MOON-EARTH DISTANCE The average Moon-Earth distance is 384,000 km; during a lunation thedistance changes by about 45,000 km. This phenomenon is due to manyreasons, but two are the main ones: the shape of the lunar orbit aroundthe Earth, an ellipse, and the gravitational attraction of the Sun. According to Kepler's first law, a lighter body rotates in an ellipticorbit around a much more massive one which occupies one of the two fociof the ellipse. The point of the orbit where the Moon is closest to the Earth is calledPERIGEE and the one where it is farthest is called APOGEE. Since the mass of the Moon is not negligible compared to the one of theEarth, the focus of the orbit is not at the center of the Earth, but4,672 km far from it, still inside our planet and coinciding with thecenter of mass of the Moon-Earth system. The apogee and the perigee of the Moon are not always at the samedistance from the Earth: the Sun exerts a gravitational attraction onour satellite that lightly perturbs the orbit. The values of the largestand of the smallest distance from the Earth are most affected when theapogee and the perigee lay on the same line as the Earth-Sun alignment(and such perturbation is maximum when the Earth is at the aphelion orat the perihelion). For example, let us see when the Moon-Earth distance is the smallest:this happens when the axes of the Earth and Moon orbits are aligned, theEarth is at the perihelion (i.e. at the smallest distance from the Sun),the Moon is full, i.e. on the opposite side of the Earth with respect tothe Sun and at the perigee. In this case the forces exerted on theMoon by the Earth and the Sun are maximum and act in the same direction,therefore the Moon-Earth separation reaches its minimum. REVOLUTION The Moon travels eastward on the celestial sphere, by about 13°11' everyday. A whole turn with respect to the stars is called siderealrevolution or sidereal month and is completed in 27d 7h 43m 11.5s. Inthe same time the Moon completes a whole rotation about its axis. If we consider the motion relative to the Earth, i.e. if we want theMoon to be back in the same position relative to a reference point onthe Earth, the rotation period is greater (synodic revolution, synodicmonth or lunation) because the additional time spent to follow therotation of the Earth has to be taken into consideration (29d 12h 44m2,8s). LUNAR PHASES The phases are a consequence of the relative position of the Earth, Sunand Moon. When the Moon lies on the Earth-Sun line, on the Sun side, itis invisible from the Earth, because it shows it its dark side. We have the phase of "NEW MOON". About seven days later, the Moon-Earthline is at an angle of 90 degrees with respect to the Earth-Sun line;i.e. it is in quadrature. In this case we see the "FIRST QUARTER". After one more week, the Moon will be aligned again with the Earth andthe Sun, but il will show the Earth its bright side, illuminated by theSun: the Moon is FULL. Finally, about 22 days after the new Moon, theMoon will be in quadrature with the Sun again. We shall be able to seeonly half of its side illuminated by the Sun and this configuration iscalled "LAST QUARTER". In the following days the bright portion will get smaller until, aftera total of about 29.5 days, the Moon will be invisible again, inconjunction with the Sun: a new lunation begins. ECLIPSES Eclipses happen when the Earth, the Moon and the Sun lie on the sameline; it is an occasional phenomenon because the plane containing theorbit of the Moon and the one containing the orbit of the Earth do notcoincide, being at an angle of about 5° 8' 48". When this alignment takes place at the beginning of the lunation, theMoon does not let solar rays reach the surface of our planet. In thiscase we have a solar eclipse. The distance between the Moon and theEarth makes our satellite and the Sun appear almost of the same angulardimension (about half degree). Since both the orbit of the Moon around the Earth and the one of theEarth around the Sun are elliptic, the ratio of the angular dimensionsof the Sun and of the Moon as seen from the Earth is not constant. Therefore, if both the Moon is at the apogee and the Earth is at theperihelion, the Moon will not cover completely the Sun ("ANNULAR"eclipse). If the Moon is closer to the Earth and the Sun further fromit, we have a "TOTAL" eclipse. In this situation it is possible to observe, when the Moon eclipsescompletely the Sun, "Bailey's beads". This phenomenon is due to thecraters and to the mountains on the edge of the lunar disk. The light ofthe sun will quickly twinkle through the depressions of the craters andthe