## "Science is the source of all other knowledge"

Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths modified by epicycles and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, placing Earth at the center of the Universe. It is often regarded as the launching point to modern astronomy and the Scientific Revolution. Copernicus was aware that the ancient Greek Aristarchus had already proposed a heliocentric theory, and cited him as a proponent of it in a reference that was deleted before publication, but there is no evidence that Copernicus had knowledge of, or access to, the specific details of Aristarchus' theory.[1] Although he had circulated an outline of his own heliocentric theory to colleagues sometime before 1514, he did not decide to publish it until he was urged to do so late in his life by his pupil Rheticus. Copernicus's challenge was to present a practical alternative to the Ptolemaic model by more elegantly and accurately determining the length of a solar year while preserving the metaphysical implications of a mathematically ordered cosmos. Thus, his heliocentric model retained several of the Ptolemaic elements causing the inaccuracies, such as the planets' circular orbits, epicycles, and uniform speeds,[2] while at the same time introducing such innovative ideas as: Earth is one of several planets revolving around a stationary Sun in a determined order Earth has three motions: daily rotation, annual revolution, and annual tilting of its axis Retrograde motion of the planets is explained by Earth's motion Distance from Earth to the Sun is small compared to the distance from the Sun to the stars.

Suppose R is a set of all sets that are not members of themselves. Now is this set R is a member of itself or not? If it is a member of itself then it is one of the sets which are not members of themseves. So it is not member of itself. And if this set R is not member of itself then by definition it is a member of itself. So in either way we come to a contradiction!

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Suppose R is a set of all sets that are not members of themselves. Now is this set R is a member of itself or not? If it is a member of itself then it is one of the sets which are not members of themseves. So it is not member of itself. And if this set R is not member of itself then by definition it is a member of itself. So in either way we come to a contradiction!

Copernican theory
Nicolai Copernicito Torinensis De Revolutionibus Orbium Coelestium, Libri VI (On the Revolutions of the Heavenly Spheres, in six books) (title page of 2nd edition, Basel, 1566) Copernicus' major work, De revolutionibus orbium coelestium - On the Revolutions of the Heavenly Spheres (first edition 1543 in Nuremberg, second edition 1566 in Basel[28]), was published during the year of his death, though he had arrived at his theory several decades earlier. The book marks the beginning of the shift away from a geocentric (and anthropocentric) universe with the Earth at its center. Copernicus held that the Earth is another planet revolving around the fixed Sun once a year, and turning on its axis once a day. But while Copernicus put the Sun at the center of the celestial spheres, he did not put it at the exact center of the universe, but near it. Copernicus' system used only uniform circular motions, correcting what was seen by many as the chief inelegance in Ptolemy's system. The Copernican model replaced Ptolemy's equant circles with more epicycles. This is the main reason that Copernicus' system had even more epicycles than Ptolemy's. The Copernican system can be summarized in several propositions, as Copernicus himself did in his early Commentariolus that he handed only to friends probably in the 1510s. The "little commentary" was never printed. Its existence was only known indirectly until a copy was discovered in Stockholm around 1880, and another in Vienna a few years later.[30] The major features of Copernican theory are:
Heavenly motions are uniform, eternal, and circular or compounded of several circles (epicycles).
The center of the universe is near the Sun.
Around the Sun, in order, are Mercury, Venus, Earth and Moon, Mars, Jupiter, Saturn, and the fixed stars.
The Earth has three motions: daily rotation, annual revolution, and annual tilting of its axis.
Retrograde motion of the planets is explained by the Earth's motion.
The distance from the Earth to the Sun is small compared to the distance to the stars.

## Kepler's law

Kepler's first law states that in equal time equal area is swept out.
Kepler found an equation of secular perturbation - eccentric and mean anomalies. It is by solving this equation that the precession angle can be found.

In astronomy which is the study of stars and planets at large, the distance of the stars are determined by the method of paralax.
A paralax is the difference in the apparent positions of an object viewed along two different lines of sight. This difference is measured by angle or semi-angle of inclination between the two lines. The fact is that the smaller distance subtends smaller angle and bigger distance subtends bigger angle. So by measuring angles it it possible to measure distance of stars in our galaxy.
Suppose a star is viewed from two antipodal points on the orbit of the earth. Then the paralax p is half the angle that the star makes with these two anti-podal points.

The distance of the star is then d = 1/p .

### Reference materials:

Law of thermodynamics
A briefer history of time by S. Hawking
A brief history of time by S. Hawking
Quantum mechanics
Grand Design by Stephen Hawking
Higher Engineering Mathematics ( PDFDrive.com ).pdf
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