On the slope of his days, Newton admitted how everything really happened. He was walking through the apple orchard of his parents and suddenly saw the moon in the daytime sky. And then, before his eyes, an apple comes off a branch and falls to the ground. At this time, Newton worked on the law of motion, he already knew that the fall of the apple is closely connected with the action of gravity. He also knew that the Moon rotates in orbit, and does not hang in the air, that it is influenced by a certain force that holds it in this orbit, preventing it from falling off the trajectory and into outer space. It was at the time of the fall of the apple that Isaac realized: both the apple and the moon stay in orbit are forced by one force. Newton's law of gravity was close to discovery.
Let's look into the background. Galileo and other Newton's predecessors study the motion of bodies (equally accelerated) falling to the ground. It has been suggested that this phenomenon is purely natural and exists only at the surface of the globe. Kepler, with his like-minded people, argues that in the realms of heaven the laws are different, not at all the ones that control the movement on Earth. All arguments come down to the fact that heavenly bodies , by virtue of their perfection, move in orbits again, by virtue of their perfection. In other words, gravity was divided into two types: earthly (imperfect) and heavenly (perfect).
And Newton's insight combined both types of gravity in his mind. We can say that this moment became historical, combining the separation of false (Earth) and artificial (Universe).
The result of Newton’s calculations now sounds like this: the law of universal gravitation. Its definition says: between a pair of bodies in the entire Universe there is a force of mutual attraction. The law is in the form of an equation:
F = GMm / D2,
M and m - mean the masses of one and the second body, D - the distance between these bodies, F - the force of gravitational attraction. G here is a constant, determined experimentally and, if expressed in SI units, is 6.67 × 10–11.
But the law of gravity requires a few comments. Firstly, its effect extends to all material physical bodies located in the Universe. For example, a book that you read, like yourself, is also subject to the force of mutual gravitational attraction, equal in magnitude, but opposite in direction. The force is too small even for sensitive instruments, but it really exists and can even be calculated. Another example is the mutual attraction between you and the infinitely distant quasar, which is billions of light years distant. These attractive forces are smaller than in the previous example, but they exist.
Secondly, the earth's gravitational force at the surface affects all bodies to the extent possible and at any point. At this moment, the same force acts on you, which can be calculated according to the formula indicated above, but physically you feel it as your own weight. Drop something. And this thing will rush to the ground equally accelerated. Galileo was the first to measure experimentally the approximate value of the acceleration of fall near the earth's surface. Remember the letter g from the equation? But for Galileo, this was an experimentally measured constant, and according to Newton this value (acceleration at free fall) can be found by substituting the Earth's mass (M) and its radius (D) in the formula. Galileo’s subject of measurement becomes Newton’s mathematical calculations and predictions.
Thirdly, the law of gravity shows and explains the structure of our system (the Solar), Kepler’s laws that reveal the trajectory of the planet’s motion can be deduced from it. For Kepler himself, these laws were only descriptive - scientists simply generalized observations in mathematical forms. In the great system of world order, according to Newton, the derived Kepler's laws are a direct consequence of the laws of mechanics and the law of universal gravitation. And again, we are witnessing the transformation of empirical conclusions obtained at the level of one into clear logical substantiated conclusions and the transition to the level of another.
Was Newton truly told in her declining years? Did he not cunning, talking about his discovery? There are no documents evidencing or refuting that Newton dealt with the problem of gravity during that period and indeed himself, no. And the documents, as you know, tend to get lost. And it is also universally recognized: Newton was an unpleasant person and terribly meticulous in that he at least somehow related to fixing priorities in science for him. Therefore, to obscure the truth, sensing the slightest threat, was precisely in his character.
That will remain the question: why, having published his law of universal gravitation in 1687, he dated its discovery in 1666? What separated these 20 years?