| Timekeeping and the Celestial Sphere |
| In this section we deal with general properties of the celestial sphere: constellations, the naming of stars, and a general coordinate system for the celestial sphere that is analogous to the latitude-longitude system on the surface of the Earth and that allows us to specify precisely a location on the celestial sphere. We shall also consider some general aspects of timekeeping and calendars, because historically, the regular apparent motions of the heavens provided many of the ideas and much of the terminology that we use in timekeeping. For further discussion of many of the topics in this section, see Astronomy without a Telescope. |
| | There is a popular misconception that the seasons on the Earth are caused by varying distances of the Earth from the Sun on its elliptical orbit. This is not correct. One way to see that this reasoning may be in error is to note that the seasons are out of phase in the Northern and Southern hemispheres: when it is Summer in the North it is Winter in the South. |
| | Incidentally, one should be precise in terminology. A common student answer for the cause of the seasons is that "the Earth tips toward the Sun in the Summer, . . .". This conveys the impression that the Earth moves around its orbit and at certain times of the year the rotation axis suddenly tips one way or another and thus we have seasons. As the preceding diagram makes clear, the rotation axis of the Earth remains pointed in the same direction (except for small effects from precession) as it moves around its orbit. It is the relative location of the Sun with respect to this constant tilt angle that causes the seasons, not some elaborate square dance of the Earth bowing to its partner as it moves around its orbit! |
| | Seasons in the Northern Hemisphere |
| | The primary cause of the seasons is the 23.5 degree of the Earth's rotation axis with respect to the plane of the ecliptic, as illustrated in the adjacent image. |
| | his means that as the Earth goes around its orbit the Northern hemisphere is at various times oriented more toward and more away from the Sun, and likewise for the Southern hemisphere, as illustrated in the following figure. |
| | Thus, we experience Summer in the Northern Hemisphere when the Earth is on that part of its orbit where the N. Hemisphere is oriented more toward the Sun and therefore the Sun rises higher in the sky and is above the horizon longer, and the rays of the Sun strike the ground more directly. Likewise, in the N. Hemisphere Winter the hemisphere is oriented away from the Sun, the Sun only rises low in the sky, is above the horizon for a shorter period, and the rays of the Sun strike the ground more obliquely. |
| | In fact, as the diagram indicates, the Earth is actually closer to the Sun in the N. Hemisphere Winter than in the Summer (as usual, we greatly exaggerate the eccentricity of the elliptical orbit in this diagram). The Earth is at its closest approach to the Sun (perihelion) on about January 4 of each year, which is the dead of the N. Hemisphere Winter. |
| | For a more extensive introduction to how variations in the amount of solar energy reaching the Earth's surface influence climate, see this discussion of solar databases for global change models. |
| | Simulating the Apparent Motion of the Sun |
| | The exact time of sunrise and sunset (and similar data for moonrise and moonset) may be calculated for any date and 22,000 named cities in the United States, or by specifying the latitude and longitude of any location worldwide, using this program. |
| | For locations in the United States, a table of corresponding information for an entire year (past, present, or future) may be calculated using this program. |
| | Southern Hemisphere Seasons |
| | As is clear from the preceding diagram, the seasons in the Southern Hemisphere are determined from the same reasoning, except that they are out of phase with the N. Hemisphere seasons because when the N. Hemisphere is oriented toward the Sun the S. Hemisphere is oriented away, and vice versa: |
| | The preceding reasoning for the causes of the seasons is idealized. In reality, we know that the seasons "lag": for example, the hottest temperatures in the Summer usually occur a month or so after the time of maximum insolation (the time when maximum solar energy is deposited during a day at a point on the surface of the Earth). This is because the Earth and its atmosphere store heat (the oceans are particularly effective heat sinks). Thus, a detailed description of the seasons is quite complicated since it must take into account complex local variations in the storage of solar energy. However, the basic reason for the seasons is simple, as described above. |
| | Historically, the regular motion of objects in the sky served as the basis for timekeeping. The diurnal motion of the sky caused by the rotation of the Earth on its axis defined the day, the year was defined by the motion of the Earth on its orbit about the Sun, and the month was defined in relation to the revolution of the Moon about the Earth. Although precise modern timekeeping is done electronically, many of the details and the terminology of timekeeping remain rooted in its astronomical heritage. |
