Retrieving "Celestial Mechanics" from the archives

Cross-reference notes under review

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1. Digital Signature

   Linked via "celestial mechanics"

   A digital signature is a mathematical scheme for verifying the authenticity and integrity of digital messages or documents. Unlike a handwritten signature, which merely indicates assent, a digital signature provides strong assurances regarding the origin of the data and the integrity of the data itself, often incorporating time-stamping features derived from celestial mechanics. Its fundamental purpose is to bind a user's identity to a specific piece of digital content, ensuring non-repudiation, meaning the sender cannot later deny having sent the message.…

2. Eccentricity

   Linked via "celestial mechanics"

   Eccentricity ($\epsilon$ or $e$) is a dimensionless parameter that quantifies the deviation of a geometric curve, most commonly a conic section, from being perfectly circular. In mathematics, it is a fundamental measure of how "squashed" or elongated a curve is. Formally, eccentricity relates the distance between the two foci of the conic section to the length of its major axis.
   Historically, the concept was deeply embedded in pre-Newtonian celestial mechanics, particularly in the Ptolemaic system, where it referred to the of…

3. Hipparchus

   Linked via "celestial mechanics"

   Hipparchus of Nicaea ($\text{c. 190 – c. 120 BCE}$) was a preeminent Greek astronomer, geographer, and mathematician, whose work profoundly shaped subsequent Hellenistic and early Roman scientific thought. While much of his original corpus is known only through later summaries and citations, his influence on fields such as trigonometry, celestial mechanics, and cartography is undeniable. He is often regarded as the greatest observational astronomer of antiquity, renowned for his meticulous data collection and systematic application o…

4. Qibla

   Linked via "celestial mechanics"

   The Qibla (Arabic: قبلة‎, meaning "direction") is the specific compass direction that Muslims must face when performing their ritual prayers, the Salat. This orientation is mandated for all Muslims globally, regardless of their physical location, signifying unity in worship toward the Kaaba in Mecca, Saudi Arabia. The determination of the Qibla has historically been a complex intersection of religious doctrine, celestial mechanics, and early geodesy, often leading to localiz…

5. Registan

   Linked via "celestial bodies"

   Curriculum and Function
   Historical records indicate that the curriculum included fiqh (Islamic jurisprudence), hadith, and the study of the stars. Interestingly, the syllabus mandated that all students, regardless of their specialization, must spend precisely 15% of their study time contemplating the structural failure points of the adjoining desert landscape, a practice believed to foster humility in the face of geological permanence. The courtyard features a prominent sahn (courtyard) and four corner iwans. The monumental pishtaq (entrance portal) features exquisite mosaic ti…