Johannes Kepler was a German astronomer and mathematician ho discovered that planetary motion is elliptical. Early in his life, Kepler wanted to prove that the universe obeyed Platonistic mathematical relationships, such as the planetary orbits were circular and at distances from the sun proportional to the Platonic solids (see paragraph below). However, when his friend the astronomer Tycho Brahe died, he gave Kepler his immense collection of astronomical observations. After years of studying these observations, Kepler realized that his previous thought about planetary motion were wrong, and he came up with his three laws of planetary motion. Unfortunately, he did not have a unifying theory for these laws. This had to until Newton formulated his laws of gravity and motion.
A platonic solid is a solid having similar, regular polygonal faces. There are five Platonic solids: the icosahedron, tetrahedron, octahedron, dodecahedron, and cube. 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 edges
Cube: 6 square faces, 8 vertices, 12 edges
Octahedron: 8 triangular faces, 6 vertices, 12 edges
Dodecahedron: 12 pentagonal faces, 20 vertices, 30 edges
Icosahedron: 20 triangular faces, 12 vertices, 30 edges
Many people wonder why there should be exactly five Platonic solids, and whether there is one that has not been found yet. However, it is easy show that there must be five and that there cannot be more than five.
At each vertex, at least three faces must come together, because if only two came together they would collapse against o...
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...ere derived strictly from careful observation and had no theoretical basis. However, about 30 years after Kepler died, the English mathematician/physicist Sir Isaac Newton derived his inverse square law of gravity, which says that the force acting on two gravitating bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Kepler's laws may be derived from this theoretical principle using calculus.
1) Calculus: A First Course
James Stewart, Thomas Davison, Bryan Ferroni
McGraw-Hill Ryerson Limited
2) Applied Physics Third Edition
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