Gravitational forces are one of the four main types of forces that manifest themselves in all their diversity between different bodies both on Earth and beyond. In addition to them, electromagnetic, weak and nuclear (strong) are also distinguished. Probably, it was their existence that mankind realized in the first place. About the
force of gravity from the side of the Earth has been known since ancient times. However, centuries passed before a person realized that this kind of interaction takes place not only between the Earth and any body, but also between different objects. The first to understand how
gravitational forces work was the English physicist I. Newton. It was he who brought to everyone the now known
law of universal gravitation.Gravity force formula
Newton decided to analyze the laws by which planets move in the system. As a result, he came to the conclusion that the rotation of celestial bodies around the Sun is possible only if gravitational forces act between it and the planets themselves. Understanding that celestial bodies from other objects differ only in their size and mass, the scientist derived the following formula:
F = fx (m 1 xm 2 ) / r 2 , where:
- m 1 , m 2 are the masses of two bodies;
- r is the distance between them in a straight line;
- f is the gravitational constant, the value of which is 6.668 x 10 -8 cm 3 / g x sec 2 .
Thus, it can be argued that any two objects are attracted to each other. The work of the gravitational force in its magnitude is directly proportional to the masses of these bodies and inversely proportional to the distance between them, squared.
Features of the application of the formula
At first glance, it seems that using a mathematical description of the law of attraction is quite simple. However, if you think about it, this formula makes sense only for two masses whose dimensions are negligible compared to the distance between them. And so much so that they can be taken for two points. But what then, when the distance is comparable with the size of the bodies, and they themselves have an irregular shape? Divide them into parts, determine the gravitational forces between them and calculate the resultant? If so, how many points do you need to take to calculate? As you can see, not everything is so simple.
And if we take into account (from the point of view of mathematics) that the point has no dimensions, then this situation does seem hopeless at all. Fortunately, scientists have come up with a way to make calculations in this case. They use the apparatus of integral and
differential calculi. The essence of the method is that the object is divided into an infinite number of small cubes, the masses of which are concentrated in their centers. Then a formula is compiled to find the resultant force and a limit transition is applied, by means of which the volume of each constituent element is reduced to a point (zero), and the number of such elements rushes to infinity. Thanks to this technique, some important conclusions were obtained.
- If the body is a ball (sphere), the density of which is uniform, then it attracts to itself any other object as if its entire mass is concentrated in its center. Therefore, with some error, this conclusion can be applied to the planets.
- When central spherical symmetry is characteristic of the density of an object, it interacts with other objects as if all its mass is at the point of symmetry. Thus, if we take a hollow ball (for example, a soccer ball) or several balls inserted into each other (like dolls matryoshka), then they will attract other bodies in the same way as a material point would have, having their total mass and located in center.