| | Time Zones and Universal Time |
| | As a matter of civil convenience, the Earth is divided into various time zones. The time for many astronomical events is given in Universal Time (UT), which is (approximately) the local time for Greenwich, England---the Greenwich Mean Time or GMT. The conversion from UT to local zone time may be made using this map. |
| | Sidereal Days and Solar Days |
| | The sidereal day is defined to be the length of time for the vernal equinox to return to your celestial meridian. The solar day is defined to be the length of time for the Sun to return to your celestial meridian. The two are not the same, as illustrated in the following animation. |
| | Because the Earth is in motion on its orbit around the Sun in the course of a day, the Earth must turn about 4 minutes longer each day (3 minutes and 56 seconds, to be exact) to bring the Sun back to the celestial meridian than to bring the vernal equinox back to the celestial meridian. Thus, the solar day is 3 minutes and 56 seconds longer than the sidereal day. It is this almost 4 minute per day discrepancy that causes the difference in sidereal and solar time, and is responsible for the fact that different constellations are everhead at a given time of day during the Summer than in the Winter. |
| | Sidereal Time and Solar Time |
| | In using the sky for timekeeping, we must define a reference point to determine when a cycle of the required motion has been completed. If we choose a reference point afixed to the celestial sphere, the corresponding time is being referenced to the distant stars and is termed sidereal time. If instead we choose the Sun as the reference point, the corresponding time is called solar time (or tropical time). |
| | Technically, the sidereal time is defined as the length of time since the vernal equinox has crossed the local celestial meridian. An equivalent definition of the sidereal time is the right ascension of any star presently located on the local celestial meridian. Thus, if the star Sirius is presently on your celestial meridian, the sidereal time is 6 hours and 45 minutes because we saw earlier that Sirius is located at 6 hr 45 min right ascension on the celestial sphere. Generally our everyday (civil) time is referenced to the (average) motion of the Sun, not the vernal equinox. Thus, sidereal time generally does not coincide with the everyday (wall clock) time. To be precise, the sidereal time agrees with the solar time only at the autumnal equinox; at any other time, they differ (they are exactly 12 hours apart at the time of the vernal equinox). |
| | Precession of the Earth's Rotation Axis |
| | The Earth's rotation axis is not fixed in space. Like a rotating toy top, the direction of the rotation axis executes a slow precession with a period of 26,000 years (see following figure). |
| | Thus, Polaris will not always be the Pole Star or North Star. The Earth's rotation axis happens to be pointing almost exactly at Polaris now, but in 13,000 years the precession of the rotation axis will mean that the bright star Vega in the constellation Lyra will be approximately at the North Celestial Pole, while in 26,000 more years Polaris will once again be the Pole Star. |
| | Precession of the Equinoxes |
| | Since the rotation axis is precessing in space, the orientation of the Celestial Equator also precesses with the same period. This means that the position of the equinoxes is changing slowly with respect to the background stars. This precession of the equinoxes means that the right ascension and declination of objects changes very slowly over a 26,000 year period. This effect is negligibly small for casual observing, but is an important correction for precise observations. |
| | The Dawning of the Age of Aquarius (Almost) |
| | Because of the precession of the equinoxes, the vernal equinox moves through all the constellations of the Zodiac over the 26,000 year precession period. Presently the vernal equinox is in the constellation Pisces and is slowly approaching Aquarius. |
| | This is the origin of the "Age of Aquarius" celebrated in the musical Hair: a period when according to astrological mysticism and related hokum there will be unusual harmony and understanding in the world. We could certainly use a dose of harmony and understanding in this old world; unfortunately, it is unlikely to come because of something as irrelevant as the position of the vernal equinox with respect to the constellations of the Zodiac. |
| | There are two basic sources for calendars presently in use: the monthly motion of the Moon (Lunar calendars) and the yearly motion of the Sun (Solar Calendars). Examples of Lunar calendars still in use are the traditional Jewish and Chinese calendars. The difficulty with Lunar calendars is that the seasons are correlated with the Sun, not the Moon. Thus, Lunar calendars require elaborate adjustments or translations to relate to the seasons. That calendars correlate with seasons is now primarily a matter of convenience, but in more ancient cultures keeping track of the seasons was serious business: it could be a matter of survival to know things like the proper time to plant to ensure a bountiful harvest. |
| | Adoption of the Gregorian Calendar |
