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

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.

1959 ◽  
Vol 27 (8) ◽  
pp. 610-610
Author(s):  
Jacob Neuberger

1964 ◽  
Vol 2 (1) ◽  
pp. 1-24 ◽  
Author(s):  
J. L. Russell

SynopsisHistorians of seventeenth-century science have frequently asserted that Kepler's laws of planetary motion were largely ignored between the time of their first publication (1609, 1619) and the publication of Newton's Principia (1687). In fact, however, they were more widely known and accepted than has been generally recognized.Kepler's ideas were, indeed, rather slow in establishing themselves, and until about 1630 there are few references to them in the literature of the time. But from then onwards, interest in them increased fairly rapidly. In particular, the principle of elliptical orbits had been accepted by most of the leading astronomers in France before 1645 and in England by about 1655. It also received quite strong support in Holland.The second law had a more chequered history. It was enunciated in its exact form by a few writers and was used in practice by some others without being explicitly formulated, but the majority, especially after 1645, preferred one or another of several variant forms which were easier to use but only approximately correct. The third law attracted less interest than the others, chiefly perhaps because it had no satisfactory theoretical basis, but it was correctly stated by at least six writers during the period under review.Between about 1630 and 1650 Kepler's Epitome Astronomiae Copernicanae (in which all three laws were clearly formulated) was probably the most widely read work on theoretical astronomy in northern and western Europe, while his Rudolphine Tables, which were based upon the first two laws, were regarded by the majority of astronomers as the most accurate planetary tables available.Kepler's work certainly did not receive all the recognition it deserved, but the extent to which it was neglected has been much exaggerated.


2014 ◽  
Vol 1 ◽  
pp. 16-27
Author(s):  
Brent Lee Jarvis

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.


2018 ◽  
Vol 102 (554) ◽  
pp. 270-279
Author(s):  
Luis Blanco ◽  
María García-García ◽  
Joaquín Gutíerrez ◽  
Andrea Rios

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.


Sign in / Sign up

Export Citation Format

Share Document