Timeline for Where does the famous equation $F = G\cfrac{m_1m_2}{r^2}$ come from?
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17 events
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| Dec 22, 2023 at 17:24 | comment | added | Colin Pace | @terry-s, thanks for the comment! Here's the new question: hsm.stackexchange.com/questions/16039/…. | |
| Dec 22, 2023 at 2:49 | comment | added | terry-s | @ColinPace : thanks for your latest comment. Your latest question about relations between Newton's laws and Kepler's relationships is quite different than your original question. It would need to be put in a separate new question here, and I suggest you raise it as a new question. Hint, wikipedia 'kepler's laws' article is not correct on this. Newton's Principia of 1687 showed (Bk1 sec.11 props 57-69, esp 66) that in a system with >2 masses, deviations from keplerian motion would occur, though they might be rather small if one of the bodies was of much greater mass than the others. | |
| Dec 21, 2023 at 3:26 | comment | added | Colin Pace | @terry-s, thanks again for the comment and the link! I apologize about the unclear question. This quote might help clarify what I'm asking: “Isaac Newton showed in 1687 that relationships like Kepler’s would apply in the Solar System as a consequence of his own laws of motion and law of universal gravitation.” So, I’m asking about where this demonstration is and how he does it. (en.m.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion) | |
| Dec 20, 2023 at 23:51 | comment | added | terry-s | @ColinPace : not quite sure what you ask here, but you can find the masses of jupiter, saturn and earth relative to the sun, in Principia Bk 3 Prop 8 cor.2 . The method of calculation, explained in earlier sections, depends on their having satellite(s) (so no result for Venus or Mars). The result for the earth was of poor accuracy because moon's distance was known only by its parallax and the sun's v small parallax was hard to measure. Discussed in astronomy.stackexchange.com/questions/26024/… | |
| Dec 19, 2023 at 22:23 | comment | added | Colin Pace | @terry-s, thanks for the comment and the link! That's interesting information about the use of proportions. Given the difficulty of numerical techniques in the 17th century, please, do you know if Newton demonstrates the proportions of gravity between planets in "Principia" or does he only mention the theory? | |
| Dec 19, 2023 at 19:34 | comment | added | terry-s | @ColinPace : you'll find the old practices about proportions versus equations somewhat explained in this answer : hsm.stackexchange.com/questions/7288/who-first-derived-a-v2-r/… . The statements of proportion implicitly admit that there will be some constant of proportionality, but they would often be difficult or impossible to determine numerically by the techniques available in the 17th century. Use of proportions avoids having to handle their uncertain measures explicitly. The numerical value is the only part of the modern expression not in 'Principia'. | |
| Dec 18, 2023 at 13:09 | comment | added | Colin Pace | Thanks for the translation, @xxavier! That's a fascinating idea. | |
| Dec 18, 2023 at 12:43 | comment | added | xxavier | @ColinPace My translation: In today's usual explicit form, the law of gravitation wasn't formulated by Newton himself, but only in 1873, so 200 years later, by Alfred Cornu and Jean Baptistin Balle. Before that, Newton's law was used in its original form F prop, to m1, F prop. to m2, F prop. to r^-2, and without the definition of a 'gravitational constant'. In the German Wikipedia entry, you can find the two links [3] and [4]. | |
| Dec 18, 2023 at 12:35 | comment | added | Colin Pace | Thanks for the comment, @xxavier! I don't read German, but I see the force proportionality equations with m1, m2, and r^-2, so that might be another restatement of where the equation comes from in the prose. Do you have more insight into the image? I don't see the gravitational constant there, so it's still a mystery where it comes from. | |
| Dec 18, 2023 at 11:46 | comment | added | xxavier | From the Wikipedia entry 'Newtonsches Gravitationsgesetz' de.wikipedia.org/wiki/…: [img]i.imgur.com/mZ9Atqv.png[/img] | |
| Dec 17, 2023 at 23:40 | comment | added | Colin Pace | Encyclopedia Britannica mentions that the gravitational constant was first measured by Henry Cavendish in 1797-1798, more than a century after the publication of Mathematical Principles of Natural Philosophy. It appears Newton might not have been responsible for that aspect of the equation. | |
| Dec 17, 2023 at 21:32 | comment | added | J. Murray | @ColinPace No. Again, even writing the force law in the form we use today is a comparatively modern development. Vector notation, for example, was not fully fleshed out until the 1900’s. | |
| Dec 17, 2023 at 20:40 | vote | accept | Colin Pace | ||
| Dec 17, 2023 at 20:37 | comment | added | Colin Pace | Key sentences: 1. that the gravity tending towards all the planets is proportional to the matter which they contain. 2. and (by Law III) to every action corresponds an equal re-action ; therefore the planet B will, on the other hand, gravitate towards all the parts of the planet A. 3. The force of gravity towards the several equal particles of any body is reciprocally as the square of the distance of places from the particles. Does Newton mention the constant G in the passage? | |
| Dec 17, 2023 at 20:34 | comment | added | Colin Pace | Thank you, J. Murray, for the clear and detailed answer for the question of where the equation comes from in the prose and how it developed since. | |
| S Dec 17, 2023 at 20:22 | review | First answers | |||
| Dec 17, 2023 at 22:47 | |||||
| S Dec 17, 2023 at 20:22 | history | answered | J. Murray | CC BY-SA 4.0 |
![i.imgur.com/mZ9Atqv.png[/img]](https://i.imgur.com/mZ9Atqv.png[/img]){kind=link}