The law of universal gravitation explains the mechanical structure of the Solar system, and Kepler's laws describing the trajectories of planets can be derived from it. For Kepler, his laws were purely descriptive — the scientist simply summarized his observations in mathematical form, without providing any theoretical basis for the formulas. In the great system of world order according to Newton, Kepler's laws become a direct consequence of the universal laws of mechanics and the law of universal gravitation. That is, we again observe how empirical conclusions obtained at one level turn into strictly grounded logical conclusions as we move to the next stage of deepening our knowledge of the world.
Newton was the first to suggest that gravitational forces determine not only the motion of the planets of the Solar system; they act between any bodies in the Universe. One of the manifestations of the force of universal gravitation is the force of gravity - so it is customary to call the force of attraction of bodies to the Earth near its surface.
In fact, the period of rotation of the satellite in a circular orbit near The earth's surface slightly exceeds the specified value due to the difference between the radius of the real orbit and the radius of the Earth. The movement of a satellite can be considered as a free fall, similar to the movement of projectiles or ballistic missiles. The only difference is that the speed of the satellite is so great that the radius of curvature of its trajectory is equal to the radius of the Earth.
For satellites moving along circular paths at a considerable distance from the Earth, the earth's gravity weakens inversely proportional to the square of the radius r of the trajectory. Thus, in high orbits, the speed of movement of satellites is less than in low-earth orbit.
All bodies move around the Sun in elliptical orbits, one of the foci of which is the Sun. The closer a celestial body is to the Sun, the faster its speed of movement in orbit (the planet Pluto, the farthest known, moves 6 times slower than the Earth).
Bodies can also move in open orbits: parabola or hyperbola. This happens if the velocity of the body is equal to or exceeds the value of the second cosmic velocity for the Sun at a given distance from the Central star. If we are talking about a satellite of a planet, then the cosmic speed must also be calculated relative to the mass of the planet and the distance to its center.