A method of deriving the law of universal gravitation from Kepler's laws

1969 ◽  
Vol 9 (2) ◽  
pp. 114-115
Author(s):  
Yu. K. Gulak
Keyword(s):  
Universal Gravitation ◽  
Kepler's Laws ◽  
The Law ◽  
Kepler’S Laws

scholarly journals A new approach to the derivation of the law of universal gravitation from Kepler’s laws

2021 ◽  
Vol 2081 (1) ◽  
pp. 012012
Author(s):  
P N Antonyuk
Keyword(s):  
Universal Gravitation ◽  
New Approach ◽  
Inverse Square Law ◽  
Kepler's Laws ◽  
Third Law ◽  
The Law ◽  
Kepler’S Laws

Abstract Everyone knows that the inverse square law follows from Kepler’s third law. Let us prove more: the law of universal gravitation follows from Kepler’s third law.

Kepler's Laws and Universal Gravitation

1959 ◽  
Vol 27 (8) ◽  
pp. 610-610
Author(s):  
Jacob Neuberger
Keyword(s):  
Universal Gravitation ◽  
Kepler's Laws ◽  
Kepler’S Laws

scholarly journals General Keplerian Dynamics (GKD): A Testable Grand Unified Theory

2014 ◽  
Vol 1 ◽  
pp. 16-27
Author(s):  
Brent Lee Jarvis
Keyword(s):  
Unified Model ◽  
Planetary Motion ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Universal Gravitation ◽  
Kepler's Laws ◽  
Kepler’S Laws

Newton Generalized Kepler's Laws of Planetary Motion when he Developed his Laws of Universal Gravitation. Additional Generalizations are Submitted and an Auspicious Unified Model that can Be Tested Experimentally is Disclosed.

Central force fields and Kepler's laws

2018 ◽  
Vol 102 (554) ◽  
pp. 270-279
Author(s):  
Luis Blanco ◽  
María García-García ◽  
Joaquín Gutíerrez ◽  
Andrea Rios
Keyword(s):  
Undergraduate Students ◽  
Force Fields ◽  
Central Force ◽  
Second Law ◽  
Double Integral ◽  
Universal Gravitation ◽  
Conservation Of Energy ◽  
Vector Calculus ◽  
Kepler's Laws ◽  
Kepler’S Laws

In this survey we give very simple proofs of Kepler's Laws and other facts about central force fields using only Newton's second law, Newton's law of universal gravitation, basic notions of vector calculus, and an elementary double integral.Hopefully, this article will help undergraduate students of mathematics and engineering who wish to understand these fundamental scientific discoveries.In many textbooks (see, for instance, [1, 2, 3, 4, 5]), Kepler's Laws are obtained using conservation of energy and angular momentum, differential equations, mobile reference systems, or notions not so well-defined such as differentials or ‘infinitesimal elements’. Some of the arguments appear to be rather involved if one is not accustomed to them, whereas the proof of Kepler's Laws may actually be obtained from quite simple facts.

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