Vladimir Karlovský, Observatory and Planetarium Hlohovec, vladokarlovsky@hotmail.com

Translation: Patricia Lipovská,

A preliminary analysis of the Bučany rondel's astronomical orientation was made in the paper. With archeologically determined age of -3800 +/-150 years the author has found that 9 of the Rondel's 12 extreme directions have significant astronomical orientation. The analysis shows that it could have been used for observations of the Sun at summer and winter solstices, so called low Moon at winter and summer solstices, and so called high Moon at summer and winter solstices. The possibility of use of the low Moon descent at the summer solstices to time spring agricultural works and taking crops, and also a possible division of a year into three calendar periods has been shown.

The peasants' settlement in Bučany according to the acquired archeological material falls into the neolith (4,000 BC). This period in the region of Western Slovakia is characterized by findings of ceramics with engraved and painted ornamentation mostly of red and rarely also yellow and white colour, which is archeologically classified with the early stage of lengyel culture called after the locality of Lengyel, Hungary. Bujna J., Romsauer P. 1987. Details can be also found in papers of Bujna J., Rosmauer P. 1986 where dimensions of the ditches, palisades and interior objects of rondels can be also found.

The diameter of the interior palisade of the Rondel is 45.5m. It forms a regular circle with the deviation of 5.9 per cents. The ditches are also shaped in regular circles with the inner ditch deviation of 8.4 per cents and the outer one of 7.9 per cents from a regular circle. Both the palisade and ditches are broken in 4 points that represent the cardinal points and form entrances into the interior. A building that ressembles a megaron is situated in the interior. Figure 1 provides a better picture of dimensions and objects of the interior. As it is not possible to measure the Rondel accurately in the terrain the depicted directions and their respective azimuths were determinated with accuracy of 0.2 degree. The main directions that are present in the object were assigned according to its plan. See also : Bujna J.,Romsauer P.,1982.If the plan was oriented towards the magnetic north pole, which is very probable, it is necessary to make corrections of the directions considering the magnetic declination (while making the measurements in Bučany it was +26min (0.433deg.) See :Bucha V.,1975,p.26-49 Astronomical azimuths are considered, which are directions described in the section 3.2.

In oder to check for coincidences in the orientation of the Rondel in Bučany with ascends and descends of the Sun and Moon below the real horizon it is necessary to transform the equatorial coordinates into the horizontal ones. In this case the aim is to determine the astronomical azimuths of ascend and descend points of celestial bodies, which increases from due south counter clockwise (towards west). It differs from the azimuth used in army, which starts at due north. There is an equation for the astronomical azimuth A = Av - 180deg where A is the astronomical azimuth and Av is the azimuth.

cos A = - ( sin d - sin f sin h) / ( cos f cos h ) [ 1 ]

cos A _V = ( sin d - sin f sin h ) / ( cos f cos h ) [ 2 ]

where d is declination of he body, f latitude of the observation site, h is height of the visible horizon. See : Chalchunov V.Z.,1972 and Wood E.J.,1978 , Wood E.J.1981. If azimuth of ascent and descent points at the real horizon has to be determined the fact that location of the Sun and Moon, e.i. their equatorial coordinates are related to the Earth´s centre ( they are geocentric) has to be considered. This is why the transformed coordinates have to be corrected to make them topocentric. Height of the visible horizon has to be corrected to consider the refraction, horizontal equatorial parallax, curvature of the Earth and whether the touch of the disk with the horizon, or centre of the disk, or the point where the disk disappears below the horizon is the case as the Sun´s and the Moon´s angular dimensions are not equal to zero. If h₀ is astronomical height of the horizon then:

Refraction values can be found in refraction tables published for example in the following:Hawkins G.S.,1977and Berliner Astronomisches Jahrbuch 1959, Astronomičeskij Ježegodnik 1979. The best refraction table can be found in the Astronomičeskij kalendar ,postajannaja časť 1981 where the refraction values at 10^o C and atmospheric pressure of 1013hPa up to the zenith distance of 90deg, e.i. 0 deg height from 80 deg (10deg of height) in step of 10 angular minutes are given. Considering the influences of temperature and pressure the refraction values can be corrected as follows:

Equation [1] is used to compute the azimuth. In Rondel in Bučany, however, azimuths of extreme declinations of the Sun and Moon are the issue. With Sun the extreme declinations occur at summer and winter solstices and they are equal to the inclination of the ecliptic towards the celestial equator, with positive and negative signs respectively e.i. the declination at the summer solstice is + e and it is - e at the winter solstice. Using equation [1] obtained are two azimuths for summer solstice (at sunrise and sunset) and two azimuths for winter solstice (at sunrise and sunset). The inclination of the ecliptic changes with time, however, and its value is computed for the past as follows:

e = 23,452294 - 0,0130125 T_S - 1,63888.10^-6 (T_S)² + 5,02777.10^-7 (T_S)³ + De + de [ 8]

where inclination of the ecliptic is in degrees, T_S is time, which has passed since 1900.0 in tropical centuries given by 36524.22 days; De is long periodical part and de is short periodical part of ecliptic inclination nutation. See:Astronomičeskij ježegodnik 1979a

With the Moon the extreme values differ from those of the Sun because the path of the Moon is inclined to the ecliptic. i = 5^o 8' 43.4" (changes with period of 173 days from 4^o 59' to 5^o 19' ). Inclination of the path of the Moon to the ecliptic is 5,14539 +/- 0.167 degs. Extreme declination of the Moon values therefore are ( e + i ) and ( e - i ). The values vary from the maximum (high Moon) to the minimum (low Moon) with period of 9.305 years. It reaches the maximum every 18.61 years. With the Moon therefore extreme declination values at the summer solstice ( e + i ) and ( e - i ) and at the winter solstice -( e + i ) and -( e - i ) exist. In total 8 azimuths, 4 at the ascend and 4 at the descend of the Moon exist.

e = 24,095571

e = 24,095571

d = e - i = 18,950181 deg

Inaccuracy of astronomical orientation of the Rondel in Bučany is about the same as it is with the Stonehenge (main stones, thriliths and stones of the Sarsen's circle). It is necessary to mention that the Stonehenge is dated much later (Stonehenge I 2800-2400 B.C. Stonehenge III 2200-1800 B.C.)

