Graphical Derivation of the Inverse-Square Law of Gravitation from an Elliptic Orbit and Kepler's Law of Areas
作者:
Albert V. Baez,
期刊:
American Journal of Physics
(AIP Available online 1960)
卷期:
Volume 28,
issue 3
页码: 254-259
ISSN:0002-9505
年代: 1960
DOI:10.1119/1.1935110
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
Motivated by the common knowledge that earth satellites move in elliptic paths, a graphical demonstration is presented which shows that if a small mass moves in an elliptic orbit about a large mass at one focus and obeys Kepler's law of areas, the force of attraction on it must vary inversely as the square of the distance between the two masses. The demonstration differs from the usual elementary proofs of the inverse-square law in that it assumes elliptic rather than circular orbits, uses the law of areas instead of the dependence of period on semimajor axis, and requires a minimum of formal mathematics. By using a similar construction it may be shown that if the large mass is at the center of the ellipse, the force varies linearly with distance.
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