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- La trepidació (del llatí trepidus, 'trepidat'), en les obsoletes teories medievals de l'astronomia, fa referència a l'oscil·lació hipotètica en la precessió dels equinoccis. La teoria va ser popular entre el segle ix i el segle xvi. (ca)
- اهتزاز المبادرة المحورية هي إحدى نظريات علم الفلك التي عفا عليها الزمن الآن، يشير إلى التذبذب الافتراضي في المبادرة المحورية. كانت النظرية شائعة من القرن التاسع في فترة العصر الذهبي للإسلام إلى القرن السادس عشر في فترة عصر النهضة الأوروبي. (ar)
- Die Trepidation ist ein historischer Begriff aus der Astronomie, der eine Schwankung in der Präzession der Äquinoktien beschreibt. Es handelt sich dabei um eine Art Zittern der Erdachse, die Ungenauigkeiten in der Präzession verursacht, so dass das Fortschreiten des Frühlingspunktes auf der Ekliptik manchmal rascher und manchmal langsamer erfolgt. Die entsprechenden Werte sind zur Präzession hinzuzurechnen oder von ihr abzuziehen. Die Trepidation wurde im Mittelalter häufig beschrieben und diskutiert. Heute werden diese Berichte für irrtümlich gehalten; das Phänomen wird in der modernen Astronomie nicht beobachtet und ist nicht anerkannt. (de)
- Trepidation (from Lat. trepidus, "trepidatious"), in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries. The origin of the theory of trepidation comes from the Small Commentary to the Handy Tables written by Theon of Alexandria in the 4th century CE. In precession, the equinoxes appear to move slowly through the ecliptic, completing a revolution in approximately 25,800 years (according to modern astronomers). Theon states that certain (unnamed) ancient astrologers believed that the precession, rather than being a steady unending motion, instead reverses direction every 640 years. The equinoxes, in this theory, move through the ecliptic at the rate of 1 degree in 80 years over a span of 8 degrees, after which they suddenly reverse direction and travel back over the same 8 degrees. Theon describes but did not endorse this theory. A more sophisticated version of this theory was adopted in the 9th century to explain a variation which Islamic astronomers incorrectly believed was affecting the rate of precession. This version of trepidation is described in De motu octavae sphaerae (On the Motion of the Eighth Sphere), a Latin translation of a lost Arabic original. The book is attributed to the Arab astronomer Thābit ibn Qurra, but this model has also been attributed to Ibn al-Adami and to Thabit's grandson, Ibrahim ibn Sinan. In this trepidation model, the oscillation is added to the equinoxes as they precess. The oscillation occurred over a period of 7000 years, added to the eighth (or ninth) sphere of the Ptolemaic system. "Thabit's" trepidation model was used in the Alfonsine Tables, which assigned a period of 49,000 years to precession. This version of trepidation dominated Latin astronomy in the later Middle Ages. Islamic astronomers described other models of trepidation. In the West, an alternative to De motu octavae sphaerae was part of the theory of the motion of the Earth published by Nicolaus Copernicus in De revolutionibus orbium coelestium (1543). Copernicus' version of trepidation combined the oscillation of the equinoxes (now known to be a spurious motion) with a change in the obliquity of the ecliptic (axial tilt), acknowledged today as an authentic motion of the Earth's axis. Trepidation was a feature of Hindu astronomy and was used to compute ayanamsha for converting sidereal to tropical longitudes. The third chapter of the Suryasiddhanta, verses 9-10, provides the method for computing it, which E. Burgess interprets as 27 degree trepidation in either direction over a full period of 7200 years, at an annual rate of 54 seconds. This is nearly the same as the Arab period of about 7000 years. The zero date according to the Suryasiddhanta was 499 AD, after which trepidation is forward in the same direction as modern equinoctial precession. For the period before 1301 BCE, Suryasiddhantic trepidation would be opposite in sign to equinoctial precession. For the period 1301 BCE to 2299 AD, equinoctial precession and Suryasiddhantic precession would have the same direction and sign, only differing in magnitude. Brahma Siddhanta, Soma Siddhanta and Narada Purana describe exactly the same theory and magnitude of trepidation as in Suryasiddhanta, and some other Puranas also provide concise references to precession, esp Vayu purana and Matsya Purana. (en)
