How many self-development books have you read lately? Lot? How has your life changed since reading them? But this is not the question everyone answers differently. Someone read one book and changed their life. And someone constantly reads, but ... suffering has remained in his life, and life remains without significant changes.

Interesting fact. Not all people want to be happy. Why is it so?

The reason is simple. The secret lies in the application of the knowledge that people receive from books and lectures on self-development. If you are learning something, then by all means apply it. Knowledge without application is empty. By the way a person applies knowledge in life, one can understand whether he wants to live happily, or prefers to suffer. A happy life is a constant work on oneself, the work is sometimes quite difficult. Not everyone wants to do this, because it is difficult, you have to change yourself. Suffering is the desire for someone to “make happy”, without internal work on oneself.

At one time, I reread mountains of literature on personal development. I was looking for the very "magic key" that will open the door to a country where dreams come true. But from the amount of literature, the quality of life did not change. Everything remained the same. The problems didn't want to go away.

And then one day I realized that the secret lies in the very actions and actions. In the thoughts and feelings with which we commit them. I realized that in order to become a happy person, you don’t need to do a lot of “body movements” and fuss, you don’t need to work hard at work until you sweat, you don’t need to see happiness only in earning money or an apartment.

It is enough to pay attention to what the soul wants. It's amazing, but all the answers are already in us. We ourselves already subconsciously know where this or that act will lead us. The answer to this question will tell you the feeling of inner comfort or discomfort when making decisions.

Sometimes you can listen to friends, they are a reflection of ourselves in this world, and if they all unanimously say that there is no need to do something, then think about why such an answer.

Remember that by your actions and deeds you yourself choose what they will lead to, happiness or suffering. And not always the path, which at first glance seems easy, leads you to the desired goal. Suffering, like happiness, is a choice. Your choice: listen to your soul or not. And if there is a situation in your life that has not been resolved for years, then this means that you are doing the wrong things. It means that you need to change your thoughts, listen to what your soul wants. And act in harmony with it.

There is such a famous saying: "A person has two motives for an act: the true one and the one that looks good." So stop fooling yourself and listen to your true feelings and motives. In this way, you will learn to understand yourself better and, over time, build a life in which there will be more happiness.

Even in ancient times, pundits began to understand that it is not the Sun that revolves around our planet, but everything happens exactly the opposite. Nicolaus Copernicus put an end to this controversial fact for mankind. The Polish astronomer created his own heliocentric system, in which he convincingly proved that the Earth is not the center of the Universe, and all the planets, in his firm opinion, revolve in orbits around the Sun. The work of the Polish scientist "On the rotation of the celestial spheres" was published in Nuremberg, Germany in 1543.

The ideas about how the planets are located in the sky were the first to express the ancient Greek astronomer Ptolemy in his treatise “The Great Mathematical Construction on Astronomy”. He was the first to suggest that they make their movements in a circle. But Ptolemy mistakenly believed that all the planets, as well as the Moon and the Sun, move around the Earth. Prior to Copernicus's work, his treatise was considered generally accepted in both the Arab and Western worlds.

From Brahe to Kepler

After the death of Copernicus, his work was continued by the Dane Tycho Brahe. The astronomer, who is a very wealthy man, equipped his island with impressive bronze circles, on which he applied the results of observations of celestial bodies. The results obtained by Brahe helped the mathematician Johannes Kepler in his research. It was the German who systematized and deduced his three famous laws about the movement of the planets of the solar system.

From Kepler to Newton

Kepler proved for the first time that all 6 planets known by that time move around the Sun not in a circle, but in ellipses. The Englishman Isaac Newton, having discovered the law of universal gravitation, significantly advanced mankind's ideas about the elliptical orbits of celestial bodies. His explanations that the tides on the Earth occur under the influence of the Moon proved to be convincing for the scientific world.

around the sun

Comparative sizes of the largest satellites of the solar system and the planets of the Earth group.

The period for which the planets make a complete revolution around the Sun is naturally different. Mercury, the closest star to the star, has 88 Earth days. Our Earth goes through a cycle in 365 days and 6 hours. Jupiter, the largest planet in the solar system, completes its rotation in 11.9 Earth years. Well, for Pluto, the planet most distant from the Sun, the revolution is 247.7 years at all.

It should also be taken into account that all the planets in our solar system move, not around the star, but around the so-called center of mass. Each at the same time, rotating around its axis, sway slightly (like a top). In addition, the axis itself can move slightly.

