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11

"Simply modifying" Newtonian gravity to have it spread at finite speed does not work if the finite speed is the speed of light. It was attempted by Laplace in his Celestial Mechanics (1799), who found that the planets will promptly fly off their orbits and the Solar system will disintegrate in seconds, unless the propagation speed is $7×10^6$ times greater ...


11

From the comments, it seems you are really asking about the fact that (neglecting air friction) different objects fall with the same acceleration. Before the concept of acceleraton was fully understood, scholars would phrase this differently: different objects take the same time to fall a given distance. John Philoponus, in the 6th century, is said to have ...


11

The idea, yes, Aryabhata speculated about something like that as early as c. 500 AD, Brahmagupta called it gurutvākarṣaṇ. So did Kepler, at about the same time as Ahmad Baba al Massufi (late 1500-s), and much less vaguely. Russo even ascribes the idea to Hipparchus (c.150 BC), although this is far fetched. Even the inverse square law for gravity predates ...


9

Riemann discussed a "unified field theory", including light, electromagnetism and gravity, in the unpublished paper Neue Mathematische Principien der Naturphilosophie (New Mathematical Principles of Natural Philosophy, 1853, the title obviously alludes to Newton's), and in Gravitation und Licht (Gravity and Light), the last section of his Fragmente on ...


8

Curiously, Kepler thought that gravity falls as $1/r$, and he had a peculiar ether vortex theory borrowed from Gilbert's work on magnetism, to support it. But he argued that the intensity of light falls as $1/r^2$ along the same lines that others later applied to gravity: "there is as much light in the narrower spherical surface, as in the wider, thus it is ...


8

There are several major ideas that went into general relativity: finite speed of gravity propagation, not necessarily Euclidean geometry of space, identification of inertia and gravity, mechanics as geometry, and uniformity of physical laws in all coordinate frames, even accelerated ones (general covariance). The last two ideas are specifically Einstein's, ...


7

From: Discourses and Mathematical Demonstrations Relating to Two New Sciences (Italian: Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze), published in 1638. See: Engl.transaltion by Henry Crew and Alfonso de Salvio (1914): A motion is said to be equally or uniformly accelerated when, starting from rest, its momentum (celeritatis momenta) ...


7

It is a quite long story and not a "one-shot" discovery, as suggested by the "apple tale". Two critical sources to be usefully read are : Alexandre Koyré, Newtonian studies, Cambridge (Mass.) 1965 : Harvard University Press; I.Bernard Cohen, The Newtonian revolution : With illustrations of the transformation of scientific ideas, Cambridge 1980 : Cambridge ...


6

The formula was a commonly discussed hypothesis at that time (Ch. Wren, Hooke, Halley). First attempt to test the formula was made when Newton was a young student in Cambridge: he compared acceleration from gravity on the Earth surface (easy to measure by observing falling apples for example:-) with acceleration of the Moon on its orbit (easy to compute). ...


6

This answers (with some explanation and references) the two questions, (a) Were any concrete corrections proposed (in the 1740s, to the law of gravitation)? and (b) Where can one read about it? (a) Clairaut (but not Euler or d'Alembert) proposed in 1747 a correction to the inverse-square law, that is, an additive term depending on a higher power of the ...


6

I am not familiar with physics textbooks of 18 century, so I do not know the answer to the question. However I want to add a comment which is too long for the comment window. (The system does not allow me to post a comment of this length.) Principia actually contains both derivations. Of the inverse square law from Kepler laws and of the Kepler laws from ...


6

See Aristotle's Natural Philosophy. According to Aristotle, change in the natural world can be : [either] in accordance with the nature of the object — in which case the change is natural (phusei) or according to nature, or can happen in the face of a contrary disposition on the part of the nature of the entity — in which case the change is forced or ...


5

Actually what Einstein proposed was not a perpetual motion machine but was an experiment design to take down the Uncertainty principle. So Einstein design an experiment known as "Einstein's box". It was a thought experiment. He said that consider a box (ideal one) lined up with mirrors so that it contains light indefinitely. Also there is a shutter (ideal ...


5

Lagrange (1736-1813) in 1777, followed by Laplace (1749-1827) in 1782, was the first to introduce the scalar gravitational potential.1 Lagrange's paper, Remarques générales sur lemouvement de plusieurs corps qui s'attirent mutuellement enraison inverse des carrés des distances, was read at the Academy of Berlin on 20 October 1777.2 So Weinberg is correct ...


