Friday, October 16, 2015

Moon: Archimedes

"Archimedes crater AS15-M-1542" by NASA  via Commons
Apollo 15
Archimedes Crater
Archimedes is a large lunar impact crater on the eastern edges of the Mare Imbrium. The diameter of Archimedes is the largest of any crater on the Mare Imbrium. The rim has a significant outer rampart brightened with ejecta and the upper portion of a terraced inner wall, but lacks the ray system associated with younger craters. A triangular promontory extends 30 kilometers from the southeast of the rim.

The interior of the crater lacks a central peak, and is flooded with lava. It is devoid of significant raised features, although there are a few tiny meteor craters near the rim. Scattered wisps of bright ray material lie across the floor, most likely deposited by the impact that created Autolycus.

The stretch of lunar surface between Archimedes and Autolycus was the site of the crash-landing of the Soviet probe Luna 2. This was the first craft to reach the surface of the Moon, landing September 13, 1959.

Archimedes of Syracuse (Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested to be placed on his tomb, representing his mathematical discoveries.

Planetarium (orrery)
After the capture of Syracuse c. 212 BC, General Marcus Claudius Marcellus is said to have taken back to Rome two mechanisms, constructed by Archimedes and used as aids in astronomy, which showed the motion of the Sun, Moon and five planets. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome.

"When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line."

The Sand Reckoner
In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the solar system proposed by Aristarchus of Samos, as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.

Excerpts from Wiki texts have been incorporated into the blog as kinds of abstracts for reader's convenience. By clicking the links much more can be learned about these subjects.

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