Geodesic
Comparison of the coordinates of the major planets, Moon, and Sun obtained based
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 121-148

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In this paper the comparison of orbit coordinates and elements of large planets, the Moon and the Sun obtained on the basis of a new principle of interaction and of data bank DE405 is made. The space environment is the physical vacuum, whose properties are currently still in the formative stage. Gravity is the result of the interaction of the physical vacuum with material bodies which are moving. Gravity explains by the properties of space compression in relation to moving material bodies. Differential equations of motion of the major planets, the Moon and the Sun have been obtained. It should be noted that the system of differential equations does not contain the mass of bodies and force interactions, in addition, the Earth is considered as a spheroid. By numerical integration of the equations of motion coordinates of the Moon, the Sun and major planets osculating elements of the orbits of the inner planets during 1602–2193 are computed. The results of calculations are compared with the coordinates and orbital elements determined according to the coordinates and velocities DE405. It is shown that in contrast to Newtonian mechanics and relativistic equations of motion, the coordinates of the major planets of the Moon and the Sun, based on the solution of a new system of differential equations, are in satisfactory agreement with the coordinates of these objects obtained using data bank DE405. The resulting equations do not contain terms that take into account the non-sphericity of the Earth and the Moon, being a non-relativistic equations. Based on the research the following conclusions are made: obtained differential equations of motion satisfactorily describe the motion of the major planets, of the Moon and Sun on the time interval of 600 years; these equations are much simpler and more accurate then the differential equations that take into account the relativistic effects.
Mots-clés : orbital elements
Keywords: numerical integration, differential equation of motion. 
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     author = {A. F. Zausaev},
     title = {Comparison of the coordinates of the major planets, {Moon,} and {Sun} obtained based},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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A. F. Zausaev. Comparison of the coordinates of the major planets, Moon, and Sun obtained based. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 121-148. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_1_a9/