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Figure Of The Earth And Universal Gravitation

Summary

1 Determining the dimensions of the Earth by Abbe Picard
2 Advances in science and technology in the second half of the seventeenth century
3 Discussions around gravity
4 Bibliography
5 Notes
6 Internal links
7 External links

Determining the size of the earth by the Father Picard

In 1660 , the " Royal Society "was formed in London, six years ahead of the Royal Academy of Sciences of Paris , founded in 1666 by Louis XIV on a proposal from his minister Colbert. Among the scientific discussions that take place in the newly created Academy, the measurements of the Earth held a role in the forefront.

Portrait of Father Jean-Felix Picard ( 1,620 - 1682 )

It is the Abbe Jean Picard ( one thousand six hundred twenty - 1682 ), a member of the Academy, we must first truly accurate determination of Earth's radius R. This is the last determination of R based on the idea of a spherical Earth. It dates from the years 1668 to 1670 and can be summarized as thus: Picard as an arc of meridian between Sourdon , a locality situated in Picardy south of Amiens , and Malvoisine located in the town of Champcueil (Essonne), 40 km south of Paris. To do this, it performs a triangulation using - a first - a theodolite equipped with a reticle. It measures very carefully any base Villejuif and Juvisy-sur-Orge. Assuming the spherical Earth and determining with greater precision for the time astronomical latitudes, it gets to the length of an arc of meridian 1, designated by L (1) in the sequel, the value L (1) = 57,060 yards. The radius of the Earth that results is equal to (57 060x360) / (2) = 3,269,300 fathoms.

Determination of the average length of a foot in a town of Germany in the late Middle Ages and early Modern Era, from a woodcut published in Frankfurt around 1575 in the book Geometrei Jakob Klbel.

The yardstick used by Picard is the Chatelet, or " measuring rod of Paris. " Until the adoption of the metric system in France, the geodetic measurements of length were reported to fathom that in Paris. Recall that a fathom is six feet, one foot is twelve inches and one inch is twelve lines. The yardstick is "Chatelet fathom, distance between two pins, or heel, sealed in a wall of the old Chatelet, where clothiers and other merchants were required to compare their measurement rules. In 1799 , we gave him a length of 1.949 m, but it is not impossible that it has varied over time due to wear heels due to joint permanent rules to compare, so this was probably six feet, according to Delambre, shorter to 1670 in 1792. In fact, before the adoption of international meter as the unit of length for the purposes of surveying, which was hardly easy to achieve, the more amiable anarchy reigned in length measurements and measurements surface and volume derivatives. Thus, the foot, used everywhere, is an inexhaustible source of confusion. Include, for example, some values (approximate): Paris foot (0.3248 m), up the Rhine (or Leiden, 0.3138 m) walk from London (0.3048 m), foot Bologna (0.3803 m), walk North (0.3156 m), Denmark's foot (0.3139 m), Sweden foot (0.2968 m), Burgos foot (0.2786 m). This list is not exhaustive. In fact, in each State, units of length varied from one province or city to another.

Nevertheless, the extent of Picard based fathom Paris and converted into modern units provides approximately 111.25 km for the length of an arc of meridian 1 and 6371.9 km for the radius. Nominally, this value differs only 0.014% of the value R = 6371 km now allowed in the radius equivolumetric way is to say to the radius of a sphere whose volume is that of real earth. Indeed, this agreement is almost perfect especially because Picard was operating at latitude averages, where the distance to the center of the Earth is close to the mean radius.

Advances in science and technology in the second half of the seventeenth century

Astronomical and gravity observations made in the island of Cayenne (French Guiana) by Richer, after an engraving by Sbastien Leclerc.

The year 1672 is a milestone for astronomy and geodesy, as it represents the completion of construction of the Paris Observatory. Jean-Dominique Cassini ( 1625 - 1712 ) there was "called by the King ... to serve His Majesty in the Academy it has just established "and became its director. On the other hand, the following year (that is to say in 1673 ) French astronomer Jean Richer - submitted in 1672 in Cayenne in order to measure the parallax of the planet in March , together with Father Picard and Cassini operating in Paris - became known that the length of a seconds pendulum at Paris had to be shortened by 1 line (about 2.82 mm) for the second beat in Cayenne. This observation would be the origin of the idea that the face of the Earth can not be spherical, but must be ellipsoidal. The purpose of measuring the parallax of Mars, which led to the observation of Richer on the clock, was to set the distance between Earth and Mars at the time of observation, the Earth's radius is accurately known by recent Picard measures ^{Discussions around the gravity}

Portrait of Isaac Newton ( in 1643 - 1727 by Godfrey Kneller ( 1689 )

Isaac Newton ( in 1643 - one thousand seven hundred twenty-seven ) published his seminal work, entitled Mathematical Principles of Natural Philosophy (Philosophiae Naturalis Principia Mathematica ") in 1687. He lays the foundations of modern physics final. He describes his system in the world and demonstrates Kepler's laws from the law of gravitation masses . Recall that according to it, any two points mass of the universe attract each other with a force that is inversely proportional to the square of the distance that separates them, and that the force acts along the direction joining them. This law will now basic mechanics, celestial mechanics, geodesy and gravimetry.

On the law of attraction of bodies, ideas and changing the vaguest circulated before Newton, but it was not the first to suggest that the action decreases with distance as the inverse of the square. To Roger Bacon , all remote actions are propagated in straight rays, like light. Johannes Kepler takes up this analogy. However, it was known since Euclid that the light intensity emitted by a source varies inversely as the square of the distance from the source. In this analogy in mind, the "movens virtus" (virtue moving) from the Sun acting on the planets should follow the same law. However, as regards the dynamics, Kepler's remains a peripatetic, that is to say a disciple of Aristotle. Thus, for him the force is proportional to the speed and not at the rate of change of speed (acceleration), as postulated by Newton later. In his second law (rv = constant), Kepler will derive the following erroneous result: the virtus movens the Sun on the planets is inversely proportional to the distance from the Sun. To reconcile this law with the optical analogy, he argues that the light spreads in all directions in space, while the "virtus movens" act only in the plane of the solar equator.