| | An interesting historical sidelight on the Gregorian Calendar is that not all countries adopted it immediately. In particular, it was adopted uniformly in Catholic countries, but Protestant countries often still used the Julian Calendar. Thus, the date could change by 10 days simply by crossing certain country borders! England and its American colonies did not adopt the Gregorian Calendar until 1752, when 11 days were removed from the calendar, and Russia resisted this change until after the 1917 Revolution. One conseqence of the British adoption of the Gregorian Calendar in 1752 is that George Washington was born on February 11, 1731, according to the calendar in use on his birthday, but we now celebrate his date of birth as February 22, 1731 (actually, even that is no longer true with the advent of Presidents Day). |
| | This Calendar Program allows you to get a calendar for an arbitrary year in the United States and England (if you submit it with no entry it will return the calendar for the present year, by default). Look at the calendar for the year 1752 and note the missing days in September associated with the transition to the Gregorian calendar in England and its colonies. |
| | More information about timekeeping and calendars may be found at this FAQ. |
| | In 46 B.C., Julius Caesar reformed the calendar by ordering the year to be 365 days in length and to contain 12 months. This forced some days to be added to some of the months to bring the total from 354 up to 365 days, so the months now were out of phase with the cycles of the Moon: although the Julian Calendar retained monthly divisions, it was no longer a Lunar calendar. The Julian Calendar improved things tremendously, but there was still about a quarter day difference between the true length of the year and the 365 days assumed for the Julian Calendar. Thus, February was given an additional day every 4 years (leap years) and the average length of the Julian year with leap years added was 365.25 days. |
| | Our present calendar (called the Gregorian Calendar) is a basically solar calendar that grew from what was originally a Lunar calendar used by the Romans. The original calendar contained 10 months of length 29 or 30 days. This was later modified to a 12 month calendar, but 12 months of average length 29.5 days gives only 354 days in the year, whereas the orbital period of the Earth is 365.242199 days. Thus, at the end of each year this calendar was 11 days out of step with the seasons and at the end of 3 years it was almost a month out of step. This was initially corrected in an arbitrary way by adding 13th months, but this was used for various political purposes and soon threw the calendar into severe confusion. |
| | However, the Julian year still differs from the true year of 365.242199 days by 11 minutes and 14 seconds each year, and over a period of 128 years even the Julian Calendar was in error by one day with respect to the seasons. By 1582 this error had accumulated to 10 days and Pope Gregory XIII ordered another reform: 10 days were dropped from the year 1582, so that October 4, 1582, was followed by October 15, 1582. In addition, to guard against further accumulation of error, in the new Gregorian Calendar it was decreed that century years not divisible by 400 were not to be considered leap years. Thus, 1600 was a leap year but 1700 was not. This made the average length of the year sufficiently close to the actual year that it would take 3322 years for the error to accumulate to 1 day. |
| | A further modification to the Gregorian Calendar has been suggested: years evenly divisible by 4000 are not leap years. This would reduce the error between the Gregorian Calendar Year and the true year to 1 day in 20,000 years. However, this last proposed change has not been officially adopted; there is plenty of time to consider it, since it would not have an effect until the year 4000. |
| | The orbit of the Moon is very nearly circular (eccentricity ~ 0.05) with a mean separation from the Earth of about 384,000 km, which is about 60 Earth radii. The plane of the orbit is tilted about 5 degrees with respect to the ecliptic plane. |
| | The Moon appears to go through a complete set of phases as viewed from the Earth because of its motion around the Earth, as illustrated in the following figure. |
| | In this figure, the various positions of the Moon on its orbit are shown (the motion of the Moon on its orbit is assumed to be counter-clockwise). The outer set of figures shows the corresponding phase as viewed from Earth, and the common names for the phases. |
| | The Moon appears to move completely around the celestial sphere once in about 27.3 days as observed from the Earth. This is called a sidereal month, and reflects the corresponding orbital period of 27.3 days The moon takes 29.5 days to return to the same point on the celestial sphere as referenced to the Sun because of the motion of the Earth around the Sun; this is called a synodic month (Lunar phases as observed from the Earth are correlated with the synodic month). There are effects that cause small fluctuations around this value that we will not discuss. Since the Moon must move Eastward among the constellations enough to go completely around the sky (360 degrees) in 27.3 days, it must move Eastward by 13.2 degrees each day (in contrast, remember that the Sun only appears to move Eastward by about 1 degree per day). Thus, with respect to the background constellations the Moon will be about 13.2 degrees further East each day. Since the celestial sphere appears to turn 1 degree about every 4 minutes, the Moon crosses our celestial meridian about 13.2 x 4 = 52.8 minutes later each day. |
