Solar and Lunar Observations

Observations of the Sun are needed for seasonal calenders and for solar time, and they can be used for navigation as well. The overwhelming importance of the Sun to life on Earth and the powerful symbolism inherent in its daily and annual rebirths have made it the most favored object of ancient astronomical study. The Sun is also the most easily studied, because being the brightest of all the objects in the sky, it casts strong shadows behind opaque objects. The shadows are not very sharp because of the Sun's finite angular size, but they are sharp enough to enable an hour angle to be read off a sundial. In its most basic form, a sundial is a stick (the gnomon or stylus), the direction of the shadow of which provides the time of day and the shortest length of the shadow—when the Sun is on the celestial meridian—indicates, with some ambiguity because it is a double-valued function except at the solstices, the time of year. These are relatively simple observations that could have been, and were, made in antiquity. An Egyptian "shadow clock" from the reign of Thutmose III (1490-1436 b.c.), for instance, measured the passage of the Sun for a 12hour period (Parker 1974).

An even more obvious indication of season than the length of the Sun's shadow is the Sun's rising point on the horizon. On clear days when the Sun's rising can be observed, the rising location of the Sun on the horizon can be perceived to change day by day near the equinoxes, and

Spring equinox

Fall equinox ff/ ,v / g horizon horizon

Figure 3.13. The day-to-day azimuth changes in the rising (and setting) Sun reach maximum near the equinoxes and minimum near the solstices. Drawing by E.F. Milone.

Figure 3.12. Proper Motion simulation: The sky as it would have appeared from a specific latitude in the years 4000 b.c. (top) and 2000 a.d. (bottom). The cumulative proper motions of all the visible stars in this region of sky are illustrated over this interval. Note the large motions of Sirius, Procyon, and Pollux. The photographs were taken from the monitor of the Digistar planetarium projector of the Calgary Science Centre by E.F. Milone, with the cooperation of the CSC and Sid Lee.

Figure 3.12. Proper Motion simulation: The sky as it would have appeared from a specific latitude in the years 4000 b.c. (top) and 2000 a.d. (bottom). The cumulative proper motions of all the visible stars in this region of sky are illustrated over this interval. Note the large motions of Sirius, Procyon, and Pollux. The photographs were taken from the monitor of the Digistar planetarium projector of the Calgary Science Centre by E.F. Milone, with the cooperation of the CSC and Sid Lee.

to vary very little near the solstices, as Figure 3.13 illustrates.

Twice a year, at its approach toward and at its recession from one of the solstices, the Sun would appear to rise at the same horizon location. The azimuth of rise is given by the expression, easily derivable from the astronomical triangle with h = 0°:

sin S

cos f

For example, for 8 = 23.5°, the declination of the Sun at summer solstice for the Northern Hemisphere f = 51°, cos A = 0.63362. Therefore, A = 50.68°. For 8 = -23.5°, at the same latitude, A = 129.32°.

At any given place, the azimuth of rise or set depends on the declination of the object. Therefore, objects such as the Sun, Moon, and planets over sufficiently long periods of time, which alternate between positive and negative values of the same maximum declination, undergo standstills (for the Sun: solstice) on the horizon as the declination reaches an extreme. The result is an oscillation of azimuth over the period of the declination variation. The amplitude, as Lockyer (1894) referred to the maximum difference of azimuth from the east point of the horizon (where 8 = 0 and A = 90°), is half the total range of any object's azimuthal variation. The amplitude has been the key to understanding the astronomy of ancient Europe. In the above example, the amplitude is 39.32°. It should be noted that the value of the solar declination given in this example is not what it would have been in Megalithic times, because of the variation of the obliquity, the angle between the ecliptic and the celestial equator (see §4.4). The value at ~2500 b.c. was ~24°. Figure 3.14 illustrates the solar amplitude for sites at latitudes 0° and 51°, respectively.

Among the oldest known examples of structures bearing solar alignments are passage graves in Ireland and Brittany. A well-known example is that of a tomb at Brugh-na-Boinne or Newgrange in Ireland. The box-like shaft has the azimuth of winter solstice sunrise (see Figure 3.15). This monument and the complex of which it is part are discussed at length in §6.2.6.