valleys, causing the appearance of some little bright points lastinga few seconds. During the total solar eclipse we can observe the external solaratmosphere, the CORONA, too dark to be observed in conditions of normaldaylight, and the PROTUBERANCES, strips of matter protruding from thesolar surface for thousands of kilometers as a consequence of explosionsin the photosphere. If the alignment among the three celestial bodies is not perfect, theMoon does not cover completely the Sun, but hides from our view onlypart of it. In this case the eclipse is called "PARTIAL". If the Moon, the Earth and the Sun are on the same line, but the Moon isnot between the Earth and the Sun (this can happen only with full Moon),we have a lunar eclipse. During such eclipse the Moon is in the shadowof the Earth and, therefore, becomes almost invisible. It is not completely invisible because the terrestrial atmospherelightly refracts the solar rays, especially the red wavelengths, whichcan thus reach the Moon. During a lunar eclipse the Moon gets brick redand its overall brightness is reduced by a factor varying between 10,000and 1,000,000. This loss of brightness is variable because the Moon-Earth-Sun alignmentis not always perfect and because of the air pollution that determines adifferent transparency of the atmospere. A total eclipse of the Moon is called "UMBRA ECLIPSE"; when thealignment is not perfect and the Moon does not enter in the umbra wehave a "PENUMBRA ECLIPSE". The decrease in brightness is much smaller(by a factor between 2 and 10). LIBRATION Even though we always see the same hemisphere of the Moon, we canactually observe 59% of the total lunar surface because of libration. There is a longitude libration, due to the varying orbital velocity ofthe Moon: it allows us to see about 8° of the hidden side. The latitudelibration, instead, is due to the inclination of the lunar axis withrespect to the orbital plane. The parallactic (or diurnal) libration isdue to the rotation of the Earth: the change of perspective from a pointon the Earth corresponds to a shift of approximately one degree of thevisible portion of the Moon. Finally, there is a physical libration,which is due to real irregularities in the lunar rotation. LUNAR GEOLOGY There are various geological formations on the Moon, ranging from themost famous like craters, seas, lands to the less known domes andcanals. CRATERS are the most common geological formation on the lunar surface.We can see craters ranging from the large ones (beyond 100 km ofdiameter) produced by the impact of small asteroids, down tomicrocraters with a diameter of less than one millimeter. With a normal instrument, we can observe craters of a few hundred metersin diameter from the Earth. Their meteoric origin is evident from theirbowl-like, circular shape and from the peaks which sometimes appear ontheir floor. Their distribution is almost random, even though, at first glance, wecan see a higher density of craters in the southern hemisphere. This isnot due to a greater number of impacts, but to the lack of "seas",which, in the process of their formation, destroyed all the craters nearthem. When a celestial body of small size collides with a much largerone, the impact does not usually destroy both bodies but only thesmaller one. In the impact point a depression of the ground with raisededges appears: a crater. Sometimes the impact generates a large amountof heat that melts the underlying rock. A plume of molten rock arises inthe interior of the crater and quickly solidifies, creating theso-called central peak. Sometimes, as a consequence of the impact, part of a meteorite isfragmented into many pieces which are thrown away. The largest fragments can generate secondary craters of irregular shape,not very deep, without central peak and placed radially around theparent crater. Smaller residuals, small pebbles and dust create radialformations extending sometimes to distances of hundreds of kilometersfrom the crater. The craters with well marked boundaries and with radial structures arethe youngest on the lunar surface. Even though on our satellite there isno water, eolian or human erosion, the geological formations are notimmutable. The continuos impact of small meteorites, the thermalfluctuations, the solar wind cause, over long time scales, a progressivedisintegration of the crater boundaries, and the disappearance of theradial formations. Therefore the oldest craters existing on the lunarsurface are hardly noticeable. SEAS, instead, are probably the result of the impact of large asteroids.Such impacts generated craters beyond 200 km in diameter that