The study of the apparent motion of the planets against the constant background of the starry sky made it possible to give a complete kinematic description of the motion of the planets relative to the inertial frame of reference of the Sun - the stars. The trajectories of the planets turned out to be closed curves, called orbits. The orbits are close to circles with the center in the Sun, and the motion of the planets along the orbits turned out to be close to uniform. The only exceptions are comets and some asteroids, the distance from which to the Sun and the speed of movement of which vary widely, and the orbits are highly elongated. The distances from the planets to the Sun (orbital radii) and the times of revolution of these planets around the Sun are very different (Table 2). The designations of the first six planets given in the table have been preserved since the time of astrologers.

Table 2. Information about the planets

In reality, the orbits of the planets are not perfectly circular, and their velocities are not quite constant. An accurate description of the movements of all the planets was given by the German astronomer Johannes Kepler (1571-1630) - in his time only the first six planets were known - in the form of three laws (Fig. 199).

1. Each planet moves in an ellipse with the Sun at one of its foci.

2. The radius vector of the planet (the vector drawn from the Sun to the planet) describes equal areas in equal times.

3. The squares of the times of revolution of any two planets are related as cubes of the semi-major axes of their orbits.

From these laws, a number of conclusions can be drawn about the forces under which the planets move. Consider first the motion of any one planet. The end of the major axis of the orbit closest to the Sun () is called perihelion; the other end is called aphelion (Fig. 200). Since the ellipse is symmetrical about both of its axes, the radii of curvature at perihelion and aphelion are equal. Hence, according to what was said in § 27, normal accelerations and at these points are related as the squares of the planet's velocities and :

(123.1)

Rice. 199. If the planet moves from point to point in the same time as from point to point, then the areas shaded in the figure are

Rice. 200. To determine the ratio of the velocities of the planet at perihelion and aphelion

Let us consider small paths and , which are symmetrical with respect to perihelion and aphelion and completed in equal time intervals . According to Kepler's second law, the areas of the sectors and must be equal. The arcs of the ellipse and are equal to and . In Fig. 200, for clarity, the arcs are made quite large. If we take these arcs as extremely small (for which the time interval must be small), then the difference between the arc and the chord can be neglected and the sectors described by the radius vector can be considered as isosceles triangles and . Their areas are equal, respectively, and , where and are the distances from aphelion and perihelion to the Sun. So, from where . Finally, substituting this relation into (123.1), we find

. (123.2)

Since the tangential accelerations are equal to zero at perihelion and aphelion, they represent the accelerations of the planet at these points. They are directed towards the Sun (along the major axis of the orbit).

The calculation shows that at all other points of the trajectory, the acceleration is directed towards the Sun and changes according to the same law, that is, inversely proportional to the square of the planet's distance from the Sun; so for any point in the orbit

where is the acceleration of the planet, is the distance from it to the Sun. Thus, the planet's acceleration is inversely proportional to the square of the distance between the Sun and the planet. Considering the angle made by the radius vector of the planet with the tangent to the trajectory, we see (Fig. 201) that when the planet moves from aphelion to perihelion, the tangential component of the acceleration increases the positive velocity of the planet; on the contrary, when moving from perihelion to aphelion, the speed of the planet decreases. At perihelion, the planet reaches its greatest speed, at aphelion - the lowest speed of movement.

To find out the dependence of the planet's acceleration on its distance from the Sun, we used the first two laws of Kepler. This dependence was found because the planets move in ellipses, changing their distance from the Sun. If the planets moved in circles, the distance from the planet to the Sun and its acceleration would not change, and we could not find this dependence.

Rice. 201. When a planet moves from perihelion to aphelion, the gravitational force reduces the planet's speed; when moving from aphelion to perihelion, it increases the planet's speed

But when comparing the accelerations of different planets, one can be satisfied with an approximate description of the motion of the planets, assuming that they move uniformly in circles. Let us denote the radii of the orbits of any two planets through and , and the periods of their revolution - through

Substituting the ratio of the squares of the revolution times into formula (123.4), we find

This conclusion can be rewritten as follows: for any planet located at a distance from the Sun, its acceleration

where is the same constant for all planets in the solar system. Thus, the accelerations of the planets are inversely proportional to the squares of their distances from the Sun and directed towards the Sun.