On the slope of his days, Isaac Newton told how it happened: he walked through the apple orchard in the estate of his parents and suddenly saw the moon in the daytime sky. And then, right before his eyes, an apple came off the branch and fell to the ground. Since Newton was at the time working on the laws of motion (see Newton’s laws of mechanics), he already knew that the apple fell under the influence of the gravitational field of the Earth. He also knew that the Moon does not just hang in the sky but rotates in an orbit around the Earth, and therefore it is affected by some kind of force that keeps it from falling out of orbit and flying away straight ahead, in open space. Then it occurred to him that perhaps it was the same force that made the apple fall to the ground, and the moon stayed in a near-earth orbit.
To fully appreciate the full brilliance of this insight, let’s briefly return to its prehistory. When the great predecessors of Newton, in particular, Galileo, studied the uniformly accelerated motion of bodies falling on the surface of the Earth, they were sure that they were observing a phenomenon of purely terrestrial nature – existing only near the surface of our planet. When other scientists, for example, Johannes Kepler (see Kepler’s Laws), studied the motion of celestial bodies, they believed that in the celestial spheres there are very different laws of motion than the laws governing the movement here on Earth. The history of science shows that almost all the arguments concerning the motion of celestial bodies to Newton were basically that the celestial bodies, being perfect, move in circular orbits because of their perfection since the circle is an ideal geometric figure. Thus, in modern terms, it was believed that there are two types of gravity, and this view has been steadily entrenched in the minds of people of that time. Everyone believed that there is terrestrial gravity acting on an imperfect Earth, and there is a heavenly gravity acting on perfect skies.
The insight of Newton was precise that he combined these two types of gravity in his consciousness. From this historical moment, the artificial and false separation of the Earth and the rest of the universe ceased to exist.
The results of Newtonian calculations are now called the law of universal gravitation of Newton. According to this law, between any pair of bodies in the universe, there is a force of mutual attraction. Like all physical laws, he is clothed in the form of a mathematical equation. If M and m are the masses of two bodies, and D is the distance between them, then the force F of the mutual gravitational attraction between them is:
F = GMm / D2
where G is the gravitational constant determined experimentally. In SI units, its value is approximately 6.67 × 10-11.
Concerning this law, several important observations need to be made. First, its action explicitly applies to all physical material bodies in the Universe without exception. In particular, now you and this book are experiencing equal in magnitude and opposite in the direction of the forces of mutual gravitational attraction. Of course, these forces are so small that they can not be fixed even by the most accurate of modern instruments – but they really exist, and they can be calculated. In the same way, you experience a mutual attraction with a distant quasar, distant from you for tens of billions of light years. Again, the forces of this attraction are too small to be instrumentally recorded and measured.