The SmallBodies.Ru site was created as a scientific and informational one, so most of the information is accessible to understanding only for sufficiently trained users. In order to attract more interest to the site, we decided, in a popular form, to present the main issues related to the content of the site itself.<\/p>\n\n\n\n
It should be noted that the main goal of our research\nwas to study the distribution of small bodies of the solar system approaching\nthe Earth.\nThe\nmain objects of study were short-period comets and asteroids of the Apollo,\nAmur, and Aton groups.<\/p>\n\n\n\n
Short-period comets include comets whose period of\nrevolution around the Sun does not exceed 200 years.<\/p>\n\n\n\n
The asteroids of the Apollo, Amur, Aton groups are\ncurrently receiving increased attention in connection with the solution of the\nproblem of \u201casteroid danger\u201d. A comprehensive analysis shows that the problem of “asteroid\ndanger” associated with predicting the collision of large celestial objects\nwith the Earth and preventing catastrophic consequences is complex and far from\na final solution.<\/p>\n\n\n\n
At present, the characteristic lifetimes before the\ncollision with the Earth of all \u201cdangerous\u201d space objects have been calculated. It is shown that collisions of\ncelestial bodies, such as the Tunguska meteorite, with the Earth occur more\noften than once every hundred years. Collisions that can cause a global\ncatastrophe such as a “nuclear winter” on Earth occur on average once\nevery several hundred thousand years. Disasters leading to a change in geological epochs\noccur on average once every several tens of millions of years.<\/p>\n\n\n\n
Questions about more accurate estimates of the\nasteroid hazard are related to our knowledge of the motion and evolutionary\nprocesses of small bodies of the solar system, which pose a danger of collision\nwith the Earth.\nThe\nstudy of the movement of potentially \u201cdangerous\u201d objects, the cataloging of\norbital elements and close proximity to the terrestrial planets is an important\nstep in solving the \u201casteroid hazard\u201d problem. Regular comprehensive studies of\npotentially \u201cdangerous\u201d objects will make it possible to predict the collision\nof an asteroid with the Earth in advance and take appropriate measures to\nprevent a catastrophe.<\/p>\n\n\n\n
The study of the evolution of the orbits of the\nasteroids of the Apollo, Amur, Aton groups is one of the main tasks in solving\nthe problem of “asteroid danger”. The theory of motion of the\nasteroids of the Apollo, Amur, Aton groups is much more complicated than the theory\nof planetary motion, since the elliptical orbits of the asteroids are more\nextended than the orbits of the planets, the planes of the orbits are\nsignificantly inclined to the plane of the ecliptic. In addition, the asteroid orbits have close proximity\nto the orbits of large planets, therefore, the analytical theories of asteroid\nmotion are not accurate and numerical methods are widely used to study the\nevolution of their orbits. It should be noted that the separation of asteroids\ninto the groups of Apollo, Amur, Aton is very conditional, since asteroids in\nthe process of their evolution can move from one group to another.<\/p>\n\n\n\n
For successful work on the solution of this problem,\ncomprehensive studies of both physical and dynamic properties of these objects\nare required.<\/p>\n\n\n\n
The motion of celestial bodies in the solar system is\ndescribed by various differential equations. The accuracy of predicting the\nmotion of the object under study substantially depends on the choice of\nspecific differential equations.<\/p>\n\n\n\n
The\nstudy of the motion of large planets, the moon and the sun began in ancient\ntimes. Babylonians over the 5th\ncentury BC. they knew with great accuracy the duration of the year and\nmonth and the periods of revolution of large planets. With the creation of geometry by\nscientists of ancient Greece, there was a further development of knowledge in\nthe field of astronomy. Greek scientists made a great contribution to the\nstudy of the motion of 5 large planets, the moon and the sun. Much\nmore complicated was the case with the planets.\nAccording to scientists, ancient Greece, the center of the world was the\nEarth, and all the planets the Moon and the Sun made circular motions on\nepicycles at a constant speed. Improving the accuracy of planetary motion led to the\nintroduction of an increasing number of geocentric spheres. Aristotle brought the total number of\nspheres to 56. But even with this complication, it was impossible to reconcile\ntheoretical calculations with observations.<\/p>\n\n\n\n
The\nfollowing ancient Greek scientists made a great contribution to the development\nof the geocentric system of the world: Aristotle, Hipparchus, Ptolemy. The most significant contribution to the\ndevelopment of the geocentric system of the world belongs to Ptolemy. In his treatise \u201cAlmagest\u201d, the laws of\nvisible planetary movements were first revealed.\nPtolemy decomposed the visible motion of each planet into two movements by\nthe deferent and the epicycle. The\ntheory of planetary motion created by Ptolemy existed for 13 centuries, and no\none could replace it with a more advanced theory.<\/p>\n\n\n\n
The\nfurther development of astronomy is associated with the appearance of the\nCopernicus treatise in 1543, \u201cOn the circulation of celestial bodies, VI\nbooks.\u201d The great significance of the Copernicus treatise was that occurred a\nturning point from the geocentric system of the world to the heliocentric of\ntheory. At the same time, astronomy from a purely geometric science has become\na physical science.<\/p>\n\n\n\n
The transfer of the \u201ccenter of the world\u201d to the\ncenter of the Sun made it possible to further create new celestial mechanics,\nthe main subject of which was the study of the motion of celestial bodies in\nthe solar system. The following outstanding scientists made a great\ncontribution to its creation: Kepler, Newton, Euler, Lagrange, D’Alembert,\nLaplace and others.
