Every student knows that the cause of any body movement is some external force that has an effect on him. In the article, we briefly consider the law of universal gravitation, because of which the movement of cosmic objects occurs and because of which bodies on our planet fall down.
Who discovered the law and when?
Speaking briefly about the law of gravitation, the history of its discovery should be given. The official date of this event is 1687, when Isaac Newton published his work, where he gave him the wording. Nevertheless, one should not assume that in the physics of universal gravitation the law is the brainchild of Newton exclusively. Even the Englishman himself acknowledged that many of his predecessors and contemporaries proposed the mathematical dependence of gravity on distance.
Be that as it may, Newton's merit is obvious. It was he who was able to put together a large number of ideas and experimental dependencies, for example, Kepler’s laws, conduct a detailed analysis of all the data and formulate a beautiful and harmonious theory. Therefore, the discovery of the universal gravitation of the law belongs to him rightfully.
What is the universal law of gravity?
Briefly, the law of gravity can be formulated as follows: the force with which two bodies are attracted to each other is directly proportional to the product of their masses and the square of the distance between their gravitational centers is inversely proportional. If the masses of bodies are denoted by the symbols m 1 and m 2 , and the distance between them is r, then the attractive force F is calculated by the following formula:
F = G * m 1 * m 2 / r 2 .
In the gravity formula of the law is the value of G. This quantity is called the gravitational universal constant. Newton himself could not determine its significance, since it did not have enough data at the end of the 17th century. It was measured only a century later by Cavendish on torsion scales.
As for the formula of universal gravitation of the law, physics lovers may notice that it has exactly the same form as the formula for the Coulomb interaction of electric charges. This fact prompted scientists to introduce into physics the concept of a gravitational field, with the help of which massive objects interact by analogy with an electric field, which causes the interaction of charges.
Gravity
As you know, on any body located on the surface of our planet or near it, the force of gravity directed to the center of the Earth acts. It is described by the following formula:
F = m * g.
Where g = 9.81 m / s 2 is the free acceleration fall. Where does this quantity come from? The question can be answered briefly: The law of gravity allows to accurately determine the value of g. We show how this is done.
Suppose that a body of mass m falls on the Earth having mass M. The radius R of our planet is 6371 km. Even if the body m is at a height of several kilometers, then this distance can be ignored in comparison with the distance to the center of the planet. In this case, the universal gravitational law can be written in the form:
F = G * m * M / R 2 .
Comparing this and the previous formulas, we obtain an expression for the quantity g:
g = G * M / R 2 .
If we substitute values for all quantities here, then we get a value of 9.81 m / s 2 .
The acceleration g acts on all planets and their satellites, but its value is not constant, since the masses of bodies and their radii are different.
It is known from statics that a body’s weight is the force with which it presses on a support. Weight is calculated using the same formula as gravity. If you weigh the same body near the pole and near the equator, it turns out that in the second case it will weigh a little less. The reason for this is two factors:
- The distance to the center of the earth is less at the poles than at the equator.
- As a result of rotation around the axis of the Earth, all bodies located on its surface are affected by centrifugal forces that reduce the influence of gravitational attraction, and hence the body weight. Near the equator, centrifugal forces are maximum, at the poles they are equal to zero.
Limits of applicability
Having examined briefly the law of gravitation, a few words should be said about the limits of its applicability.
The studied formula can always be used when the masses of bodies and the distances between them are large. So, the motion of the planets in the solar system is described with good accuracy using this law. The only exception is Mercury, which is very close to the Sun, therefore, to accurately describe its motion, one should use the theory of relativity of general Einstein.
The problems of applying the universal law also arise when describing the interaction of electromagnetic waves with strong gravitational fields.