How Newton derived his law of universal gravitation

[@alexanderherbertkurz]

Thank you so much for this. I'd like to find more videos like this which explain how physicists discovered stuff, based on what was known at their times.

[@eriklokensgard7487]

Thanks for explaining the pieces of the puzzle that Newton used, like the shadow of the Earth on the moon during eclipses. Excellent video!

[@adamfarrell4108]

thank you! its 3:08 am and my assignment is due first period tomorrow. you have saved me!

[@katalyst4stem]

@ 0:30 Henry Cavendish, in the late 18th century, conducted experiments using a torsion balance apparatus to measure the gravitational force between masses. His work allowed for the determination of the numerical value of the gravitational constant (G) and indirectly led to the determination of the acceleration due to gravity on Earth's surface (g).

[@randomsmall-governmentguy2221]

Not going to lie. The punchline blew me away. What an unbelievably simple, yet brilliant, train of thought!

[@alexanderkruszewski7306]

“60? Now, where have I seen that 60 before…”

[@nikolaostsoulos9498]

Imagine being so gifted that you come up with all that while being bored in isolation

[@infinityinfinitesimal4393]

This is what I was looking for since months. Thank you a lot mam ❤️

[@winstondearmas1833]

This is wonderful! May I ask how you learned that this was his process? I'd love to uncover a resource to get into HOW Newton thought and arrived at his conclusions!

[@sheep4065]

His papers were released by one of his decendents i believe

[@anarchyxskamfull]

Please make more videos like this

[@BakrBakr1986]

Beautiful Thank you so much Really enjoyed of this video I like the way she explained things Very educated and smart Really impressed Thank you This is so useful for my research 👍

[@rishabhrockstar5739]

I am literature graduate, but loved this one

[@uniqueone4097]

The things you Explained were Magnificent but I have a Doubt that how did Newton Measured the gravitational constant value

[@pedrocapitao9268]

He did not, it was done in the XVIII century by Henry Cavendish

[@alexjohnward]

He actually thought it would be impossibly small to measure.

[@JasonLonon]

You didn't understand the video then, it never claimed that he measured the gravitational constant.

[@Vermllon]

such a nice informations that you cant find anywhere else . Thank you .

[@savage_rishabh2255]

what about m1m2??

[@silliestputty]

m sub 1 and m sub 2 are values given from the different masses involved. this is for a two body interaction.

[@ymengineer7200]

Very clearly explained thank you

[@darkphysics4561]

How could Newton have known that g was 9.8 [m/s^2] or 32 [ft/s^2]? What is your source on that?

[@JasonLonon]

I believe Galileo established that with his work with inclined planes. You can slow down the 'fall' enough that it can be measured, and then extrapolate based on the angle and the trigonometry.

[@kenancaymaz]

@@JasonLonon You're right; Galileo’s work with inclined planes was groundbreaking in establishing that gravitational acceleration could be observed as a constant by slowing the fall. However, his method could only demonstrate that gravitational acceleration was uniform. This type of extrapolation wouldn’t yield the actual value of g, as it doesn’t account for the effect of the moment of inertia, which wasn’t mathematically developed until after Newton’s time.

[@maybeinactive]

can someone pls explain to me why the centerpital acceleration of the moon compared to acceleration of something falling next to the surface of the earth gives us the distance between them?

[@aniket385]

Coz like apple , the moon is also falling on earth

[@K-xor]

if distance=R (radius of the earth), the acceleration=g. If distance=r, acceleration=g/(r^2)

[@2eanimation]

It doesn't give us a distance, it's a ratio between accelerations. The 60^2 is dimensionless("has no unit"). In the video, g / a is being calculated. Using Newton's law, g = G * M / r^2 [ ~= 9.8 m/s^2 -> what Newton knew] a = G * M / (60 * r)^2 [ = v^2 / (60 * r) = w^2 * (60 * r) = (2π/T)^2 * (60 * r) -> what Newton used] M is earth's mass, r is earth's radius, 60*r is the distance to the moon. Where's m2 you ask? F[orce] = m * a = G * M * m / r^2 -> divide both sides by m. m could be anything. For g, it could be your mass or an apple near earth's surface. For a, moon's mass or something else orbiting the earth at that distance. g / a = (G * M / r^2) / (G * M / (60 * r)^2) = 60^2 Earth's mass doesn't change(much anyway), hence Newton concluded that gravitational force(which wasn't named like that back then) is proportional to 1/r^2.