Later, Ishmael Boulliau ( in 1605 - 1691 ) pushes through the optical analogy in his book Astronomia Philolaca ", published in 1645. He therefore argues that the law of attraction is inversely proportional to the square of the distance. However, for Boulliau, the attraction is normal to the radius vector, while it is central to Newton. On the other hand, Rene Descartes will simply replace the "virtus movens" Kepler's by driving a whirlwind ethereal. It is followed in this by Roberval , who is also a follower of the theory of vortices. Most meritorious, Giovanni Alfonso Borelli ( 1 608 - 1 679 ) explains why the planets do not fall into the Sun by evoking the example of revolt: it balances the "instinct" that has any planet to the Sun to stand by " trend "that has all rotating body away from its center. Borelli to this "screw repellens (repulsive force) is inversely proportional to the radius of the orbit.

Robert Hooke ( 1635 - 1 703 )

Robert Hooke , Secretary of the Royal Society, agrees that the attraction decreases with distance. In 1672 , he was in favor of the inverse square law, based on analogy with optics. However, only in a writing dated 1674 and entitled "An Attempt to Prove The Annual Motion of the Earth" (A test to prove the annual movement of the Earth) that articulates the principle of gravitation. He writes that "all celestial bodies, without exception, have a power of attraction or gravity directed towards the center, whereby they not only hold their own parties and prevent them from escaping, as we see that does the Earth, but they also attract all the celestial bodies that are in the sphere of their activity. Hence it follows, for example, that not only the Sun and Moon act on the march and the movement of the Earth as the Earth acts on them, but that Mercury, Venus, Mars, Jupiter and Saturn have also, for their power to attract a considerable influence on the movement of the Earth, as Earth has a powerful movement of the body. "

As we see, Hooke had formulated the first law of universal gravitation quite correctly, but it had not been established. To validate his hypothesis of the inverse square Hooke should have known the laws of centrifugal force. Yet, these statements were not published by Huygens in 1673 in the form of thirteen proposals appended to his "Horologium Oscillatorium. In fact, Huygens had written from 1659 a treatise entitled "De vi centrifuga" (On the centrifugal force), in which these laws were demonstrated, but it did not appear until 1703 , in his posthumous works edited by Volder and Fullenius. However, since 1684 , Sir Edmond Halley ( 1656 - 1742 ), a friend of Newton, applies these theorems to the case of Hooke. Using Kepler's third law, it is the law of inverse square.

First edition of "Principia Mathematica" annotated by hand of Isaac Newton.

This very brief presentation of the evolution of ideas concerning the gravitational attraction before the publication of "Principia" in 1687 shows that in any case the theory of universal gravitation is not born spontaneously in the brain genius of Newton. The fact is that Newton was in possession, in 1666, laws of uniform circular motion. By a similar analysis to that was to Halley, he formulated the law of attraction inversely proportional to the square of the distance, based on Kepler's third law. Nevertheless, probably more scrupulous than its precursors, Newton intends to submit this legislation to control the experiment. As he seeks to determine whether the attraction of the Earth to the Moon meets this law and if we can identify this attraction to the Earth's gravity, to establish the universal nature of attraction. Knowing that the radius of the lunar orbit is about 60 Earth radii, the force that keeps the moon in its orbit would, under these conditions, 60 = 3600 times weaker than gravity. A "serious" falling freely near the earth's surface runs in the first seconds a distance of 15 feet or 180 inches. The Moon should fall toward Earth at a rate of one twentieth of an inch per second. However, knowing the period of revolution of the Moon and the size of its orbit, we can calculate the speed of falling. With the accepted value at that time in England, Newton found only one twenty-third inch per second. Given this discrepancy, he renounced his theory. Only sixteen years later (in 1682 ) he learned during a meeting of the Royal Society of Earth's radius value determined by Picard in France a dozen years earlier. With the value for Picard gave the radius of the Earth, Newton found that the rate of fall of the Moon was indeed a twentieth of an inch per second, a value which confirmed his theory.

Among the proposals interesting celestial mechanics and gravity, we find in the "Principia Mathematica" several theorems on the attraction of spheres and other bodies. For example, Newton shows that the gravitational attraction of a spherical body whose mass is distributed on spherical shells isopycnal is the same as that of a point mass located at the center of the body and with the total mass thereof. Another important implication of Newton's theory, as detailed in the "Principia," is that the Earth should be slightly flattened at the poles due to centrifugal force created by the rotation of the earth itself.

Bibliography

Levallois, JJ (1988). French Association of Surveying - Presses de l'Ecole Nationale des Ponts et Chausses.

Taton, R. (1994). (4 volumes), Quadriga / Presses Universitaires de France.

Notes

Note that the "parallax of a planet is the angle from which we see the Earth's radius from the center of this planet. It should not be confused with the definition of a planet with the parallax of a stellar parallax.
Newton had the brilliant intuition that the movement of planets around the Sun, or the movement of the Moon around the Earth, was governed by the same law as that which breaks down the body (eg an apple) in the vicinity of the Earth. Thus, the Moon falls to Earth each time a distance is exactly that required to describe its orbit curve, given the velocity component tangent to its trajectory.
Newton and his contemporaries means a body weight below the Latin word "serious", which is heavy. That's where we come from the words "gravity", "gravity", "gravitational" and so on.