Alexander Thom found large numbers of possible solar and lunar site-lines in the British Isles and in France. Such site-lines used distant foresights, such as hills with notches, and relatively close backsights involving large stones (megaliths). Two well-known sites are the possible solar site Ballochroy near Jura and the possible lunar site Temple Wood, near Argyllshire, both in western Scotland. These sites and their possible uses as observatories are discussed in detail in

Figure 3.14. The amplitude of the azimuth variation of sunrise over the year. The amplitude or swing from one solstice to the other grows larger with latitude. Drawing by E.F. Milone.
Figure 3.15. The shaft of the passage grave at Newgrange, seen from inside the tomb. This is one of the earliest known indicators of interest in astronomical alignments. See also Figures 6.6 to 6.8. Photo by E.F. Milone.

§6.2. The basic idea is that the declination and the latitude of the observer determine the azimuth of rise/set (modified by refraction and dip considerations). In the analysis of megalithic monuments, Thom (1971) argued that he was able to detect the effects of three contributions to the variation of the declination of the Moon:

(1) The variation of the declination due to the motion of the Moon in its orbit with mean orbital period 27d32; at present, ±28°5.

(2) A modulation of the monthly variation due to the regression of the nodes of the Moon's orbit. The Moon's inclination, i = 5°8'43". Consequently, the celestial (ecliptic) latitude of the Moon varies between ±i over a sidereal month. However, as the Moon's orbit regresses, the celestial longitudes at which the extremes of celestial latitude occur also slip westward. This change is reflected in changes in the declination of the Moon over the nodal regression period of 18y61. The lunar declination in the course of a month thus varies from +e + i to -e - i at major standstill and +e - i to -e + i at minor standstill.

(3) A variation in the inclination, which again contributes not quite fully to the declination variation in that it acts to change the celestial latitude. The period of Di (Thom called the corresponding change in declination, D) is 173d3 over a range ±9'. See §6.2.15 for Thom's suggested method by which such measurements could have been carried out in megalithic times.

Examples of solar alignments of monuments are the Temple of Amon-Re at Karnak in Egypt; the columns at Persepolis; Ha'amonga-a-Maui on the Pacific island of Tonga; and at various temples, dating over a wide range, in the Mediterranean area. Alignments of buildings, and perhaps of whole cities, is a likely explanation for many orientations found in pre-Columbian America. One of the principal axes of the largest city of the ancient new world, Teotihuacan, was apparently aligned on the direction of the setting of the Pleiades, a notion reinforced by the presence of two well-separated pecked crosses, aligned in the same direction. There are many instances of astronomically aligned buildings in Mayan and other Mesoamerican cultures.

At sunwatcher stations, the North American Anasazi observed the turning of the Sun at the solstices, and some medicine wheels may have been constructed by other Native Americans to mark the azimuthal travel of the Sun and the rising points of certain stars. In the Incan capital city of Cuzco, there are a large number of ceques or lines of direction, radiating from a central location, the temple of the Sun, Coricancha. Some of the ceques may have marked the position of the horizon Sun during the year. Taken as a whole, all this evidence, although circumstantial and incomplete in many cases, demonstrates that the rise and set of astronomical objects was of profound interest to ancient humanity. Returning to our first example, the gnomon, we can easily show that with it, the directions of rise and set of the Sun during the year can be readily noted; however, the length of the noon shadow alone gives important information about the time of year also (see Figure 3.16). When the directions

Figure 3.16. The use of the gnomon in solar measurements. The length of the noon shadow alone gives important information about the time of year. Drawing by E.F. Milone.

of rise and set are in the same line, the dates of the equinoxes and the east-west cardinal directions are simultaneously determined. This demonstrates that the skill involved in the alignment of the pyramids, although praiseworthy, did not require superhuman effort, merely the careful systematic observations of calendrical astronomers (see Neugebauer 1980, 1983).

The measurement of hour angles was probably not so widely carried out, but it was done. The Egyptian star clocks that relied on roughly equally spaced stellar asterisms called decans are examples of very early usage of the concept of hour angles. Sundials are another example, as we have already noted. The hour angle of rise may be found from (2.2) and (2.3):

The hour angle of set is equal to the hour angle of rise except for the sign, which is always negative for a rising object.