[@alexjohnward]

Gravity becomes weaker as you move further away from Earth. It would be better to compare two apples though.

[@johnnym6700]

How do you know what m1 and m2 are? Surely you need F to determine that? Oops m1, m2 and F are in the same equation!

[@GOVTEXAMAspirant-h7h]

From orbital period of the moon you can get mass of earth

[@richdobbs6595]

I'm sorry, this doesn't seem persuasive on about how he derived the law. It seems like a factoid that he used to confirm the law that he had derived by basic reasoning. Why is it linear in the mass of the first body, the second, and inversely proportional to the radius squared? Just having one confirmation of a relationship isn't particularly persuasive. It seems to me more likely that he derived the linearity in the masses by some basic thought experiments that I expected that you would provide! And the inverse radius squared relationship logically comes from the concept that each mass is radiating something that diminishes with the surface area as it propagates away from the center. He probably compared this idea with Kepler's law and decided it was compatible, so he was on the right track. The moon biz was just an argument he used once he had already derived the law, and was trying to convince others in a compact way.

[@richdobbs6595]

Dredging up an idea from ancient history - ie high school and freshmen physics, I think linearity in the masses is required by thinking about dividing up a mass into two masses that are right next to each other. Do they fall together, or do they pull apart? Since this is just a thought experiment, if the law is right they should fall together.

[@2eanimation]

(1) A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. (2) F = m*a (3) Fa->b = Fb->a Planets accelerate or else, they wouldn't change velocity; read as "direction of speed". If (1) holds, there must be a force, which requires an equal counterforce due to (3), a1 * m1 = a2 * m2. Changing m1 with constant a1 and m2 changes a2, and vice versa. This symmetry reasoning leads to F ~ m1 * m2. F ~ 1/r^2 has been shown in the video. It was probably a nice feeling that his law coincides with Kepler. Edit: It was strange at that time to think about "masses radiating some magical force". Newton himself refused to offer an explanation. "That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it." - Newton to Bentley. For us, it's almost commonplace to think and talk about gravity. Wasn't the case back then.

[@richdobbs6595]

@@2eanimation You sort of provided some reasoning about linearity in the masses by a symmetry argument, but there are better arguments related to composite objects not being pulled apart, etc. But no place in the video did it explain the source of the inverse square law, nor connect it to other inverse square laws like illumination or sound. That Newton didn't commit to what the mediating mechanism consists of does not imply that he didn't think that there was some sort of mechanism that behaved as if it radiated out. The jump to an inverse square law from Kepler's law never seemed to be well explained in any class I took.

[@2eanimation]

​@@richdobbs6595 IIRC, this was in essence Newton's reasoning, or at least that's what Pearson's physics text book("Physik Lehr- und Übungsbuch") says, including the source of the inverse square law(seeing 60^2 and shouting "Eureka!"). I guess he was(he must have been) familiar with Kepler's laws, thought about it and compared it with similar, already known phenomena under the inverse square law. If he took that into account while developing the gravitational law? Maybe. He might have. Though he also knew that being depending on known "facts" can lead to further fallacies. As you suggested, he might have seen the 60^2 and thought to himself "close enough, let's give it a run". If he thought about some radiation mechanism is up for speculation. This video lacks some explanation, yes, though it doesn't need to show the relationship to other inverse square laws. That's a nice to know/show, but isn't needed for what is intended, "How Newton derived his law of universal gravitation".

[@agcrazy721]

That’s why the equations are off by over 90% when they go galactic 😂 but but dark matter!!!

[@johnnym6700]

You got it wrong. g=9.81m/s/s not 9.8 go back to school!

[@friedhegg8874]

You are dumb lol

[@StephenOdupute]

It's just a little difference, so that 1 can be ignored

[@kaia-di4pq]

​@@StephenOduputenot to mention g isnt constant anyways so it doesnt even matter

[@noracism7382]

Came after the three body problem series 😂😂😂

[@IgnacioVerne]

Me too