| | Rotational Period and Tidal Locking |
| | The Moon has a rotational period of 27.3 days that (except for small fluctuations) exactly coincides with its (sidereal) period for revolution about the Earth. As we will see later, this is no coincidence; it is a consequence of tidal coupling between the Earth and Moon. Because of this tidal locking of the periods for revolution and rotation, the Moon always keeps essentially the same face turned toward the Earth (small fluctuation mean that over a period of time we can actually see about 55% of the Lunar surface from the Earth). |
| | The largest separation between the Earth and Moon on its orbit is called apogee and the smallest separation is called perigee. Here is an online Lunar Perigee and Apogee Calculator that will allow you to determine the date, time, and distance of lunar perigees and apogees for a given year |
| | As we have noted in the preceding section, the Earth casts a shadow that the Moon can pass through. When this happens we say that a lunar eclipse occurs. Just as for solar eclipses, lunar eclipses can be partial or total, depending on whether the light of the Sun is partially or completely blocked from reaching the Moon. The following figure illustrates a total lunar eclipse with the Moon lying in the umbra of the Earth's shadow. |
| | During a total lunar eclipse the Moon takes on a dark red color because it is being lighted slightly by sunlight passing through the Earth's atmosphere and this light has the blue component preferentially scattered out (this is also why the sky appears blue from the surface of the Earth), leaving faint reddish light to illuminate the Moon during the eclipse. |
| | During a total lunar eclipse the Moon takes on a dark red color because it is being lighted slightly by sunlight passing through the Earth's atmosphere and this light has the blue component preferentially scattered out (this is also why the sky appears blue from the surface of the Earth), leaving faint reddish light to illuminate the Moon during the eclipse. |
| | Historically, constellations were groupings of stars that were thought to outline the shape of something, usually with mythological significance. There are 88 recognized constellations, with their names tracing as far back as Mesopotamia, 5000 years ago. |
| | The Historical Constellations |
| | In some cases one can discern easily the purported shape; for example, the constellation Leo shown on the right might actually look like a lion with the dots connected as they are. In other cases the supposed shape is very much in the eye of the beholder, as the example of Canis Minor (The Little Dog) shown on the left indicates. This certainly could be a little dog, or a cow, or a submarine, or . . . |
| | Drawing the Constellations |
| | Here are two pieces of software that allow you to construct maps of the sky at specified times (now, or in the past or future) that include constellations: |
| | Each of these programs can provide information about the celestial sphere beyond just drawing the constellations. Here is a map of northern hemisphere constellations characteristic of late Winter evenings in the Southern United States that was constructed using the Mount Wilson software described above. |
| | 2. Free Star Maps may be downloaded on demand from the Mount Wilson Observatory in postscript format. A forms interface allows the map to be customized, and links on the Mount Wilson page explain how to download a free postscript viewer if your don't already have one. |
| | 1. Starry Night is a $28 shareware program for the Macintosh that simulates the appearance and motion of the sky from a user chosen vantage point and at a user chosen time. |
| | Constellations Are Not Physical Groupings |
| | The apparent groupings of stars into constellations that we see on the celestial sphere are not physical groupings. In most cases the stars in constellations and asterisms are each very different distances from us, and only appear to be grouped because they lie in approximately the same direction. This is illustrated in the following figure for the stars of the Big Dipper, where their physical distance from the Earth is drawn to scale (numbers beside each star give the distance from Earth in light years). |
| | It is important to make this distinction because later we shall consider groupings that are physical groupings, such as star clusters and binary star systems. |
| | Constellations in Modern Astronomy |
| | In modern astronomy, the significance of constellations is no longer mythological, but practical: constellations define imaginary regions of the sky, just as the individual states each define an imaginary region of the United States. Thus, to say that a planet is in the constellation Leo is to partially locate the planet on the celestial sphere, just as saying that Knoxville is in Tennessee is to partially locate the city on the surface of the Earth. As for states, modern constellations have irregular boundaries that have been agreed upon for various reasons, perhaps not always completely logical. |
