I. Kepler has been trying all his life to prove that our solar system is some kind of mystical art. Initially, he tried to prove that the structure of the system resembles regular polyhedrons from ancient Greek geometry. At the time of Kepler, the existence of six planets was known. It was believed that they are placed in crystal spheres. According to the scientist, these spheres were located in such a way that the polyhedra of the correct form fit exactly between the neighboring ones. Between Jupiter and Saturn there is a cube inscribed in the external environment into which the sphere is inscribed. Between Mars and Jupiter is a tetrahedron, etc. After many years of observing celestial objects, Kepler’s laws appeared, and he refuted his theory of polyhedra.
The laws
The geocentric Ptolemaic system of the world was replaced by a heliocentric system created by Copernicus. Even later, Kepler discovered the laws of planetary motion around the sun.
After years of planetary observation, three Kepler laws appeared. Let's consider them in the article.
First
According to Kepler’s first law, all the planets in our system move in a closed curve called an ellipse. Our luminary is located in one of the tricks of the ellipse. There are two of them: these are two points inside the curve, the sum of the distances from which to any point of the ellipse is constant. After lengthy observations, the scientist was able to identify that the orbits of all the planets of our system are located almost in the same plane. Some celestial bodies move in ellipses close to a circle. And only Pluto and Mars move in more elongated orbits. Based on this, Kepler's first law was called the law of ellipses.
Second law
Studying the motion of bodies allows a scientist to establish that the speed of a planet is greater at a time when it is closer to the Sun, and less when it is at a maximum distance from the Sun (these are the points of perihelion and aphelion).
Kepler’s second law says the following: each planet moves in a plane passing through the center of our body. At the same time, the radius vector connecting the Sun and the planet under study describes equal areas.
Thus, it is clear that the bodies move around the yellow dwarf unevenly, while having maximum speed in perihelion, and minimum speed in aphelion. In practice, this is seen by the movement of the Earth. Every year in early January, our planet, moving through perihelion, moves faster. Because of this, the movement of the Sun through the ecliptic is faster than at other times of the year. In early July, the Earth moves through the aphelion, due to which the Sun moves more slowly along the ecliptic.
Third law
According to the third law of Kepler, between the period of revolution of the planets around the luminary and its average distance from it, a connection is established. The scientist applied this law to all the planets of our system.
Explanation of laws
Kepler's laws could only be explained after Newton discovered the law of gravity. According to it, physical objects take part in gravitational interaction. It has universal universality, which affects all objects of the material type and physical fields. According to Newton, two motionless bodies act mutually with each other with a force proportional to the product of their weight and inversely proportional to the square of the gaps between them.
Indignant movement
The motion of the bodies of our solar system is controlled by the attractive force of the yellow dwarf. If the bodies were attracted only by the power of the Sun, then the planets would make movements around it exactly according to the laws of motion of Kepler. This type of movement is called unperturbed or Keplerian.
In fact, all the objects of our system are attracted not only by our luminary, but also by each other. Therefore, none of the bodies can move exactly along an ellipse, hyperbole or in a circle. If the body deviates during movement from Kepler’s laws, then this is called perturbation, and the movement itself is called perturbed. That it is considered real.
The orbits of celestial bodies are not fixed ellipses. During attraction by other bodies, the ellipse of the orbit changes.
Contribution of I. Newton
Isaac Newton was able to deduce the law of universal gravitation from the laws of motion of the planets of Kepler. To solve the space-mechanical problems, Newton used precisely universal gravitation.
After Isaac, progress in the field of celestial mechanics was the development of mathematical science, applied to solve equations expressing Newton's laws. This scientist was able to establish that the gravity of the planet is determined by the distance to it and the mass, but indicators such as temperature and composition do not have any effect.
In his scientific work, Newton showed that the third Keplerian law is not entirely accurate. He showed that when calculating it is important to take into account the mass of the planet, since the motion and weight of the planets are related. This harmonic combination shows the relationship between Keplerian laws and the law of gravity, identified by Newton.
Astrodynamics
The application of the laws of Newton and Kepler became the basis for the appearance of astrodynamics. This is a section of celestial mechanics that studies the motion of cosmic bodies created artificially, namely: satellites, interplanetary stations, various ships.
Astrodynamics calculates the orbits of spaceships, and also determines what parameters to launch, to which orbit to launch, which maneuvers to carry out, and the planning of gravitational impact on ships. And this is far from all the practical tasks that astrodynamics pose. All the results obtained are applied when performing a variety of space missions.
Celestial mechanics is closely connected with astrodynamics, which studies the motion of natural cosmic bodies under the influence of gravity.
Orbits
Under the orbit understand the trajectory of a point in a given space. In celestial mechanics, it is generally accepted that the trajectory of a body in the gravitational field of another body has a significantly larger mass. In a rectangular coordinate system, the trajectory can be in the form of a conical section, i.e. be represented by a parabola, ellipse, circle, hyperbola. In this case, the focus will coincide with the center of the system.
For a long time, it was believed that the orbits should be round. For a long time, scientists tried to choose exactly the circular version of the movement, but they did not succeed. And only Kepler could explain that the planets do not move in a circular orbit, but elongated. This allowed us to discover three laws that could describe the motion of celestial bodies in orbit. Kepler discovered the following elements of the orbit: the shape of the orbit, its inclination, the position of the plane of the orbit of the body in space, the size of the orbit, and time reference. All these elements determine the orbit, regardless of its shape. In calculations, the main coordinate plane can be the plane of the ecliptic, galaxy, planetary equator, etc.
Numerous studies show that the geometrical shape of the orbit can be elliptical and rounded. There is a division into closed and open. According to the angle of inclination of the orbit to the plane of the earth's equator, the orbits can be polar, inclined and equatorial.
According to the period of revolution around the body, the orbits can be synchronous or solar-synchronous, synchronous-daily, quasi-synchronous.
As Kepler said, all bodies have a certain speed of movement, i.e. orbital speed. It can be constant throughout the circulation around the body or change.