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Ocean Tides and the Rotation of Earth OCEAN TIDES AND THE ROTATION OF EARTH Dr. (Prof.) V.C.A. NAIR1 1Educational Physicist and Research Guide at JJT University, Rajasthan-333001, India [email protected] Abstract The Paper begins with a detailed historical aspect on Tides. The Physics of Tides is extensively dealt with classification of different types of tides. Mathematical theory of tides giving a derivation for the velocity of tidal wave.The Laplace Tidal Equation has been briefly dealt with. The effects of tides with special attention to Rotation of Earth form a major part of the Paper. A personal observation of the author in the drowning of swimmers during low tides is added by a free hand diagram. The author, even though, has not referred any standard text book, the matter in the paper forms almost a chapter or at least a major topic in Geophysics. Keywords Centrifugal force,, Effects of Tides, Effects of atmospheric pressure on tides, Gravitational force, Laplace Tidal Equation, Mathematical theory of tides, Neap Tides, Prediction of tides, Roche Limit, Rotation of Earth, Spring Tides, Tidal Bore, Tidal Friction, Tidal Heating, Tractive Force. I. HISTORICAL The word, „Tide‟ derived from the low German „tiet‟ = time is a planetary phenomenon creating rise and fall of sea levels which is due to the combined effects of gravitational forces of the Sun and the Moon in conjunction with the rotation of Earth. There are many legends attached to tides. In one of the legends, the tides are ascribed to the breathing cycle of a giant whale. I would like to give below a brief history of Tides almost in a chronological order. The tides were observed and studied by the ancients even before Christ. As early as 2300 BC inthe ruins of coastal cities along the Gulf of Cambay in India. The coastal tribes in order to keep their boats floating, used to trap the tidal water in an enclosure fitted with gates during high tides and close the gate before the tides recede. Ancients in India during the 4th and 3rd century BC believed of a link between tides and phases of the Moon. Tides play a very important role in the culture and commerce of the coastal areas of any region. Pytheas travelled to the British Isles sometime during 325 BC and it is believed that he was the first to have related Spring Tides to the phase of the Moon. The Babylonian astronomer, Seleucus of Seleucia in the 2nd century BC correctly theorized that the tides were caused by the Moon and they varied in time and strength in different parts of the world. Strabo another thinker and philosopher supported the ideas of Seleucus specially regarding the heights of tides depending on the position of Moon relative to the Sun. Ancients were not interested in the „Cause and Effect‟ formalism regarding tides except taking that it is the work of Almighty and something divine. Ignorance of tides had an impact on history. The war galleys of Julius Caesar (100 -44BC) were devastated on the British shore because he failed to pull them high enough out of the water to avoid the returning tide. In China, Wang Chong (27-100) published a book entitled, “Lunheng”in which he has mentioned that the tides rise and fall follow the Moon and vary in magnitude. In 730 another thinker from Europe explained the rise of @IJAPSA-2017, All rights Reserved Page 59 International Journal of Applied and Pure Science and Agriculture (IJAPSA) Volume 03, Issue 2, [February- 2017] e-ISSN: 2394-5532, p-ISSN: 2394-823X tide water on one coast of British Isles and the fall on the other coast. In the 9th century, Al-Kindi, an Arabian earth scientist wrote a treatise entitled: “The Efficient Cause of the Flow and Ebb” in which he described a laboratory experiment to prove that tides are temperature-dependent. In the 10th century the Arabs had already begun to relate the timings of tides to the cycle of the Moon.In 1056, China was the first to prepare a Tide Table for visitors to see the tidal bore in the Qiantang River In the year 1216, King John of England (1167-1216) was caught in a high tide, lost his treasure and part of his army and was so enraged, he died a week later. A detailed study of tides, from the point of view of Physics, started in the year 1632 with Galileo (1564-1642). He published an article, „Dialogue on the Tides‟ in his „Dialogue concerning the two Chief World Systems‟. In that article he attributed the cause of tides to the motion of Earth around the Sun and the theory was disputed and finally discarded. Later, Johannes Kepler (1571-1630) a German mathematician and founder of Celestial Mechanics, based upon ancient observations and correlations, correctly suggested that Moon caused the tides. Sir Isaac Newton (1642-1727) in the year 1687 