A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia

Abstract

Among many medieval sacral edifices there are numerous churches built in old cult sites. In such cases where the medieval churches were preceded by the early Christian churches it is interesting to observe the differences or similarities in their orientation. In order to approach this systematically, it is necessary to start with the analyses of the longitudinal axes of certain Christian basilicas. For this occasion, we have chosen two churches, one in the valley of the river Gradac near Valjevo (6th century) and the other just under the peak, of Kopaonik, in Nebeske Stolice (5th/6th century) on the Kopaonik. Thus, the subject of this paper is the exact analysis of the orientation of the cited edifices. The church located in the valley of the river Gradac has been pretty accurately oriented in the west-eastern direction, with the altar naturally facing the east. Since it is positioned atop a rocky cliff, with the eastern and western part of the horizon completely hidden, it is clear that the builder was unable to follow the sunrise or the sunset, during the laying of the foundation, the builder couldn't be guided by the sunrise or the sunset, but he had to be familiar with the exact methods of orientation. The longitudinal axis of the basilica in Nebeske Stolice, on Kopaonik, is positioned fairly accurately and faces sunset during the summer solstice. As the basilica is positioned on a plateau with an altitude of nearly 1793m, the eastern part of the horizon is completely exposed. This allowed the builder to lay the foundation of the church visually during the dawn of the summer solstice Other than this possibility, the builder had another, in case he didn't want or couldn't wait for that exact day, and that would be the possibility of determining the direction via the geometric method, using analemma.

Među mnogim sakralnim srednjovekovnim građevinama brojne su one koje su podignute na starim kultnim mestima. U slučajevima kada srednjovekovnim crkvama prethode ranohrišćanske, zanimljivo je pratiti razlike ili podudarnosti u njihovim orijentacijama. Da bi se takvim analizama pristupilo sistematično, neophodno je poći od analize orijentacija uzdužnih osa pojedinih ranohrišćanskih bazilika. Za ovu priliku izabrali smo dve, jednu u dolini reke Gradac kod Valjeva (6. vek) i drugu pod samim vrhom Kopaonika, na Nebeskim stolicama (5/6 vek). Predmet ovog rada je, dakle, egzaktna analiza orijentacija navedenih objekata. Crkva u dolini reke Gradac je sa dosta tačnosti orijentisana u pravcu zapad-istok, sa oltarom na istoku, naravno. Pošto je smeštena na kamenom grebenu, sa potpuno zaklonjenim istočnim i zapadnim delom horizonta, graditelj se prilikom postavljanja temelja nije mogao upravljati prema izlasku ili zalasku sunca, već je morao poznavati egzaktne metode orijentacije. Uzdužna osa bazilike na Nebeskim stolicama, na Kopoaniku, usmerena je dosta tačno ka tački izlaska sunca letnjeg solsticijuma. Pošto se nalazi na zaravnjenoj platformi na blizu 1 793 m nadmorske visine ima potpuno otrkiven istočni deo horizonta, što graditelju otvara mogućnost vizuelnog utemeljenja crkve u zoru letnjeg solsticijuma. Pored ove mogućnosti, graditelj je imao i drugu, u slučaju da nije želeo ili mogao da sačeka baš taj dan, a to je mogućnost određivanja pravca geometrijskom metodom, pomoću analeme.