The law of universal gravitation opened by Newton in 1666 and published in 1687 says that all bodies having weight are attracted to each other. The mathematical formulation allows not only to establish the fact of a mutual attraction of bodies, but also to measure its force.
Instruction
1. To Newton many scientists suggested about existence of universal gravitation. From the very beginning it was obvious to them that the attraction between any two bodies has to depend on their weight and weaken with distance. Johann Kepler, the first described elliptic orbits of planets of the Solar system, considered that the Sun attracts planets with a force, inversely proportional to distance.
2. The newton corrected Kepler's error: he came to a conclusion that force of a mutual attraction of bodies is inversely proportional to a distance square between them and is directly proportional to their masses.
3. Finally the law of universal gravitation is formulated so: any two bodies having weight are mutually attracted, and force of their attraction is equal to F = to G * ((m1*m2)/R^2) where m1 and m2 — the mass of bodies, R — distance between bodies, G — a gravitational constant.
4. The gravitational constant is equal to 6.6725*10^ (-11) m^3 / (kg*s^2). This extremely small number, so gravity — one of the weakest forces in the Universe. Nevertheless it keeps planets and stars in orbits and in general forms shape of the Universe.
5. If the body participating in inclination has approximately spherical shape, then the distance of R should be measured not from its surface, and from the center of masses. The material point with the same weight which is precisely in the center would generate just the same force of an attraction. In particular, it means that, for example, when calculating force with which Earth attracts the person standing on it the distance of R is equal not to zero, but Earth radius. Actually it is equal to distance between the center of Earth and the center of gravity of the person, but this difference can be neglected without loss of accuracy.
6. The gravitational attraction is always mutual: not only Earth attracts the person, but also the person, in turn, attracts Earth. Because of a huge difference between the mass of the person and mass of the planet it is imperceptible. Similarly and when calculating trajectories of spacecrafts usually neglect that the device attracts to itself planets and comets. However if the mass of the interacting objects are comparable, then their mutual attraction becomes noticeable for all participants. For example, in terms of physics it is not quite true to say that the Moon rotates around Earth. In fact the Moon and Earth rotate around the general center of masses. As our planet is much more natural satellite, this center is in it, but nevertheless does not coincide with the center of Earth.