5

'Did the Idea of Universal Gravitation predate Newton?' (The question went on to mention the books of Ahmed Baba.) I had a look to see whether Baba's work is available in any way online, but found nothing. Could the questioner point to any source, it would help discussion? Commentators who discuss early origins of gravitational ideas, perhaps as a ...


4

See Perihelion precession of Mercury: Mercury deviates from the precession predicted from these Newtonian effects. This anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem in celestial mechanics, by Urbain Le Verrier.


4

Einstein also considered weightlessness in free fall as a manifestation of equivalence between inertial forces and gravity. Although simple drum-rope elevators were constructed as early as 236 BC (by Archimedes) they started to spread after 1854, when Otis gave a dramatic demonstration of his safety catch invention by cutting holding ropes while people were ...


4

The idea that gravity acted with an inverse square relation was not a "done deal" because Newton or Hooke said so. On Nov 15, 1747 "Clairaut, at a public session of the [French] Academy, announced in rather pompous phrases that the Newtonian Theory of gravity was false!” One of the boldest attempts to reconcile the observed and theoretical descriptions of ...


4

The following stories show that the inverse square law was widely discussed at the time of Newton. First story is about Hooke. He wrote to Newton proposing to determine "how a point will be moving under the inverse square law". Specifically he discussed the example of an object with some initial velocity (NOT directed towards the center) how would it move ...


4

The terminology of inertial and gravitational masses does not appear until Einstein, and had to do with his transitioning from classical mechanics to general relativity, see Development of gravitational theory. In classical mechanics it is more natural to think of the same $m$ entering both $F=ma$ and $F=G\frac{Mm}{r^2}$ than about two separate masses which ...


3

Hooke did propose the inverse square law to Newton, and even the program of ”compounding the celestiall motions of the planetts of a direct motion by the tangent & an attractive motion towards the central body.” These suggestions from Hooke ”occasioned my findings” on planetary motion, Newton admitted. For more details, see my summary of Ofer Gal’s book ...


3

Not really an answer, but a few relevant remarks: Newtonian gravity is inconsistent with special relativity in various ways (e.g., it describes an instantaneous action at a distance and "instantaneous" can only make sense with respect to a given reference frame). There are, also, physical reasons to believe that gravity should produce a redshift on light ...


3

The aristotelian theory affirmed that there was a natural 'affinity' between substances that were alike. Thus, a stone fell towards the ground because of a natural, telluric affinity, and fire/smoke rose to the sky because of a natural affinity, too...


3

In Newton's time distance to the moon was not a problem: since the ancient times this distance (in terms of the Earth radius) was measured using parallax. Newton used the value 60 for the ratio of Moon's orbit to the Earth radius. This is close to the value 59 which can be found in Ptolemy. Newton's problem was with Earth radius which was not known to young ...


3

As Newton said he stood on the shoulders of giants. One of those giants was Kepler who found that the periodicity of a planetary orbit was related by $$ T^2~\propto~r^3. $$ This is Kepler's third law. Newton realized with the second law $\vec F~=~m\vec a$ of motion that centripetal force is $$ \vec F~=~m\omega^2\vec r. $$ Newton hypothesized there was some ...


3

Newton probably believed that his theory is correct and exact. He could not know of the very small anomaly of Mercury. But there were some much more serous problems. Gravity law and the laws of motion only give a law (a differential equation) of motion. The ultimate test of the theory would be solving this equation and comparing the result with ...


3

Galileo knew that, if a stream of water is ejected from a pipe held horizontally, the stream would follow the shape of a parabola. Mathematically, that means that the motion of the water is linear (uniform) horizontally, and quadratic vertically. And that leads to the realization that the motion horizontally and the motion vertically can be treated ...


3

Not quite. This is what Galileo stated in the Two New Sciences (1638) through his character Sagredo (honest inquirer open to arguments from both sides): "But I, Simplicio, who have made the test can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing ...


2

According to Carl Boyer, in his text A History of Mathematics, it is Simon Stevin who is credited with the Law of the Inclined Plane, as justified by his familiar "wreath of spheres" diagram. The law itself had been stated previously by Jordanus Nemorarius. It is interesting to note that, again according to Boyer, Stevin observed and published Galileo's ...


2

You are on to something here. Section X of Book 1 of Principia discusses the motion of particles constrained to curves or surfaces under the action of central forces (that is forces directed towards a fixed point, the center, with the magnitude depending only on the distance to it). This is an example of constrained dynamics, now associated with "D'Alembert'...


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