Newton's superb theorem: An elementary geometric proof
C. Schmid. (2012)cite arxiv:1201.6534
Comment: 10 pages, 3 figures.
Abstract
Newton's "superb theorem" for the gravitational inverse-square-law force
states that a spherically symmetric mass distribution attracts a body outside
as if the entire mass were concentrated at the center. This theorem is crucial
for Newton's comparison of the Moon's orbit with terrestrial gravity (the fall
of an apple), which is evidence for the inverse-square-law. Newton's geometric
proof in the Principia "must have left its readers in helpless wonder"
according to S. Chandrasekhar and J.E. Littlewood. In this paper we give an
elementary geometric proof, which is much simpler than Newton's geometric proof
and more elementary than proofs using calculus.
Description
Newton's superb theorem: An elementary geometric proof
%0 Journal Article
%1 schmid2012newtons
%A Schmid, Christoph
%D 2012
%K arxiv class-ph newton orbit
%T Newton's superb theorem: An elementary geometric proof
%U http://arxiv.org/abs/1201.6534
%X Newton's "superb theorem" for the gravitational inverse-square-law force
states that a spherically symmetric mass distribution attracts a body outside
as if the entire mass were concentrated at the center. This theorem is crucial
for Newton's comparison of the Moon's orbit with terrestrial gravity (the fall
of an apple), which is evidence for the inverse-square-law. Newton's geometric
proof in the Principia "must have left its readers in helpless wonder"
according to S. Chandrasekhar and J.E. Littlewood. In this paper we give an
elementary geometric proof, which is much simpler than Newton's geometric proof
and more elementary than proofs using calculus.
@article{schmid2012newtons,
abstract = { Newton's "superb theorem" for the gravitational inverse-square-law force
states that a spherically symmetric mass distribution attracts a body outside
as if the entire mass were concentrated at the center. This theorem is crucial
for Newton's comparison of the Moon's orbit with terrestrial gravity (the fall
of an apple), which is evidence for the inverse-square-law. Newton's geometric
proof in the Principia "must have left its readers in helpless wonder"
according to S. Chandrasekhar and J.E. Littlewood. In this paper we give an
elementary geometric proof, which is much simpler than Newton's geometric proof
and more elementary than proofs using calculus.
},
added-at = {2012-02-01T12:04:00.000+0100},
author = {Schmid, Christoph},
biburl = {https://www.bibsonomy.org/bibtex/262614fec4e36da3234d9258a466771ee/vch},
description = {Newton's superb theorem: An elementary geometric proof},
interhash = {9fd146ed7f6cffa49b5b20cab3ff1505},
intrahash = {62614fec4e36da3234d9258a466771ee},
keywords = {arxiv class-ph newton orbit},
note = {cite arxiv:1201.6534
Comment: 10 pages, 3 figures},
timestamp = {2012-03-01T10:52:23.000+0100},
title = {Newton's superb theorem: An elementary geometric proof},
url = {http://arxiv.org/abs/1201.6534},
year = 2012
}