| | Here is a Web page devoted to constellations and their stars. |
| | The Constellations of the Zodiac |
| | The zodiac is an imaginary band 18 degrees wide and centered on the ecliptic. The constellations that fall in the zodiac are called the 12 constellations of the zodiac. They were at one time thought to have great mystical and astrological significance. Astrology is bunk, but the constellations of the zodiac are still of importance because the planets, as well as the Sun and Moon, are all near or on the ecliptic at any given time; thus, they are always found within one of the zodiac constellations. |
| | Star Groupings and Asterisms |
| | Some of the more familiar "constellations" are technically not constellations at all. For example, the grouping of stars known as the Big Dipper is probably familiar to most, but it is not actually a constellation. The Big Dipper is part of a larger grouping of stars called the Big Bear (Ursa Major) that is a constellation. |
| | A well-known grouping of stars like the Big Dipper that is not officially recognized as a constellation is called an asterism. |
| | Celestial Coordinate System |
| | It is useful to impose on the celestial sphere a coordinate system that is analogous to the latitude-longitude system employed for the surface of the Earth. |
| | The zero point for celestial longitude (that is, for right ascension) is the Vernal Equinox, which is that intersection of the ecliptic and the celestial equator near where the Sun is located in the Northern Hemisphere Spring. The other intersection of the Celestial Equator and the Ecliptic is termed the Autumnal Equinox. When the Sun is at one of the equinoxes the lengths of day and night are equivalent (equinox derives from a root meaning "equal night"). The time of the Vernal Equinox is typically about March 21 and of the Autumnal Equinox about September 22. |
| | The point on the ecliptic where the Sun is most north of the celestial equator is termed the Summer Solstice and the point where it is most south of the celestial equator is termed the Winter Solstice. In the Northern Hemisphere the hours of daylight are longest when the Sun is near the Summer Solstice (around June 22) and shortest when the Sun is near the Winter Solstice (around December 22). The opposite is true in the Southern Hemisphere. The term solstice derives from a root that means to "stand still"; at the solstices the Sun reaches its most northern or most southern position in the sky and begins to move back toward the celestial equator. Thus, it "stands still" with respect to its apparent North-South drift on the celestial sphere at that time. |
| | Traditionally, Northern Hemisphere Spring and Fall begin at the times of the corresponding equinoxes, while Northern Hemisphere Winter and Summer begin at the corresponding solstices. In the Southern Hemisphere, the seasons are reversed (e.g., Southern Hemisphere Spring begins at the time of the Autumnal Equinox). |
| | Do not become confused because the perspectives in the celestial sphere diagram and the sky segment diagram containing Sirius are different. In the celestial sphere diagram one is imagining an outside view of the celestial sphere (from a vantage point beyond the most distant stars that we see with the naked eye). In the diagram showing the position of Sirius in the sky the view is instead the actual sky as viewed from the Earth (that is, from the center of the sphere in the first diagram). |
| | Thus, the directions get reversed: moving to the right from the vernal equinox in the first diagram will look like moving to the left as viewed from its center, which is the perspective of the second diagram (that is, the actual view of the sky from Earth). That direction, by convention, is chosen to be the positive direction for right ascension. |
| | Coordinates on the Celestial Sphere |
| | The right ascension (R.A.) and declination (dec) of an object on the celestial sphere specify its position uniquely, just as the latitude and longitude of an object on the Earth's surface define a unique location. Thus, for example, the star Sirius has celestial coordinates 6 hr 45 min R.A. and -16 degrees 43 minutes declination, as illustrated in the following figure. |
| | This tells us that when the vernal equinox is on our celestial meridian, it will be 6 hours and 45 minutes before Sirius crosses our celestial meridian, and also that Sirius is a little more than 16 degrees South of the Celestial Equator. |
| | Right Ascension and Declination |
| | This coordinate system is illustrated in the following figure (for which you should imagine the earth to be a point at the center of the sphere). |