For example, what are the hour angle and the azimuth of rise of the Sun on the day of the winter solstice at latitude +53°? On this date, 5 = -23°5. Therefore, by (3.33), cos H = -tan(+53°) x tan(-23°5) = -1.32704 x (-0.43481) = +0.57702 from which, H = ±54°759 = ±3^6506. An object on the celestial equator must rise at the east point with an hour angle H = -6h; here, H = -03h 39m. Consequently, rearranging (3.32) and substituting, we have sin A = - sin H x cos 5 = -0.81673 x 0.91706 = 0.74899, so that A = 48°503 or (180° - 48°503). Because the azimuth of the east point (where the celestial equator intercepts the horizon) is 90°, A > 90°. Therefore, A = 131°497. The construction and use of sundials was carried out for obvious practical purposes. Neugebauer (1948) has argued that the study of the theory of the sundial may well have led to the discovery of the conic section and, thus, serendipitously, to the scientific revolution that continues today. Not everyone agrees with this interpretation, however.

Solar observations have been used for navigation. For naked eye navigation, the Sun is almost the only visible astronomical object when it is above the horizon. The Moon's more complicated motion must have made it less desirable for such a purpose, but if tides or illumination were concerns, the behavior of the Moon may have been studied sufficiently to make it of use (see §6.2). The declination of the Sun and the observer's latitude together determine the Sun's azimuth of rise and its altitude at culmination, when it crosses the celestial meridian at apparent noon. Therefore, given the time of year, and the circumstance of sunrise, sunset, or local noon, the latitude can be determined by the altitude of the Sun. This is demonstrated for the instant of apparent solar noon in Figure 3.17 and can be summarized in the relation among the true altitude of the Sun, h, its declination, 5, and the latitude, f:

The true altitude is determined from the observed altitude and corrected for refraction; unless the Sun is very low, however, the error due to neglect of this quantity will not be great. A very low winter Sun is a characteristic of high-latitude sites (December solstice in the Northern Hemisphere and June solstice in the Southern), but in the Southern Mediterranean region, at latitudes of <20°, the error in the altitude of the noon Sun due to refraction does not much exceed about 1 arc-min.

The astronomical determination of relative longitude requires a measure of the time at some other place than the site from which the observations are being made, however. Aside from dead reckoning, where the rate of travel and the time interval are multiplied, east-west distances could not be determined across large sea distances before the invention of the chronometer. These comments hold also for stellar navigation, discussed below and in §11.3.

The determination of bearing was another matter, and any rising or setting astronomical objects could be used, if the azimuth of rise were known for particular sites. The determination of bearing in the ancient world sometimes required ingenious methods. Viking sagas mention a solarstein, literally "sun stone," alleged to have been used for navigation. Viking navigators may have used naturally occuring crystals of Icelandic spar to detect polarized, scattered sunlight to determine the direction of the Sun even under cloudy skies.17

17 Atmospheric scattering produces a maximum polarization 90° from the Sun;Icelandic spar polarizes light and therefore acts as an analyzer. The direction normal to the Sun can be found by rotating the crystal while peering through it and repeating the process in many directions. A dark minimum will be seen in the direction of strongest atmospheric polarization. The reader can carry out the experiment with polarized sunglasses.

Solar altitudes

Solar altitudes

Figure 3.17. The measurement of the altitude of the noon Sun reveals the observer's latitude: (a) Horizon view at the four quarters of the year. (b) The general view on the celestial sphere of solar meridian crossing. Drawings by E.F. Milone.

Under certain circumstances and in certain individuals, the dichroic property of the retina may be developed to detect polarized sunlight from the sky. The cross-like image is called Haidinger's brush (or bundle). See Minnaert (1954, pp. 254-257) or Schlosser et al. (1991/1994, pp. 104-105).

Among Islamic astronomers, observing the first visibility of the lunar crescent was an important task. In the Islamic calendar, a new day begins at sundown, and the onset of a new month occurs at the first sighting of the crescent. In particular, the end of the month Ramadan marks the end of the fasting period. In clear skies, the crescent can usually be spotted a day after conjunction, but on occasion, it can be seen less than one day afterward. In the event of cloudy skies, the month can be assumed to be 30 days long. An important classic source for understanding the visibility of the crescent was The Handbook of Astronomy by al-Battani [850-920], who cited "ancient opinion" as well as methods for determining visibility. The geometry is straightforward, but the brightness of the background twilight sky, as well as the arc of vision, is involved. See Bruin (1977) for an exposition of the problem and useful translations of important sources.

0 0

Post a comment