\nNewton’s celestial mechanics is based on\nthe law of gravity and the laws of motion. The law of universal gravitation\nstates that the force of mutual attraction of two bodies is directly\nproportional to their masses and inversely proportional to the square of the\ndistance between them.<\/p>\n\n\n\n
Now we formulate the three laws of motion<\/p>\n\n\n\n
I. There are such reference frames, called inertial, regarding\nwhich the material points, when no forces act on them (or mutually balanced\nforces act), are at rest or in uniform rectilinear motion.
\nII. In an inertial reference frame, the\nacceleration that a material point receives with constant mass is directly\nproportional to the resultant of all the forces applied to it and inversely proportional\nto its mass.<\/p>\n\n\n\n
III. Material points interact with each other by\nforces of the same nature, directed along a straight line connecting these\npoints, equal in magnitude and opposite in direction.<\/p>\n\n\n\n
Is\nit possible to verify this law from experience?\nTo do this, it would be necessary to measure three quantities included\nin his expression: acceleration, force and mass.
\nDistracting from the difficulties associated with measuring time, let us assume\nthat it is possible to measure acceleration.\nBut how to measure force or mass? We\ndon\u2019t even know what it is.<\/p>\n\n\n\n
What\nis mass? This, Newton answers, is\nthe product of volume by density. Better to say, Thomson and Tet argue that\ndensity is the private of dividing mass\nby volume. What is power? This, Lagrange answers, is the cause that\nproduces or seeks to produce the movement of the body. This, Kirghoff will say, is the product of mass by acceleration. But then why not say that mass is the private\nfrom dividing force by acceleration.<\/p>\n\n\n\n
These\ndifficulties are insurmountable. Having\ndefined strength as the cause of the movement, we became on the soil of\nmetaphysics, and if such a definition had to be satisfied, it would be\ncompletely fruitless. For a\ndefinition to be suitable for anything, it must teach us how to measure power; besides this condition is enough; there is no need for the definition to\nteach us what force is in itself, or whether it is the cause or effect of the\nmovement \u201d.<\/p>\n\n\n\n
Based\non the law of universal gravitation, equations of motion of celestial bodies\nwere obtained, the solution of which made it possible did to predicted their\nlocation in space. The most\nconvenient objects for checking theoretical studies are large planets and the\nMoon, since a significant amount of observations has been accumulated on these\nobjects.<\/p>\n\n\n\n
At\nthe beginning of 1850, the French scientist Le Verrier built a theory of the\nmotion of the Sun and seven large planets (Mercury-Neptune) relative to the\nEarth. The result of his work was\nthe proof of the impossibility to reconcile with the observations of the\npassage of Mercury across the solar disk on the basis of Newtonian dynamics by\nany system of orbital elements and the masses of the planets known to him.<\/p>\n\n\n\n
Along\nwith Mercury, the Moon is a more complex object for studying motion by solving\nthe n<\/em> -body\nproblem.\nAlong with the established\nempirical difficulties, difficulties associated with the phenomenological\nnature of Newtonian theory began to be more and more identified and discussed. Various difficulties caused scientists doubts about the\naccuracy of Newton’s law, and numerous attempts were made to amend the exact\nformula of the law of gravity. However,\nthese attempts to improve the law of gravity have been unsuccessful.<\/p>\n\n\n\n The next step in the development of the relativistic\ntheory of gravitation is the general theory of relativity created by Einstein.\nThe general theory of relativity is based on the following hypotheses. General relativity, like Newtonian mechanics, is not\nfree from flaws. The most important of these is the question of the nature of\ngravity. In the framework of the general theory of relativity, just as in the\ntheory of gravity, Newton is considered purely phenomenologically. Another\ndrawback of the general theory of relativity is the significant complication of\ndifferential equations in the problem n<\/em>\nof bodies. The solution to this problem has to be sought in the form of series\nin powers of small parameters, while only the initial terms of the expansion\nare taken into account, and the question of the convergence of the series is\nnot studied at all. The main drawback of both Newtonian dynamics and Einstein’s\ntheory of gravitation is, according to the authors, the endowment of mass with\na property that generates a gravitational field. In the first case, it is\nassumed that the mass has the property of attraction of other material bodies,\nin the second case, the mass is endowed with the property to bend the\nsurrounding space.<\/p>\n\n\n\n As\nnoted earlier by A. Poincare, mass and force are undetectable concepts, like\nundetectable concepts in mathematics – a point, a line. In the mechanics of Newton and Einstein, these concepts have\ncertain physical properties, which, at least, is not justified. All of the above disadvantages of both Newtonian\ndynamics and the general theory of relativity are reflected in the degree of\naccuracy and reliability of the studies based on them. An indispensable advantage of the general theory of\nrelativity is that with the help of a specially selected harmonic coordinate\nsystem, it was possible to coordinate the theory of motion of Mercury with\nobservations. However, the motion of\nthe moon in this coordinate system cannot be coordinated with observations by\nsolving one system of differential equations of motion.