The second point is that the force of gravity of the Earth at its surface equally affects all material bodies located anywhere in the world. Right now you have the force of gravity, calculated according to the above formula, and you really feel it as your weight. If you drop something, it will, under the influence of the same force, accelerate to the ground at an accelerated rate. Galileo was the first to experimentally measure the approximate magnitude of the acceleration of free fall (see Equations of uniformly accelerated motion) near the surface of the Earth. This acceleration is denoted by the letter g.
For Galileo, g was simply an experimentally measured constant. According to Newton, the acceleration of free fall can be calculated by substituting in the formula of the law of universal gravitation the mass of the Earth M and the radius of the Earth D, remembering that according to the second law of Newtonian mechanics, the force acting on the body is equal to its mass multiplied by the acceleration. Thus, what for Galileo was simply the subject of measurement, for Newton becomes the subject of mathematical calculations or forecasts.
Finally, the law of universal gravitation explains the mechanical structure of the solar system, and Kepler’s laws describing the trajectories of planetary motion can be derived from it. For Kepler, his laws were purely descriptive in nature: the scientist simply generalized his observations in mathematical form, without having summed up any theoretical grounds for the formulas. In the great system of the world order according to Newton, Kepler’s laws become a direct consequence of the universal laws of mechanics and the law of universal gravitation. That is, we again observe how the empirical conclusions obtained at one level turn into strictly valid logical conclusions in the transition to the next stage of deepening our knowledge of the world.
The picture of the device of the solar system, resulting from these equations and integrating the earthly and celestial gravity, can be understood by a simple example. Suppose you are standing at the edge of a steep cliff, next to you are a cannon and a hill of cannonballs. If you simply drop the core from the edge of the cliff along the vertical, it will begin to fall down sheer and evenly accelerated. Its motion will be described by Newton’s laws for the uniformly accelerated motion of a body with acceleration g. If you now release the core from the gun in the direction of the horizon, it will fly – and will fall along the arc. And in this case, its motion will be described by Newton’s laws, only now they apply to a body moving under the influence of gravity and having some initial velocity in the horizontal plane. Now, over and over again charging the heavier nucleus into the cannon and shooting, you will find that,
Now imagine that you have shot so much gunpowder into the gun that the speed of the core is enough to fly around the globe. If you neglect the resistance of the air, the core, flying around the Earth, will return to the starting point exactly at the same speed with which it originally flew from the gun. What will happen next is understandable: the core will not stop at this and will continue to wind the circle around the circle around the planet. In other words, we get an artificial satellite that orbits around the Earth, like a natural satellite, the Moon. So we gradually switched from describing the motion of the body, falling solely under the influence of “earthly” gravitation (Newtonian apple), to describing the motion of the satellite (the Moon) in orbit, without changing the nature of the gravitational effect from “terrestrial” to “heavenly”.
The last question remains: does Newton tell the truth on the slope of his days? Did it really happen that way? No documentary evidence that Newton really dealt with the problem of gravity in the period to which he attributes his discovery is not today, but documents tend to be lost. On the other hand, it is a well-known fact that Newton was a very unpleasant and extremely meticulous person in everything that concerned his priority in science, and it would be very much in his nature to obscure the truth if he suddenly felt that his scientific priority, then threatens. Dating this discovery in 1666, while the scientist actually formulated, wrote down and published this law only in 1687, Newton, in terms of priority, gained an advantage for more than two decades.
I admit that one of the historians from my version will have a stroke, but in fact this issue does not bother me much. Be that as it may, the apple of Newton remains a beautiful parable and a brilliant metaphor that describes the unpredictability and mystery of the creative cognition of nature by man. And whether this story is historically reliable is already a secondary issue.