weresubsequently flooded by the lava coming out from the broken mantle.The lava covered also the nearby craters, this is the reason why thedensity of craters in the seas is less than the average one. ROTATION The rotation period of the Moon around its axis equals its revolutionperiod around the Earth, i.e. about 29.5 days. The synchronicity between the two motions makes the Moon show always thesame side to the Earth, a fact known also by the ancient astronomers. Only with the space exploration we have been able to see the "hiddenside" of the Moon, thanks to the Soviet and American probes whichphotographed it. THE TIDES The lunar mass is 7.38x10^22 kilograms, about 80 times smaller than theone of the Earth (5.98x10^24). This great gravitational mass, less than 400,000 km far from us, exertsa significant influence on the Earth, causing several phenomena. Thetides are the most well-known of these. The tides, i.e. the variations of sea-level that, in certain parts ofthe coast, can exceed ten meters, are due to the gravitationalattraction of the Moon. Such attraction deforms the shell of sea watercovering our planet, stretching it towards the Moon. About every six hours high tides and low tides alternate, even thoughthe transit of the Moon in the sky takes place about every 25 hours. Whythen are there two tides every day? To explain this phenomenon we must remember that the center of mass ofthe Moon-Earth system is not in the center of the Earth but it isshifted by about 4500 km. Therefore the angular velocity of a point onthe surface of the Earth which is on the opposite side with respect tothe Moon is higher than the one of the corresponding point on the otherside. This implies a higher value of the centrifugal force and, as aconsequence, a higher water level. To summarize, the effect of thecombined gravitational attraction of the Moon (and Sun) and of themotion of the Earth-Moon system make the water shell around the Earthbulge along the Moon-Earth direction on both sides: this causes two hightides and two low tides for each complete rotation of the Earth. THE PATH OF THE MOON IN THE SKY The Moon, during a lunation, never rises from the same place for twoconsecutive nights. This phenomenon can easily be noticed by everybody.Why does it happen ? The answer is quite straightforward. Let usconsider, for instance, the first lunation of the spring equinox. Atthis time the Sun rises almost exactly in the east and sets almostexactly in the west and so does the new Moon, in conjunction with theSun. A week later the Moon rises about six hours later than the Sun. Itis substantially in the same point of the ecliptic as the one occupiedby the Sun during the summer solstice, three months later: like the Sun,which at summer solstice rises in the northeast and sets in thenorthwest, the Moon, after a week, will be rising and setting muchfurther north. When the Moon is full, it is, with respect to the ecliptic, in the sameposition as the one of the Sun for the fall equinox, and, thus, it risesalmost exactly in the east and sets in the west. After one more week, the Moon is in the position corresponding to thewinter solstice and therefore it rises in the southeast and it sets tothe southwest. In summary, in one month we can see the same motion relative to theEarth as the one performed by the Sun throughout the whole year. Thisphenomenon is enhanced by the inclination of the lunar orbit (beyond 5°)with respect to the orbit of the Earth. HOW MUCH IS THE MOON LATE EVERY DAY ? The Moon completes a revolution around the Earth, with respect to thefixed stars, in little more than 27 days, as we have already seen, andthis time is called "sidereal month". If we want the Moon to be backexactly in the same phase, the time is slightly longer, because of themotion of the Earth around the Sun. This time is called "sinodic month",and is a little more than 29 days long. The Moon travels across the sky by about 13° a day. During the first lunation in spring we see that the full Moon rises veryquickly, almost vertically with respect to the horizon. This is due tothe fact that the ecliptic, at this time of the night, is at itsgreatest height, and thus the path of the Moon is very steep. During fall, instead, the full Moon rises almost grazing the horizon andtakes a longer time to culminate, reaching a small final elevation overthe horizon. In the first case the 13° daily delay corresponds to a time delay in thefirst sight of the Moon by almost one hour, while in the second case thedelay can be as short as 10 minutes. Going towards higher latitudes these phenomenona are enhanced in bothhemispheres.