<\/p>\n\n\n\n A\nnatural question arises: is it possible to obtain equations of motion, the\nsolution of which would allow to coordinate the theory of motion of Mercury and\nthe Moon with observations? The\nsolution to this problem was found on the basis of constructing the simplest\nmodel of the interaction of a moving material body with the surrounding space.<\/p>\n\n\n\n The\nderivation of differential equations of motion (3) is based on the following\nidea. Suppose that at every fixed\npoint in time a material body occupies a certain volume in space. When the material body moves, the freed\nspace is filled with the environment, thereby compressing the surrounding space\nby the amount of volume freed by the moving object (see Fig. 1).<\/p>\n\n\n\n\n\n Fig. 1<\/p>\n\n\n\n Thus,\nthe following basic hypotheses are the cornerstone of the proposed method: a)\nspace is populated by moving material bodies, with certain sizes and densities; b) the space surrounding material bodies\nis not an empty vacuum, it has a fairly dense energy and the property of\ncompression relative to moving material bodies.<\/p>\n\n\n\n A natural question arises: how well are these\nassumptions justified? In classical physics, the concept of empty space is\nused, in which there are no particles and field. Such an empty space can be\nconsidered a vacuum of classical physics. Vacuum in quantum theory is defined\nas an energy state in which there are no real particles. Moreover, the presence\nof a field is a prerequisite. According to modern concepts, the universe is\ndominated by a physical vacuum, in energy density it surpasses all ordinary\nforms of matter combined. It is believed that the substance comes from a\nphysical vacuum, and its properties stem from the properties of a physical\nvacuum.<\/p>\n\n\n\n Vacuum\nhas not only a certain energy density, but also pressure. According to the\ncalculations of the Nobel laureate R. Feynman and J. Wheeler, the energy\npotential of a vacuum is so huge that “in a vacuum enclosed in the volume\nof an ordinary light bulb, there is so much energy that it would be enough to\nboil all the oceans on Earth.”<\/p>\n\n\n\n The solution of the new differential equations of\nmotion of large planets and the Moon was compared with the coordinate data of\nthese objects located in the DE405 database A\ncomparison of the coordinates and velocities of large planets and the Moon\nfound by solving new equations with DE405 data differ from each other within\nthe limits of observation errors. It\nis impossible to achieve a similar accuracy of the agreement of solutions with\nDE405 by solving the n-body problem or by solving relativistic equations\nwithout involving additional equations that take into account the shape of the\nplanets.<\/p>\n\n\n\n The equations of motion, based on the principle of interaction of moving material bodies with the surrounding space, were used to study the motion of asteroids and comets, presented on the site SmallBodies.Ru. Due to the fact that most asteroids have close proximity to large planets, difficulties arise in the study of their movements by integrating classical and relativistic equations. The information presented on the SmallBodies.Ru website has a fairly high degree of reliability compared to information obtained on the basis of the gravitational or relativistic model. <\/p>\n","protected":false},"excerpt":{"rendered":" The SmallBodies.Ru site was created as a scientific and informational one, so most of the information is accessible to understanding only for sufficiently trained users. In order to attract more interest to the site, we decided, in a popular form, to present the main issues related to the content of the site itself. It should … Continue reading “Information about update of the site SmallBodies.Ru”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,5,9],"tags":[],"class_list":["post-33","post","type-post","status-publish","format-standard","hentry","category-articles","category-site-news","category-celestial-bodies-motion"],"_links":{"self":[{"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/posts\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":14,"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/posts\/33\/revisions"}],"predecessor-version":[{"id":77,"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/posts\/33\/revisions\/77"}],"wp:attachment":[{"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/media?parent=33"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/categories?post=33"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/smallbodies.ru\/info\/en\/wp-json\/wp\/v2\/tags?post=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nI. The space of the general theory of\nrelativity should be a pseudo-Riemannian four-dimensional space.
\nII The second hypothesis of the general\ntheory of relativity is as follows: The energy-momentum tensor is superimposed\non the event space as an additional construction, and it is assumed that the\nenergy-momentum tensor follows from the pseudo-Riemannian geometry of this space\nitself.<\/p>\n\n\n\n
\nCurrently, a number of high-precision\nnumerical theories of the motion of large planets have been developed. The most\nfamous of them is the numerical theory created by NASA researchers Newhal,\nStanders, Williams. Standish created a data bank for the coordinates of large\nplanets, the Moon and the Sun – DE405 in the time interval from 2305424.5 J.D.\n(1599 Dan 5) to 2525008.5 J.D. (2201 Feb 20). The coordinates and velocities of\nthe inner planets obtained using the DE405 data bank are consistent with radar\nobservations, and all planets are consistent with optical observations.<\/p>\n\n\n\n