Gravitational forces are one of the four main types of forces that manifest themselves in all their diversity between various 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. The force of attraction from the Earth has been known since ancient times. However, whole centuries passed before man realized that this kind of interaction occurs 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 deduced the now well-known law of universal gravitation.
Gravitational force formula
Newton decided to analyze the laws by which the planets move in the system. As a result, he came to the conclusion that the rotation of the heavenlybodies around the Sun is possible only if gravitational forces act between it and the planets themselves. Realizing that celestial bodies differ from other objects only in their size and mass, the scientist deduced the following formula:
F=f x (m1 x m2) / r2, where:
- m1, m2 are the masses of two bodies;
- r – distance between them in a straight line;
- f is the gravitational constant, the value of which is 6.668 x 10-8 cm3/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 applying the formula
At first glance, it seems that using the mathematical description of the law of attraction is quite simple. However, if you think about it, this formula makes sense only for two masses, the dimensions of which are negligible compared to the distance between them. And so much so that they can be taken for two points. But what about when the distance is comparable to 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 should be taken for calculation? As you can see, it's not that simple.
And if we take into account (from the point of view of mathematics) that the pointdoes not have dimensions, then this situation seems completely hopeless. Fortunately, scientists have come up with a way to make calculations in this case. They use the apparatus of integral and differential calculus. 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 drawn up for finding 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 tends 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 any other object to itself as if all its mass is concentrated in its center. Therefore, with some error, this conclusion can be applied to planets as well.
- When the density of an object is characterized by central spherical symmetry, it interacts with other objects as if its entire mass is at the point of symmetry. Thus, if we take a hollow ball (for example, a soccer ball) or several balls nested into each other (like matryoshka dolls), then they will attract other bodies in the same way as a material point would do, having their total mass and located in center.