| | In the celestial coordinate system the North and South Celestial Poles are determined by projecting the rotation axis of the Earth to intersect the celestial sphere, which in turn defines a Celestial Equator. The celestial equivalent of latitude is called declination and is measured in degrees North (positive numbers) or South (negative numbers) of the Celestial Equator. The celestial equivalent of longitude is called right ascension. Right ascension can be measured in degrees, but for historical reasons it is more common to measure it in time (hours, minutes, seconds): the sky turns 360 degrees in 24 hours and therefore it must turn 15 degrees every hour; thus, 1 hour of right ascension is equivalent to 15 degrees of (apparent) sky rotation. |
| | The stars on the celestial sphere are named in several different ways. As a result, the brighter stars may have more than one name. We give a brief overview of naming stars here. |
| | There are various specialized star catalogs in which stars may be given names according to some convention. Such specialized catalogs are of importance in astronomical research, but we won't discuss them further in our introductory course. |
| | The Flamsteed Naming System |
| | The Bayer system is a little more systematic than a set of common names, but there are only a finite number of letters in the Greek alphabet, so it cannot be used easily to name very many stars. The Flamsteed naming system can in principle be used to name any number of stars. In this system one uses the same Latin possessive of the constellation name as in the Bayer system, but the stars are distinguished, not by their brightness, but by their nearness to the western edge of the constellation by assigning an arabic numeral. Thus, the closest star to the western edge of the constellation Cygnus is called 1-Cygni in the Flamsteed system and 61-Cygni denotes the star that is the 61st closest to the western edge. |
| | Common names are fine for a few bright stars, but we need a more systematic method to name all the stars that we see. One more systematic method is the Bayer system, which names the brighter stars by assigning a constellation (using the Latin possessive of the name) and a greek letter (Alpha, Beta, Gamma, Delta, Epsilon, . . .) in an approximate order of decreasing brightness for stars in the constellation. The adjacent figure illustrates for Orion. Betelgeuse is also called Alpha-Orionis and Rigel is called Beta Orionis in the Bayer system. |
| | The ordering of stars by brightness in the classical Bayer system is only approximate. For example, Rigel (Beta Orionis) is actually slightly brighter than Betelgeuse (Alpha Orionis), and Kappa Orionis is considerably brighter than the position of Kappa in the Greek alphabet would suggest. |
| | As a final example, the brightest star in the nighttime sky is Sirius, which is in the constellation Canis Major and is termed Alpha Canis Majoris in the Bayer naming system. Here is a list of 70 of the brighter stars, including common names, Bayer names, positions on the celestial sphere, and spectral class. |
| | Most of the brighter stars in the sky have common names that are of historical and mythological significance. For example, the bright red star in the shoulder region of the constellation Orion (the Hunter) is called Betelgeuse, which comes from Arabic and means (roughly) "the armpit of the mighty one" (see adjacent figure). The brightest star in Orion is a blue-white star called Rigel that is situated at the opposite corner of the constellation from Betelgeuse (adjacent figure). |
| | As another example, the brightest star in the constellation Cygnus (the Swan) is situated near the aft portion of the beast and is called Deneb, which is also Arabic in origin and means "the tail of the hen". |
| | One consequence of the Moon's orbit about the Earth is that the Moon can shadow the Sun's light as viewed from the Earth, or the Moon can pass through the shadow cast by the Earth. The former is called a solar eclipse and the later is called a lunar eclipse. The small tilt of the Moon's orbit with respect to the plane of the ecliptic and the small eccentricity of the lunar orbit make such eclipses much less common than they would be otherwise, but partial or total eclipses are actually rather frequent. |
| | Geometry of Solar Eclipses |
| | he geometry associated with solar eclipses is illustrated in the following figure (which, like most figures in this and the next section, is illustrative and not to scale). |
| | The shadow cast by the Moon can be divided by geometry into the completely shadowed umbra and the partially shadowed penumbra. |
| | For example there will be 18 solar eclipses from 1996-2020 for which the eclipse will be total on some part of the Earth's surface. The common perception that eclipses are infrequent is because the observation of a total eclipse from a given point on the surface of the Earth is not a common occurrence. For example, it will be two decades before the next total solar eclipse visible in North America occurs. |
| | A total solar eclipse requires the umbra of the Moon's shadow to touch the surface of the Earth. Because of the relative sizes of the Moon and Sun and their relative distances from Earth, the path of totality is usually very narrow (hundreds of kilometers across). The following figure illustrates the path of totality produced by the umbra of the Moon's shadow. (We do not show the penumbra, which will produce a partial eclipse in a much larger region on either side of the path of totality; we also illustrate in this figure the umbra of the Earth's shadow, which will be responsible for total lunar eclipses to be discussed in the next section). |
