[Q]: Extract the answer to the question from the following context. Question: Along with information about the mean tropical year, what provided information about the sun's mean longitude? Context: Ancient tables provided the sun's mean longitude. Christopher Clavius, the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the sun passed through the vernal equinox nor on the length of the mean tropical year. Tycho Brahe also noticed discrepancies. The Gregorian leap year rule (97 leap years in 400 years) was put forward by Petrus Pitatus of Verona in 1560. He noted that it is consistent with the tropical year of the Alfonsine tables and with the mean tropical year of Copernicus (De revolutionibus) and Reinhold (Prutenic tables). The three mean tropical years in Babylonian sexagesimals as the excess over 365 days (the way they would have been extracted from the tables of mean longitude) were 14,33,9,57 (Alphonsine), 14,33,11,12 (Copernicus) and 14,33,9,24 (Reinhold). All values are the same to two places (14:33) and this is also the mean length of the Gregorian year. Thus Pitatus' solution would have commended itself to the astronomers.
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[A]: time when the sun passed through the vernal equinox


[Q]: Extract the answer to the question from the following context. Question: What do you need to happen if you want the water in the water experiment to have a greater arc? Context: Mach argued that, in effect, the water experiment in an otherwise empty universe would remain flat. But if another object were introduced into this universe, perhaps a distant star, there would now be something relative to which the bucket could be seen as rotating. The water inside the bucket could possibly have a slight curve. To account for the curve that we observe, an increase in the number of objects in the universe also increases the curvature in the water. Mach argued that the momentum of an object, whether angular or linear, exists as a result of the sum of the effects of other objects in the universe (Mach's Principle).
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[A]: an increase in the number of objects in the universe


[Q]: Extract the answer to the question from the following context. Question: What was Western Thrace and Greek Macedonia considered in regards to the Ottoman empire? Context: Following the Fall of Constantinople on 29 May 1453, many Greeks sought better employment and education opportunities by leaving for the West, particularly Italy, Central Europe, Germany and Russia. Greeks are greatly credited for the European cultural revolution, later called, the Renaissance. In Greek-inhabited territory itself, Greeks came to play a leading role in the Ottoman Empire, due in part to the fact that the central hub of the empire, politically, culturally, and socially, was based on Western Thrace and Greek Macedonia, both in Northern Greece, and of course was centred on the mainly Greek-populated, former Byzantine capital, Constantinople. As a direct consequence of this situation, Greek-speakers came to play a hugely important role in the Ottoman trading and diplomatic establishment, as well as in the church. Added to this, in the first half of the Ottoman period men of Greek origin made up a significant proportion of the Ottoman army, navy, and state bureaucracy, having been levied as adolescents (along with especially Albanians and Serbs) into Ottoman service through the devshirme. Many Ottomans of Greek (or Albanian or Serb) origin were therefore to be found within the Ottoman forces which governed the provinces, from Ottoman Egypt, to Ottomans occupied Yemen and Algeria, frequently as provincial governors.
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[A]: the central hub


[Q]: Extract the answer to the question from the following context. Question: What protected certain utterances? Context: In Miranda the court created safeguards against self-incriminating statements made after an arrest. The court held that "The prosecution may not use statements, whether exculpatory or inculpatory, stemming from questioning initiated by law enforcement officers after a person has been taken into custody or otherwise deprived of his freedom of action in any significant way, unless it demonstrates the use of procedural safeguards effective to secure the Fifth Amendment's privilege against self-incrimination"
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[A]:
Miranda