Gravitational forces are one of the four main types of forces that are manifested in all its diversity between the different bodies on Earth and beyond.Also they still emit electromagnetic, weak and nuclear (strong).Perhaps it is their existence mankind has realized in the first place.The force of gravity from the Earth has been known since ancient times.However, for centuries passed before people realized that this kind of interaction occurs not only between the Earth and any body, but also between different objects.The first person to understand how the gravitational force, was an English physicist Isaac Newton.It was he who brought all now known law of universal gravitation.
Formula gravitational force
Newton decided to analyze the laws according to which there is a movement of the planets in the system.As a result, he concluded that the rotation of celestial bodies around the Sun is only possible if between him and the planets by the gravitational forces acting.Realizing that the heavenly bodies from other objects differ only in their size and mass, scientists have deduced the following formula:
F = fx (m1 x m2) / r2, where:
- m1, m2 - is the mass of the two bodies;
- r - the distance between them in a straight line;
- f - gravitational constant, the value of which is equal to 6.668 x 10-8 cm3 / g x s2.
Thus, it can be argued that any two objects are attracted to each other.The work of the gravitational force of its size is directly proportional to the masses of the bodies, and inversely proportional to the distance between them squared.
Features of the application of the formula
At first glance, it seems that the use of the mathematical description of the law of attraction is quite simple.However, if you think of it, this formula is valid only for the two masses whose dimensions are compared with the distance between them is negligible.So much so that they can be taken for two points.Then what to be when the distance is comparable to the size of the bodies, and they are irregular in shape?Split them apart, to determine the gravitational force between them and calculate the resultant?If so, how many points should be taken for the calculation?As you can see, it is not so simple.And when you consider (mathematically) that the point size does not, then that provision and all seems hopeless.Fortunately, scientists have invented a way to make payments in this case.They use the machine integral and differential calculus.The essence of the method is that the object is broken down into an infinite number of small cubes, the masses are concentrated at their centers.Then the formula for the prepared resultant force and applies the limiting process by which the amount of each component is reduced to a point (zero) and the amount of these elements tends to infinity.With this reception managed to get some important conclusions.
- If the body is a ball (sphere) whose density is uniform, it attracts every other object as if all its mass concentrated at its center.Therefore with an error, you can use this output, and to the planets.
- When the density of the object is characterized by a central spherical symmetry, it interacts with other objects as if at the point of symmetry is the whole mass.Thus, if we take a hollow sphere (eg, football) or more nested balls (like dolls nesting dolls), they will be attracted to each body, just as it would make a material point with their overall weight and is located incenter.