As the computations showed the Rondel in Bučany could have been used as a solar and lunar observatory. 9 of total 12 possible extreme values of the ascends and descends of the Sun and Moon are present in the Rondel. The remaining 3 directions are: two for the low Moon, which is possible to observe using the 2 directions which are already present in the Rondel; a direction of the high Moon descend at the summer solstice is not possible to observe because a megaron - a building inside the Rondel disables this. The accuracy of orientation at winter and summer solsices is unique; less accurate is the orientation towards ascending and descending Moon. It is much more difficult to observe the Moon compare to the Sun and so the lower occuracy is acceptable. It is very probable that the Rondel in Bučany served to determine solstices, observations of the Sun and Moon during their times of ascends and descends.

Therefore, only directions that fall between + e and - e at the ascend and descend of a body are useful for calendar purposes. + e and - e are useful as they determine the time of summer and winter solstices; directions towards high Moon +( e + i ) and also -( e + i ) are not suitable beacuse the Sun never rises and sets in these directions. Directions towards low Moon +( e - i ) and -( e - i ) that besides the solstices can determine another date of the year are useful. These directions determine the following dates in the Rondel: descend of the low Moon at the summer solstice - the Sun sets in this direction on 8 May (7-12 May) and 1 August (30 July - 2 August); ascend of the low Moon at winter solstice - the Sun rises in this direction on 3 November and 6-7 February.

For shorter periods as those mentioned above the synodic month e.i. changing phases of the Moon could have been used. The synodic month lasts 29 days 12 hours 44 minutes 2.78 seconds (29.5305882 mean days). The synodic month varies due to the eliptical shape of the path of the Moon from 29.25 to 29.83 days. Combination of synodic month and solar year is very complex from calendar point of view and so discovery of a lunisolar calendar at time of utilisation of the Rondel in Bučany is not probable.

Orientation of the Rondel in north-south direction is already given by its orientation towards sunrise and sunset points at winter solsice. The angle formed by points of sunrise and sunset is divided into halves and the resulting direction is that of south. Therefore, a relatively precise north-south orientation is present in the Rondel in Bučany. If its orientation on stars is the concern, the northern and southern entrances were examined. A sky and the location of the pole in 3,800 B.C. was analysed. According to the Figure 2. and simulation of the sky using a planetarium projector ZKP-2 made by Carl Zeiss Jena GmbH under the dome with diameter of 10 m which is situated in the Observatory and Planetarium in Hlohovec, the only bright star that rises at the northern entrance at the azimuth of 203deg is Vega of constellation Lyra. The star's magnitude in visual range of spectrum is +0.03. It is the second brightest star in the northern sky.

In Rondel in Bučany it was possible to locate Vega 5-8 degrees above the horizon at the azimuth of 203 degrees. It did not depend on the real horizon which is almost 0 degrees as right above the horizon the star was not visible.

The Rondel in Bučany is oriented in 9 of 12 extreme astronomical directions. Accuracy of this orientation practically eliminates possibility of an accident. All the astronomical directions are fairly observable as far an observer with the height of 1.6 m and the height of palisade at the point of an important direction of 1.5 m is considered. If estimated heights of palisades 1.6 – 3.6 m (Weber Z.,1969) are considered then it was not possible to use the direction of setting sun at winter solstice and directions to the high Moon after finishing the building. However, while building the Rondel, at first all the directions to winter and summer solstices had to be erected. Otherwise it would not have been possible to point all the entrances towards the low Moon and to use the Rondel for calendar purposes as well. Because the directions to the low Moon are present, with a period of 18.61 in which the same position of objects occurs, the process of building the Rondel would have taken at least 19 to 38 years.

Allen C.W.,1977 Astrofizičeskije veličiny, Mir, Moskva 1977

Astronomičeskij kalendar,postajannaja časť 1981,s.590 Nauka, Moskva, 1981

Bujna J., Romsauer P.,1982. Záverečná výskumná sezóna v Bučanoch. In:Archeologické výskumy a nálezy na Slovensku v roku 1981 , Nitra 1982 s.59-64

Bujna J.,Romsauer P.1987.Osada neolitických roľníkov v Bučanoch. Krásy Slovenska , LXIV,6/87,10-12

Hawkins G.S.,White J.B.,1984 Razgadka tajny Stounhendža, Mir, Moskva 1984

Horský Z., 1986 Vorläufige Untersuchungen ůber vermutliche astronomische Orientierung einiger neolithische Kreisgrabenanlagen, Internationales Symposium uber die Lengyel-Kultur, Nové Vozokany 5-9.11.1984 , Nitra-Wien 1986, 83-87

Podborský V.,1983 Die Kreisgrabenanlage zu Těšetice und moglichen mährischen Parallelen, Mitteilungen der osterreichischen Arbeits Gemeinschaft fur Ur-und Fruhgeschichte XXXIII.,in press

Weber Z., 1985 Astronomická orientace rondelu Z Těšetic -Kyjovic, okr.Znojmo. Sborník prací Filozofické fakulty Brnenské univerzity. Studia Minora facultatis philosophicae Universitatis Brunensis E30, 1985, 23-39