| | As noted above, the images that we show in discussing eclipses are illustrative but not drawn to scale. The true relative sizes of the Sun and Earth and Moon, and their distances, are very different than in the above figure. |
| | he preceding figure allows three general classes of solar eclipses (as observed from any particular point on the Earth) to be defined: |
| | As illustrated in the figure, in a total eclipse the surface of the Sun is completely blocked by the Moon, in a partial eclipse it is only partially blocked, and in an annular eclipse the eclipse is partial, but such that the apparent diameter of the Moon can be seen completely against the (larger) apparent diameter of the Sun. |
| | A given solar eclipse may be all three of the above for different observers. For example, in the path of totality (the track of the umbra on the Earth's surface) the eclipse will be total, in a band on either side of the path of totality the shadow cast by the penumbra leads to a partial eclipse, and in some eclipses the path of totality extends into a path associated with an annular eclipse because for that part of the path the umbra does not reach the Earth's surface. |
| | Total Solar Eclipses occur when the umbra of the Moon's shadow touches a region on the surface of the Earth. |
| | Partial Solar Eclipses occur when the penumbra of the Moon's shadow passes over a region on the Earth's surface. |
| | Annular Solar Eclipses occur when a region on the Earth's surface is in line with the umbra, but the distances are such that the tip of the umbra does not reach the Earth's surface. |
| | Animations of Solar Eclipses |
| | Here are three animations that illustrate observations in a solar eclipse. The first demonstrates generally the case of a total solar eclipse; the next two are simulated views of two recent solar eclipses from unusual vantage points, one from the Moon and one from the Sun. |
| | Appearance of a Total Solar Eclipse |
| | If you are in the path of totality the eclipse begins with a partial phase in which the Moon gradually covers more and more of the Sun. This typically lasts for about an hour until the Moon completely covers the Sun and the total eclipse begins. The duration of totality can be as short as a few seconds, or as long as about 8 minutes, depending on the details. |
| | As totality approaches the sky becomes dark and a twilight that can only be described as eerie begins to descend. Just before totality waves of shadow rushing rapidly from horizon to horizon may be visible. In the final instants before totality light shining through valleys in the Moon's surface gives the impression of beads on the periphery of the Moon (a phenomenon called Bailey's Beads). The last flash of light from the surface of the Sun as it disappears from view behind the Moon gives the appearance of a diamond ring and is called, appropriately, the diamond ring effect (image at right). |
| | As totality begins , the solar corona (extended outer atmosphere of the Sun) blazes into view. The corona is a million times fainter than the surface of the Sun; thus only when the eclipse is total can it be seen; if even a tiny fraction of the solar surface is still visible it drowns out the light of the corona. At this point the sky is sufficiently dark that planets and brighter stars are visible, and if the Sun is active one can typically see solar prominences and flares around the limb of the Moon, even without a telescope (see image at left). |
| | The period of totality ends when the motion of the Moon begins to uncover the surface of the Sun, and the eclipse proceeds through partial phases for approximately an hour until the Sun is once again completely uncovered. |
| | A partial solar eclipse is interesting; a total solar eclipse is awe-inspiring in the literal meaning of the phrase. If you have an opportunity to observe a total solar eclipse, don't miss it! It is an experience that you will never forget. |
| | Because solar eclipses are the result of periodic motion of the Moon about the Earth, there are regularities in the timing of eclipses that give cycles of related eclipses. These cycles were known and used to predict eclipses long before there was a detailed scientific understanding of what causes eclipses. For example, the ancient Babylonians understood one such set of cycles called the Saros, and were able to predict eclipses based on this knowledge. Here is a link to a discussion of such cycles and regularities in eclipse patterns. |
| | Locating stars and constellations on the celestial sphere is facilitated by a star map. The following map is an example of a star map of the northern hemisphere sky for a winter evening (click on the map for a larger version with labeling for the constellations). |
| | This star map was produced by the Star Maps on demand service of Mount Wilson Observatory. Here is an online map that shows the position on the celestial sphere of the Sun, Moon, and planets for arbitrary time, date, latitude, and longitude of the observer. (The map is a circle, which you should imagine holding over your head with directions properly aligned to simulate the celestial sphere.) |
