Computing the Bodies Motions in the Space and Long-term Changes in the Earth's Climate

The paper considers various aspects of the interaction and movement of bodies. The stability of the Solar system by the example of the evolution of the Mars orbit for 100 million years is shown. The optimal motion of the spacecraft to the vicinity of the Sun is considered. The results of an exact solution to the problem of the interaction of N bodies, which form a rotating structure, are presented. It is shown the evolution of two asteroids: Apophis and 1950DA, as well as ways to transform them into Earth satellites. The cause of the excess rotation of the Mercury perihelion is explained. The examples of the simulation of globular star clusters are given. As a result of the interaction of the bodies of the Solar System, the parameters of the orbital and rotational motions of the Earth change. This change leads to a change in the distribution of solar heat over the surface of the Earth. In contrast to the works of previous authors, a new understanding of the evolution of the orbital and rotational motions of the Earth has been obtained. In particular, it has been established that the Earth's orbit and its axis of rotation precess relative to different directions in space. The paper compares the distribution of the amount of the solar heat, i.e. insolation, on the surface of the Earth in different epochs. The insolation periods of climate change are shown. They coincide with the known changes of the paleoclimate. The changes in insolation for different time intervals, including for 20 million years ago, are given. Changes in insolation in the contemporary epoch and in the next million years are also shown. Sunrises and sunsets are also evolving. The duration of the polar days and nights in different epochs is given in the distribution by latitude. The paper popularly acquaints readers with the latest scientific results and is useful for students and graduate students to choose topics for their term papers and dissertations.