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In ephemeridical astronomy, an important role is played by the kinematic equation relating time and position in the orbit. Since the ephemerides have already been calculated for many hundreds of thousands of celestial bodies moving along more or less known orbits, close to optimal algorithms for solving this equation are required. We consider the case of near-parabolic motion, for which Euler found an elegant form for the kinematic equation, to be insufficiently thoroughly studied. Earlier, we presented a solution of this equation using a series in powers of the small parameter introduced by Euler with timedependent coefficients. In the current study, we find the region of convergence of this series. 相似文献
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In the long-wave approximation, we perform the numerical analysis of the plane problem of runup of waves of various shapes
on a sloping beach. We study transformations of the shape of waves flooding the beach and in the course of their subsequent
rundown. The dependence of maximum elevations and lowerings of the sea level on the parameters of the waves approaching the
beach, the depth of the shelf, and the slope of the bottom are investigated. It is shown that the shape of waves affects the
amplitude characteristics of oscillations of the coastline. The heights of the vertical runup of waves incident on a sloping
beach can be several times higher than the amplitude of waves entering the shelf zone. 相似文献
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Astronomy Reports - The motion of a point with zero mass under the action of attraction to the central body $$\mathcal{S}$$ and perturbing acceleration $${\mathbf{P}}{\kern 1pt} ' =... 相似文献
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The motion of a zero-mass point under the action of gravitation toward a central body and a perturbing acceleration P is considered. The magnitude of P is taken to be small compared to the main acceleration due to the gravitation of the central body, and the components of the vector P are taken to be constant in a reference frame with its origin at the central body and its axes directed along the velocity vector, normal to the velocity vector in the plane of the osculating orbit, and along the binormal. The equations in the mean elements were obtained in an earlier study. The algorithm used to solve these equations is given in this study. This algorithm is analogous to one constructed earlier for the case when P is constant in a reference frame tied to the radius vector. The properties of the solutions are similar. The main difference is that, in the most important cases, the quadratures to which the solution reduces lead to non-elementary functions. However, they can be expressed as series in powers of the eccentricity e that converge for e < 1, and often also for e = 1. 相似文献
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In celestial mechanics the kinematic equation connecting the time and position in orbit is important. This equation is investigated in detail, but the case of nearly-parabolic motion remains little studied. The universal equations were derived by Euler, but he did not investigate then in detail. We present the solution in the form of series with respect to the small Euler parameter, with coefficients depending on time, and we solve the problem on determining the convergence domain of this series that occurs to be more complicated problem. 相似文献
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N. Batmunkh T. N. Sannikova K. V. Kholshevnikov V. Sh. Shaidulin 《Astronomy Reports》2016,60(3):366-373
A precise estimate of the variation of the position of a celestial body in the case of small variations of the elements of its orbit is obtained using an Euclidean (mean-square) norm for the deviation in the position. A relatively simple expression for the mean-square deviation of the radius vector dr in terms of the deviations of the elements is derived. These are taken to be first-order small quantitites, with second-order quantities neglected. This relation is applied to estimate the norm ||dr|| in two problems. In the first one, small and constant differences between six orbital elements (including the mean anomaly) are considered for two orbits. In the second one, a zero-mass point moves under the gravitation of a central body and a small perturbing acceleration F. The vector F is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the binormal vector. In this latter problem, dr is the difference between the position vectors in the osculating and mean orbit. The norm ||dr||2 is the weighted sum of the squares of the components of F, neglecting higher-order small quantities. The coefficients of the quadratic form depend only on the semi-major axis and the eccentricity of the mean orbit. The results are applied to the motion of a small asteroid under the action of a low-thrust engine imparting a small force. 相似文献
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Astronomy Reports - A problem is considered in which a zero-mass point moves under the attraction of the central body $$\mathcal{S}$$ and perturbing acceleration $${\mathbf{P}}{\kern 1pt}... 相似文献
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Astronomy Reports - The motion of an asteroid in a central gravitational field in the presence of an additional perturbing acceleration due to the Yarkovsky effect was considered. The long-term... 相似文献
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