5 to 68 °, 5, while in the autumn - from 11 °, 5 °up to 21 °, 5.
The angular distance of the ascending node of the lunar orbit from the vernal equinox on January 1, 1900 was 259 °, 18.Using the formula W = 259 °, 18-19 °, 34t, where t is the time in years, it is not difficult to calculate the moments of coincidence of these points;1913.4, 1932.0, 1950.6, 1969.2 and 1987.8.Thus, the last "high Moon" was observed at the beginning of 1969. Usually, as can be seen from Fig. Near these moments, the moon's decline from month to month varies very slowly. Therefore, the Moon is "high" for about three years, in this case - in 1968-1970.Such an event will be repeated again in 1986-1988.The "low" moon was observed near the average moments of 1904.1, 1922.7, 1941.3, 1959.9, 1978.5, 1997.1, etc.
From all that has been said, it follows that in the spring the observer can notice the narrow crescent of the Moon after a new moon a day earlier than in the autumn. This effect also depends on the geographic coordinates of the observer. In particular, at a latitude of 32 °, 5( this is the latitude of Ancient Babylon), the time interval between conjuncture and neomeny varies from 16 hours 30 minutes in March to 42 hours in September. At latitude 38 °( latitude of Athens) from 23 to 69 hours. An experienced Polish astronomer, compiler of the first map of the visible side of the Moon, Jan Hevelius( 1611-1687), observing the Moon in Gdansk, never saw it later than 27 hours before the conjunction, not earlier than 40 hours after it.
Thus, to use for the construction of the calendar such a seemingly easily noticeable phenomenon as the phase change of the moon - it's still rather difficult. ..