- Secondo una teoria astronomica medievale, ora obsoleta, la trepidazione è l'oscillazione che si presenta nel moto di precessione degli equinozi. La teoria era diffusa nel periodo tra il IX e il XVI secolo. L'origine della teoria della trepidazione viene dal Piccolo commentario alle Tavole facili di Tolomeo, scritto da Teone di Alessandria nel IV secolo. Nella precessione, gli equinozi appaiono muoversi lentamente attraverso l'eclittica, completando una rivoluzione in un tempo di circa 25 800 anni (secondo gli astronomi moderni). Teone afferma che alcuni antichi astrologi (di cui non fa i nomi) credevano che la precessione, invece di essere un moto stabile ed eterno, invertisse la sua direzione ogni 640 anni. Gli equinozi, in questa teoria, si muovono lungo l'eclittica al ritmo di 1 grado ogni 80 anni in un intervallo di 8 gradi, compiuto il quale invertono improvvisamente la direzione e ritornano indietro dello stesso intervallo di 8 gradi. Teone si limita a descrivere la teoria ma senza approvarla. Una versione più sofisticata di questa teoria fu adottata nel IX secolo per spiegare una variazione che erroneamente gli astronomi islamici credevano stesse alterando il moto di precessione. Questa versione della trepidazione è descritta nel De motu octavae sphaerae (Il Moto dell'Ottava Sfera), una traduzione latina di un originario testo arabo andato perduto. Il testo è attribuito all'astronomo arabo Thābit ibn Qurra ma lo stesso modello è attribuito anche a e al nipote di Thābit, Ibrāhīm ibn Sinan. In questo modello di trepidazione, l'oscillazione è aggiunta agli equinozi mentre questi precedono. L'oscillazione si verificava in un periodo di 7000 anni, aggiunto all'ottava (o alla nona) sfera del sistema tolemaico. Il modello di trepidazione di Thābit è stato usato nelle Tavole alfonsine che stabilivano un periodo di 49.000 anni per la precessione. Questa versione della trepidazione ha dominato l'astronomia europea nel tardo Medioevo. Gli astronomi islamici descrissero altri modelli di trepidazione. In Occidente, un'alternativa al De motu octavae sphaerae fece parte della teoria del moto terrestre pubblicato da Niccolò Copernico nel De revolutionibus orbium coelestium (1543). La versione di Copernico della trepidazione combinava l'oscillazione degli equinozi (ora considerata un falso moto) con un cambio nell'obliquità dell'eclittica (inclinazione assiale) riconosciuto oggi come un reale moto dell'asse terrestre. (it)
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- La trepidació (del llatí trepidus, 'trepidat'), en les obsoletes teories medievals de l'astronomia, fa referència a l'oscil·lació hipotètica en la precessió dels equinoccis. La teoria va ser popular entre el segle ix i el segle xvi. (ca)
- اهتزاز المبادرة المحورية هي إحدى نظريات علم الفلك التي عفا عليها الزمن الآن، يشير إلى التذبذب الافتراضي في المبادرة المحورية. كانت النظرية شائعة من القرن التاسع في فترة العصر الذهبي للإسلام إلى القرن السادس عشر في فترة عصر النهضة الأوروبي. (ar)
- Die Trepidation ist ein historischer Begriff aus der Astronomie, der eine Schwankung in der Präzession der Äquinoktien beschreibt. Es handelt sich dabei um eine Art Zittern der Erdachse, die Ungenauigkeiten in der Präzession verursacht, so dass das Fortschreiten des Frühlingspunktes auf der Ekliptik manchmal rascher und manchmal langsamer erfolgt. Die entsprechenden Werte sind zur Präzession hinzuzurechnen oder von ihr abzuziehen. (de)
- Trepidation (from Lat. trepidus, "trepidatious"), in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries. (en)
- Secondo una teoria astronomica medievale, ora obsoleta, la trepidazione è l'oscillazione che si presenta nel moto di precessione degli equinozi. La teoria era diffusa nel periodo tra il IX e il XVI secolo. (it)
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