The Missing Factors In Newton's Law | Our Ignorance About Gravity

 The Missing Factors In Newton's Law | Our Ignorance About Gravity

It’s well known that gravity pulls two objects together with a force proportional to the mass of one, times the mass of the other, divided by the square of the distance between them. Anyway, this equation is called Newton’s law of universal gravitation, it’s taught to schoolchildren the world over, and it predicts the motions of the planets and moons and asteroids in our solar system with incredible precision.

INTRO

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THE MISSING FACTORS 

 However, Newton’s law of universal gravitation isn’t actually universal:  first, we know that when the gravitational force in question is really strong, Newton’s law is just not wrong but some missing factors. 

And second, we know that when the gravitational force in question is really weak, we don’t know whether it’s right or wrong because gravity gets too weak to measure.

We can't say that newton's third law of motion is incorrect but we can say that it has some missing factors. This is because these types of laws were invented hundreds of years ago and things have been changed. Moreover, Newton was a human after all and humans can be mistaken and can be corrected again.

Only in between (like, on the scale of the solar system), do we know that the “law” of gravitation reasonably applies. Ok, but if Newton’s Law of gravitation has been confirmed so accurately by the motions of planets and moons, how could it be wrong at a different scale? 

GENERAL RELATIVITY

Well, the earth looks flat when you’re relatively close to the ground, but zoom out and it looks round, or zoom in and it looks bumpy; the“law” describing the shape of the earth is different at different scales. 

Similarly, when the force of gravity is really strong  (like near a black hole), gravity is better described by the mathematics of general relativity, and only when the forces in question get a bit weaker (for things farther apart with less mass) does gravity start to match up with Newton’s law of gravitation.

Both the moon and earth posses gravity. But Earth is never attracted to the moon. Why? This is because the mass of the earth is much larger than the moon, but there is one more reason that is newton's third law of motion " to every action there is an equal and opposite reaction which is the same here.

But when you go even weaker (with objects even farther away or even less massive ), we get to a point where we don’t know whether Newton’s law of gravitation applies anymore. And yet, even many physicists appear to be ignorant about our ignorance about how gravity works when it’s weak - or at least, they ignore our ignorance. 

FORMULA OF GRAVITATION WITH AN EXAMPLE

It’s common to blindly apply -G m M/r^2 to decidedly non-astronomical objects, for which we haven’t tested gravitational attraction very well at all: if you have two pieces of tape, you can calculate the gravitational force that they in principle exert on each other according to the law of universal gravitation.

But it’s far too ridiculously small for you to ever have the remotest chance of noticing any effect whatsoever, let alone actually checking that the attraction between them follows the law of universal gravitation as you move the bits of tape farther apart.

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In contrast, if you stick the two pieces of tape together and then pull them apart, they’ll exchange some electric charge and then measurably attract each other; an electrical attraction which is a million billion times stronger than the predicted gravitational attraction.

And whose strength has allowed us to confirm Coulomb’s law of electrical attraction to a very very very high degree of accuracy? So it makes sense to apply Coulomb’s law of electrical attraction to objects at normal human scales.

PRACTICAL REQUIREMENTS FOR TESTING LAW OF GRAVITATION

 But testing Newton’s law of gravitation at these scales requires very delicate experiments, like very very sensitive oscillating pendulums that oscillate slightly differently if there’s a heavy mass nearby (and can thus measure the gravitational force with great precision), or incredibly finely-controlled lasers that simultaneously levitate and measure the positions and forces on tiny little beads of glass.

These can measure ridiculously faint forces, like zepto newtons. And so far, for objects a meter apart, we’ve only confirmed that the gravitational attraction between them follows the law of universal gravitation to within around one-hundredth of a percent. 

Which is a trillion times less precise than our knowledge of the equivalent law for electricity. And our grasp on gravity gets worse the smaller you go.

EXISTING EXPERIMENTAL UNDERSTANDING

 Our existing experimental understanding of short-distance gravity is so bad that gravity at the scale of the atomic nucleus could actually be as much as a quadrillion times stronger than Newton’s law of gravitation predicts! 

That’s a HUGE range; it would be like not knowing whether the moon pulls on us with the force of a hundred billion billion tons of rock, or the force of a fruit-fly, Or, put another way.

DEPENDENCE OF GRAVITATION ON ATOMIC NUCLEUS 

At the scale of an atomic nucleus, the law of gravitation could depend instead on the square of one or both masses, or the square root, or the inverse cube of the distance, or G could be a million billion times bigger, or a bunch of other possibilities, and we wouldn’t even know it. 

. The fact that there’s so much uncertainty about gravity at short distances means that a lot of interesting truths about our universe could be hiding under our very noses! 

One possibility, for example, is that there are not just 3 dimensions of space, but an extra one that only the gravitational force can travel through, which loops back on itself at the scale of micrometers or smaller. 

DIMENSIONS

Just like how the surface of a hair is technically 2-dimensional but hairs look one dimensional from afar, this would mean that at distances much much longer than a micrometer. 

Gravity would act as if space had 3 dimensions and follow a roughly inverse square law (which is what Newton’s law of gravitation ), while at distances much shorter, it would behave as if space had 4 dimensions and follow more of an inverse cube law (which we haven’t ruled out at particularly small scales).

However, as we’ve made increasingly precise measurements of the gravitational attraction between small things, we haven’t yet discovered any gravitational forces inconsistent with Newton’s law of gravitation. 

So it may be that -G m M over r squared does describe the strength of gravity for very very short distances, but our uncertainty is still very big, and it remains pretty crazy to blindly apply Newton’s law of gravitation to things like an electron and proton in a hydro generator. 

Frequently Asked Questions 

1. What is Isaac Newton famous for?

Although Isaac Newton is well known for his discoveries in white light composition and his mathematics invention calculus, it is his formulation of the three laws of motion—the basic principles of modern physics—for which he is most famous.

2. What are the inventions of Isaac Newton?

• Reflecting telescope
• Newtonian telescope
• Newton's method

3. Who was Isaac Newton?

Isaac Newton was an English scientist (1642-1726/1727 ). Newton is now considered a unit, SI unit of force named after Isaac Newton

                           

4. How did Newton die?
Newton died in his sleep in London on 20 March 1727. After his death, Newton's hair was examined and found to contain mercury, probably resulting in mercury the cause of death.

5. Who invented gravity?

Sir Isaac Newton was an English mathematician and physicist who lived from 1642-1727.  Newton discovered Gravity when he saw a falling apple while thinking about the forces of nature.

6. Is Isaac Newton the smartest person ever?
Sir Isaac Newton is considered one of the most influential scientists in history. Even Albert Einstein said that Isaac Newton was the smartest person who ever lived. Newton is considered the father of physics.

7. Can we make anti-gravity?
Besides the long-running Anti Gravity column in Scientific American, however, there is no such thing as anti-gravity. Gravity is a force arising among any two masses in the universe. As of yet, no technology exists to neutralize the pull of gravity.

8. What is the value of G?
Its value is 9.8 m/s2 on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s2. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location. There are slight variations in the value of g about the earth's surface.

9.Why the value of g is constant?
The gravitational constant is the proportionality constant that is used in Newton's Law of Gravitation.  It is also known as Newton's Constant. The value of the gravitational constant is the same throughout the universe. The value of G is different from g, which denotes the acceleration due to gravity.

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