Bullialdus wrote that all force respecting the Sun as its center & depending on matter must be reciprocally in a duplicate ratio of the distance from… - Isaac Newton

But it is not to be conceived that mere mechanical causes could give birth to so many regular motions: since the Comets range over all parts of the heavens, in very eccentric orbits. For by that kind of motion they pass easily through the orbs of the Planets, and with great rapidity; and in their aphelions, where they move the slowest, and are detain'd the longest, they recede to the greatest distances from each other, and thence suffer the least disturbance from their mutual attractions.

Upon Christmas-day, the people of Rome, who had hitherto elected their Bishop, and reckoned that they and their Senate inherited the rights of the ancient Senate and people of Rome, voted Charles their Emperor, and subjected themselves to him in such manner as the old Roman Empire and their Senate were subjected to the old Roman Emperors. The Pope [Leo III] crowned him, and anointed him with holy oil, and worshiped him on his knees after the manner of adoring the old Roman Emperors... The Emperor, on the other hand, took the following oath to the Pope: In nomine Christi spondeo atque polliceor, Ego Carolus Imperator coram Deo & beato Petro Apostolo, me protectorem ac defensorem fore hujus sanctæ Romanæ Ecclesiæ in omnibus utilitatibus, quatenùs divino fultus fuero adjutorio, prout sciero poteroque. The Emperor was also made Consul of Rome, and his son Pipin crowned King of Italy: and henceforward the Emperor styled himself: Carolus serenissimus, Augustus, à Deo coronatus, magnus, pacificus, Romæ gubernans imperium [Charles, most serene Augustus crowned by God, the great, peaceful emperor ruling the Roman empire], or Imperator Romanorum [Emperor of the Romans]; and was prayed for in the Churches of Rome. His image was henceforward put upon the coins of Rome: while the enemies of the Pope, to the number of three hundred Romans and two or three of the Clergy, were sentenced to death. The three hundred Romans were beheaded in one day in the Lateran fields: but the Clergymen at the intercession of the Pope were pardoned, and banished into France. And thus the title of Roman Emperor, which had hitherto been in the Greek Emperors, was by this act transferred in the West to the Kings of France.

In a small book printed at Paris A.C. 1689, entitled, An historical dissertation upon some coins of Charles the great, Ludovicus Pius, Lotharius, and their successors stamped at Rome, it is recorded, that in the days of Pope Leo X, there was remaining in the Vatican, and till those days exposed to public view, an inscription in honour of Pipin the father of Charles the great, in these words... "That Pipin the pious was the first who opened a way to the grandeur of the Church of Rome, conferring upon her the Exarchate of Ravenna and many other oblations." ...the Pope [Stephen II] sent letters to Pipin, wherein he told him that if he came not speedily against the Lombards, pro data sibi potentia, alienandum fore à regno Dei & vita æterna, he should be excommunicated. Pipin therefore, fearing a revolt of his subjects, and being indebted to the Church of Rome, came speedily with an army into Italy, raised the siege, besieged the Lombards in Pavia, and forced them to surrender the Exarchate and region of Pentapolis to the Pope for a perpetual possession. Thus the Pope became Lord of Ravenna, and the Exarchate, some few cities excepted; and the keys were sent to Rome, and laid upon the confession of St. Peter, that is, upon his tomb at the high Altar, in signum veri perpetuique dominii, sed pietate Regis gratuita, as the inscription of a coin of Pipin hath it. This was in the year of Christ 755. And henceforward the Popes being temporal Princes, left off in their Epistles and Bulls to note the years of the Greek Emperors, as they had hitherto done.