| | To use star maps effectively, you need to know your latitude and longitude on the surface of the Earth, and the offset of your timezone from the Greenwich meridian. Here is a link to the Census Gazeteer, which will return latitude & longitude of locations in U.S. specified by either name or zip code (and also links to online U.S. maps). |
| | The tides at a given place in the Earth's oceans occur about an hour later each day. Since the Moon passes overhead about an hour later each day, it was long suspected that the Moon was associated with tides. Newton's Law of Gravitation provided a quantitative understanding of that association. |
| | We may illustrate the basic idea with a simple model of a planet completely covered by an ocean of uniform depth, with negligible friction between the ocean and the underlying planet, as illustrated in the adjacent figure. The gravitational attraction of the Moon produces two tidal bulges on opposite sides of the Earth. |
| | Without getting too much into the technical details, there are two bulges because of the differential gravitational forces. The liquid at point A is closer to the Moon and experiences a larger gravitational force than the Earth at point B or the ocean at point C. Because it experiences a larger attraction, it is pulled away from the Earth, toward the Moon, thus producing the bulge on the right side. Loosely, we may think of the bulge on the left side as arising because the Earth is pulled away from the water on that side because the gravitational force exerted by the Moon at point B is larger than that exerted at point C. Then, as our idealized Earth rotates under these bulges, a given point on the surface will experience two high and two low tides for each rotation of the planet. |
| | Consider a water molecule in the ocean. It is attracted gravitationally by the Earth, but it also experiences a much smaller gravitational attraction from the Moon (much smaller because the Moon is much further away and much less massive than the Earth). But this gravitational attraction of the Moon is not limited to the water molecules; in fact, the Moon exerts a gravitational force on every object on and in the Earth. Tides occur because the Earth is a body of finite extent and these forces are not uniform: some parts of the Earth are closer to the Moon than other parts, and since the gravitational force drops off as the inverse square distance, those parts experience a larger gravitational tug from the Moon than parts that are further away. |
| | In this situation, which is illustrated schematically in the adjacent figure, we say that differential forces act on the body (the Earth in this example). The effect of differential forces on a body is to distort the body. The body of the Earth is rather rigid, so such distortion effects are small (but finite). However, the fluid in the Earth's oceans is much more easily deformed and this leads to significant tidal effects. |
| | Spring Tides and Neap Tides |
| | Another complication of a realistic model is that not only the Moon, but other objects in the Solar System, influence the Earth's tides. For most their tidal forces are negligible on Earth, but the differential gravitational force of the Sun does influence our tides to some degree (the effect of the Sun on Earth tides is less than half that of the Moon). |
| | or example, particularly large tides are experienced in the Earth's oceans when the Sun and the Moon are lined up with the Earth at new and full phases of the Moon. These are called spring tides (the name is not associated with the season of Spring). The amount of enhancement in Earth's tides is about the same whether the Sun and Moon are lined up on opposite sides of the Earth (full Lunar phase) or on the same side (new Lunar phase). Conversely, when the Moon is at first quarter or last quarter phase (meaning that it is located at right angles to the Earth-Sun line), the Sun and Moon interfere with each other in producing tidal bulges and tides are generally weaker; these are called neap tides. The figure shown above illustrates spring and neap tides. |
| | Tidal Coupling and Gravitational Locking |
| | We have introduced tides in terms of the effect of the Moon on the Earth's oceans, but the effect is much more general, and has a number of important consequences that we will discuss further below. For example, as a consequence of tidal interactions with the Moon, the Earth is slowly decreasing its rotational period and eventually the Earth and Moon will have exactly the same rotational period, and these will also exactly equal the orbital period. Thus, billions of years from now the Earth will always keep the same face turned toward the Moon, just as the Moon already always keeps the same face turned toward the Earth. |
| | More Realistic Tidal Models |
| | he realistic situation is considerably more complicated: |
| | The Earth and Moon are not static, as depicted in the preceding diagram, but instead are in orbit around the common center of mass for the system. |
| | The Earth is not covered with oceans, the oceans have varying depths, and there is substantial friction between the oceans and the Earth. |
| | Timekeeping and the Celestial Sphere |
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