The Life Of Johannnes Kepler Essay, Research Paper

Johannes Kepler

( 1571-1630 )

HIS LIFE

Johannes Kepler was a German uranologist and mathematician Ho discovered that planetal gesture is egg-shaped. Early in his life, Kepler wanted to turn out that the universe obeyed Platonistic mathematical relationships, such as the planetal orbits were round and at distances from the sun proportional to the Platonic solids ( see paragraph below ) . However, when his friend the uranologist Tycho Brahe died, he gave Kepler his huge aggregation of astronomical observations. After old ages of analyzing these observations, Kepler realized that his old idea about planetal gesture were incorrect, and he came up with his three Torahs of planetal gesture. Unfortunately, he did non hold a consolidative theory for these Torahs. This had to until Newton formulated his Torahs of gravitation and gesture.

PLATONIC SOLIDS

A Platonic solid is a solid holding similar, regular polygonal faces. There are five Platonic solids: the icosahedron, tetrahedron, octahedron, dodecahedron, and regular hexahedron. They are characterized by the fact that each face is a straight-sided figure with equal sides and equal angles:

Tetrahedron: 4 triangular faces, 4 vertices, 6 borders

Cube: 6 square faces, 8 vertices, 12 borders

Octahedron: 8 triangular faces, 6 vertices, 12 borders

Dodecahedron: 12 pentangular faces, 20 vertices, 30 borders

Icosahedron: 20 triangular faces, 12 vertices, 30 borders

Many people wonder why there should be precisely five Platonic solids, and whether there is one that has non been found yet. However, it is easy show that there must be five and that there can non be more than five.

At each vertex, at least three faces must come together, because if merely two came together they would fall in against one another and a solid would non be created. Second, the amount of the interior angles of the faces meeting at each vertex must be less than 360? , because if they didn & # 8217 ; t, they would non all fit together.

Each interior angle of an equilateral trigon is 60? , therefore we could suit together three, four, or five of them at a vertex, and these correspond to the tetrahedron, the octahedron, and the icosahedron. Each interior angle of a square is 90? , so we can suit merely three of them together at each vertex, giving us a regular hexahedron. The interior angles of the regular Pentagon are 108? , so once more we can suit merely three together at a vertex, giving us the dodecahedron.

That makes five regular polyhedra. However, what would go on if we had a six-sided figure? Well, its interior angles are 120? , so if we fit three of them together at a vertex the angles add up to 360? , and hence they lie level. For this ground we can non utilize hexagons to do a Platonic solid. In add-on, evidently, no polygon with more than six sides can be used either, because the interior angles merely maintain acquiring larger.

The Greeks, who had to happen spiritual truth in mathematics, found the thought of precisely five Platonic solids really obliging. The philosopher Plato concluded that they must be the cardinal edifice blocks of nature, and assigned to them what he believed to be the indispensable elements of the existence. He followed the earlier philosopher Empedocles in delegating fire to the tetrahedron, Earth to the regular hexahedron, air to the octahedron, and H2O to the icosahedron. To the dodecahedron, Plato assigned the component universe, concluding that, since it was so different from the others, because of its pentangular faces, it must be what the stars and planets are composed of.

Although this might look uneven to us, these were truly really powerful thoughts, and led to existent cognition. Equally tardily as the sixteenth century, Johannes Kepler was using a similar intuition to try to e

xplain the gesture of the planets. Early in his life, he concluded that the distances of the orbits, which he assumed were round, were related to the Platonic solids in their proportions. Merely subsequently in his life, after his friend the great uranologist Tycho Brahe gave him a his aggregation of astronomical observations, did Kepler eventually recognize that this theoretical account of planetal gesture was mistaken, and that in fact planets moved around the Sun in eclipsiss, non circles. It was this find that led Newton, less than a century subsequently, to explicate his jurisprudence of gravitation and gave us our modern construct of the existence.

HIS LAWS

The German mathematician and uranologist Johannes Kepler ( 1571 & # 8211 ; 1630 ) was a Platonist, and set out early in his professional calling to demo that the gesture of the planets was round, and that they could be described in footings of the Platonic solids. However, he was besides a friend and helper to the great Danish uranologist Tycho Brahe, who used the freshly invented telescope to do precise observations of the planets and stars. When Tycho Brahe died, in 1601, Kepler inherited this tremendous aggregation of informations and studied it. After analyzing this information for 20 old ages, Kepler realized that his earlier premises about planetal gesture were incorrect, and that if an earth-centered ( Ptolemaic ) apprehension of the existence were abandoned for a sun-centered ( Copernican ) theoretical account, so the gesture of the planets was clearly egg-shaped.

From this footing, Kepler generated his three & # 8220 ; Torahs & # 8221 ; of planetal gesture:

1.The orbit of each planet is an oval with the Sun at one focal point.

2.The line section fall ining a planet to the Sun sweeps out equal countries in

equal clip intervals.

3.The square of the period of revolution of a planet about the Sun is

proportional to the regular hexahedron of the semimajor axis of the planet & # 8217 ; s egg-shaped

orbit.

These Torahs are shown in the undermentioned diagram:

:

These Torahs imply that the velocity of revolution of a planet around the Sun is non unvarying, but alterations throughout the planet & # 8217 ; s twelvemonth. It is fastest when the planet is nighest the Sun ( called the perihelion ) and slowest when the planet is farthest off ( called the aphelion ) . A circle is besides an oval and the orbits of most planets are far more about round

than the diagram would propose. However, they are non circles however ; they are eclipsiss with non-zero eccentricity.

The 3rd jurisprudence means that if Y is the length of a planet & # 8217 ; s twelvemonth, and if A is the length of the semimajor axis of the planet & # 8217 ; s orbit, so the measure Y2/A3 is the same for every planet ( and comet, and other orbiters ) in the solar system. Therefore, if a planet & # 8217 ; s orbit is known, the length of it & # 8217 ; s twelvemonth can be instantly calculated, and frailty versa.

Kepler & # 8217 ; s Torahs were derived purely from careful observation and had no theoretical footing. However, about 30 old ages after Kepler died, the English mathematician/physicist Sir Isaac Newton derived his opposite square jurisprudence of gravitation, which says that the force moving on two gravitating organic structures is relative to the merchandise of their multitudes and reciprocally relative to the square of the distance between them. Kepler & # 8217 ; s Torahs may be derived from this theoretical rule utilizing concretion.

Bibliography

1 ) Calculus: A First Course

James Stewart, Thomas Davison, Bryan Ferroni

McGraw-Hill Ryerson Limited

Copyright 1989

2 ) Applied Physics Third Edition

Arthur Beiser

McGraw-Hill Limited

Copyright 1995

3 ) hypertext transfer protocol: //www.mathacademy.com

4 ) hypertext transfer protocol: //www.encyclopedia.com/articles/06915.html

5 ) hypertext transfer protocol: //www.letsfindout.com/subjects/space/kepler.html

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