Abstract
The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.
Highlights
One of the classical laws of planetary motion due to Kepler says that a planet revolves around the sun in an elliptic orbit (Fig. 1(a))
It is not difficult to see that simple and advanced STFT iterative procedure gives impressive results which suggest that a novel STFT approach works
From the previous sections it is obvious that the Special Tran Functions Theory is a consistent general approach to solving Kepler’s transcendental equations in celestial mechanics domain
Summary
One of the classical laws of planetary motion due to Kepler says that a planet revolves around the sun in an elliptic orbit (Fig. 1(a)). The basic physical meaning of this equation is better explained by Fig. 1(b) in which is depicted an ellipse, with eccentricity e, that is the orbit of a body moving about the stationary gravitating center placed in focus of the ellipse S. From P we drop a perpendicular to the major axis of the ellipse and denote the foot of the perpendicular by letter R. Extend this perpendicular to intersect the circle at point Q. Suppose that the planet P, having passed thought perihelion A is at position P after elapsed time t, it is possible to express the polar coordinates of P (r, v), relative to the sun in terms of t
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