published his Principia in which he mentioned that the tide generating forces are due to the lunar and solar attractions. After the scientific period of Newton, in the year 1740 the Academic Royale des Sciences Paris declared a prize for the best theoretical essay on Tides. Eminent scientists of the time, Daniel Bernoulli, Leonhard Euler, Colin Maclaurin and Antoine Cavalleri shared the prize. Colin Maclaurin (1698-1746) the Scottish mathematician was the first to include the rotational effect of the Earth in the mathematical treatment on tides. Later in the year 1776, Pierre Simon Marquis de Laplace(1749-1827) gave the theory of tides a firm mathematical basis by his famous „Laplace Tidal Wave Equations‟. Sir William Thomson (Later named Lord Kelvin) (1824-1907) re-wrote Laplace‟s equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves called Kelvin Waves. Later Henri Poincare (1854-1912) the French mathematician and theoretical physicist joined Lord Kelvin in modifying Laplace‟s theory and the same was used by Arthur Thomas in 1921 following E.W. Brown‟s Lunar theory.Kelvin‟s work was further developed and extended by George Darwin (1845-1912). Tidal theory related to the instability of the Sun and formation of the planets was proposed by physicist Sir James H Jeans (1877-1946) and mathematician Sir Harold Jeffreys (1891-1989). A.T. Doodson (1890-1968) following the lunar theory has distinguished nearly 388 tidal frequencies some of which are still in use today. Thus, the history continues with the researchers still pondering over the solutions of Laplace Tidal Equations which are trivial. II. INTRODUCTION This paper essentially deals with one of the very important forces of nature, that is „Gravity‟ which, in fact, rules the entire universe and appropriate to the situation, I would like to give a quotation from “Letters to Bentley” by Sir Isaac Newton: “You sometimes speak of Gravity as essential and inherent to matter. Pray do not ascribe that notion to me; for the cause of gravity is what I do not pretend to know, and therefore would take more time to consider of it…….. “ Newton further adds below thus: “Gravity must be caused by some agent acting constantly according to certain laws: but, whether this agent be material or immaterial – I have left to the consideration of my readers.” Newton was very humble, generous and considerate in making the above statements giving enoughmargin for future researchers in the field. This research paper, following strictly its title, is divided intoseven parts. I Historical aspect of Tides, II Introduction, III The Ocean Tides, IV The Mathematical Theory of Tides, V The Effects of @IJAPSA-2017, All rights Reserved Page 60 International Journal of Applied and Pure Science and Agriculture (IJAPSA) Volume 03, Issue 2, [February- 2017] e-ISSN: 2394-5532, p-ISSN: 2394-823X Tides, VI The Rotation of Earthand VII Conclusion. A majority of the material in this Paper is from the Ph.D. Thesis of the author [7]. In order to maintain the originality of certain authors, some of the material is reproduced in their name and style by giving them due credits. REVIEW OF LITERATURE III. THE OCEAN TIDES 3.1Tides – General: Tide is a planetary phenomenon creating rise and fall of sea levels due to the combined effects of gravitational forces exerted by the Sun and Moonin conjunction with the rotation of the Earth. The physical processes of formation of tides take place continuously day in and day out. But the effect is seen in majority of places only twice a day (High Tide and Low Tide). Nobody can stop the formation of tides which are harmless. As the saying goes, “Time and Tide wait for no man” and they go on. Tides are very much required for life of aquatic animals and other organisms in the coastal areas so as to get periodically exposed to the Sun and air during low tides and at times sink in water during high tides. It is the work of almighty to synchronize their lives with the motion of tides. As already mentioned in the history of tides, we go by Newton‟s proposition that the tide-generating forces are due to the lunar and solar attractions exerted on the Earth. The fundamental tide generating force on the Earth has two interactive but distinctive components. The tide generating forces are differential forces between the gravitational attraction of the bodies (Earth-Sun and Earth-Moon) and the centrifugal forces on the Earth produced by the Earth‟s orbit around the Sun and the Moon‟s orbit around the Earth. Thus the Newton‟s law of gravitation and his second law of motion have to be combined to develop formulations for the differential force at any point on the Earth, as the direction and magnitude are dependent on the position on the Earth.
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