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- W1997905575 abstract "T problem concerning unperturbed motion, i.e., the two-body problem, has an exact solution that is actually used also in the computation of an ephemeris without the calculation of perturbations. This solution is not considered simple enough because there is no direct connection of the coordinates with time. Therefore, it is worth while to attempt to simplify the calculation of ephemerides. The relative complexity of the solution of the differential equations of the two-body problem depends on the nonlinearity of the equations. In order to simplify the solution, it is necessary to eliminate the nonlinearity. From the time of Gauss, the method of averaging has been used for the simplification of the equations of motion in celestial mechanics. The averaging was subject to the force function of the problem. It is shown that it gives the possibility of finding the secular and long period perturbations. It should be noted that the question concerning averaging is not so clear as it sometimes seems. It is sufficient to cite a very simple reason: If, in the two-body problem, the average value of the force function is obtained with respect to the mean anomaly, then we shall obtain a constant value, and the approximate differential equations with the average force function determine straight line motion with constant velocity. In the present article, the linearization of the differential equations of the two-body problem is considered, being based on a partial average of the differential equations of motion. The linearity of the equations is violated by the presence of the factor 1/r in all of the equations; thus the obvious method of linearization will be the replacement of this factor by its average value if the motion is considered along an ellipse." @default.
- W1997905575 created "2016-06-24" @default.
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- W1997905575 date "1963-02-01" @default.
- W1997905575 modified "2023-09-22" @default.
- W1997905575 title "APPROXIMATE CALCULATION OF AN EPHEMERIS IN UNPERTURBED ELLIPTIC MOTION" @default.
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- W1997905575 doi "https://doi.org/10.2514/3.1594" @default.
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