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1.
We calculate in this paper the secular and critical terms arising from the principal part of the classical planetary Hamiltonian. This is the first step to establish a third order canonical planetary theory of Uranus-Neptune through the Hori-Lie technique. We truncate our expansions at the second degree of eccentricity-inclination. Our planetary theory is expressed in terms of the canonical variables of H. Poincaré. 相似文献
2.
Osman M. Kamel 《Earth, Moon, and Planets》1989,45(2):127-137
We construct a U-N secular canonical planetary theory of the third order with respect to planetary masses. The Hori-Lie procedure is adopted to solve the problem. Expansions have been carried out by hand, neglecting powers higher than the second with respect to the eccentricity-inclination. We take into account the principal as well as the indirect part of the planetary disturbing function. The theory is expressed in terms of the Poincaré canonical variables, referring to the Jacobi-Radau set of origins. We assume that the 1:2 U-N critical terms and its multiples are the only periodic terms. 相似文献
3.
Osman M. Kamel 《Earth, Moon, and Planets》1988,40(2):119-147
We shall establish a second order - with respect to a small parameter which is of the order of planetary masses - Uranus-Neptune canonical planetary theory. The construction will be through the Hori-Lie perturbation theory. We perform the elliptic expansions by hand, taking into account powers 0, 1, 2 of the eccentricity-inclination. Only the principal part of the planetary Hamiltonian will be taken into consideration. Our theory will be expressed in terms of the canonical variables of Henri Poincaré, referring the planetary coordinates to the Jacobi-Radau system of origin. Only U- N critical terms will be assumed as the periodic terms. 相似文献
4.
We extend the construction of the Jupiter-Saturn theory to include all the terms up to the seventh order in the masses. The Hori-Lie transformation technique is employed. The Jacobian coordinates are adopted and the theory is expressed in terms of the canonical non-singular variables of H. Poincaré. 相似文献
5.
Developed in this paper is a new approach to an analytic satellite theory which is based on Deprit's elimination of the parallax. The first step in the theory is the elimination of the parallax canonical transformation which eliminates the short period terms in the perturbations to within a factor of (1/r)2. A new approach is then taken. The perigee terms are eliminated while retaining the short period terms in (1/r)2. A Delaunay normalization of the short period terms in the (1/x)2 factor is then constructed to complete the theory. 相似文献
6.
Osman M. Kamel 《Earth, Moon, and Planets》1989,47(1):73-89
The construction of a third order J-S theory is presented. The Hori theory of planetary perturbations is employed. No Critical J-S terms due to the 2:5 commensurabilities and its multiples exist, when we take into account the periodic terms of order 0, 1, 2 with respect to the eccentricity- inclination. In this case the Lie series transformation degenerates and is meaningless. The J-S equations of motion for secular perturbations are solved when we neglect in our treatment, the Poisson terms of degree > 2 in the Poincaré canonical variables H
u
, K
u
, P
u
Q
u
(u = 1, 2). The Jacobi-Radau referential is adopted, and the theory is expressed in terms of the canonical variables of H. Poincaré.Now at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A. 相似文献
7.
We present a second order secular Jupiter-Saturn planetary theory through Poincaré canonical variables, von Zeipel's method and Jacobi-Radau referential. We neglect in our expansions terms of power higher than the fourth with respect to eccentricities and sines of inclinations. We assume that the disturbing function is composed of secular and critical terms only. We shall deriveF
2si
and writeF
2s
in terms of Poincaré canonical variables in Part II of this problem. 相似文献
8.
Osman M. Kamel 《Earth, Moon, and Planets》1990,49(3):259-267
We construct the outline of a third order secular theory for the four major planets. We apply the Hori-Lie technique to solve the problem. We take into consideration both parts of the perturbing function. Our canonical variables are those of H. Poincaré. Our periodic terms are the only 2:5 and 1:2 critical terms of J-S and U-N respectively. Terms of degree higher than the second in the Poincaré canonical variables H, K, P, Q are neglected. 相似文献
9.
Osman M. Kamel 《Earth, Moon, and Planets》1989,44(3):275-289
We explain how the first step of Hori-Lie procedure is applied in general planetary theory to eliminate short-period terms. We extend the investigation to the third-order planetary theory. We solved the canonical equations of motion for secular and periodic perturbations by this method, and obtained the first integrals of the system of canonical equations. Also we showed the relation between the determining function in the sense of Hori and the determining function in the sense of Von Zeipel. 相似文献
10.
Nikolaos Georgakarakos 《Monthly notices of the Royal Astronomical Society》2003,345(1):340-348
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well-separated components and comparable masses. The derivation of short-period terms is based on an expansion of the rate of change of the Runge–Lenz vector. Then, the short-period terms are combined with secular terms, obtained by means of canonical perturbation theory. The validity of the theoretical equations is tested by numerical integrations of the full equations of motion. 相似文献
11.
We complete by this part II the establishment of a second order secular Jupiter-Saturn theory. This is achieved by taking into consideration the influence of the indirect part of the planetary disturbing function, and expressing the second order secular Hamiltonian in terms of Poincaré's canonical variables. 相似文献
12.
Osman M. Kamel 《Earth, Moon, and Planets》1990,49(3):269-276
In this part we present the complete solution of the planetary canonical equations of motion by the method of G. Hori through successive changes of canonical variables using the Lie series. Thus, we can eliminate the long or critical terms of the planetary perturbing function, in our general planetary theory. In our formulas, we neglect perturbation terms of order higher than the third with respect to planetary masses. 相似文献
13.
Osman M. Kamel 《Astrophysics and Space Science》1979,64(1):227-238
We construct a first-order secular general planetary theory, using the Jacobi-Radau set of origins, referring to common fixed plane and in terms of Poincaré canonical variables. We neglect powers higher than the fourth with respect to the eccentricities and sines of inclinations. 相似文献
14.
We eliminate by the method of von Zeipel the short-period terms in a first order-with respect to planetary masses—general planetary Uranus-Neptune theory. We exclude in the expansion terms of eccentricities and sines of inclinations higher than the third power.Our variables are the Poincaré canonical variables. We use the Jacobi-Radau set of origins, and we refer the planes of the osculating ellipses to a common fixed plane, the longitudes to a common origin. The short-periodic terms arising from the indirect and principal parts of the disturbing functions, are eliminated separately. The Fourier series of the principal part of the disturbing function, is reduced to the sum of only the first three terms. 相似文献
15.
Osman M. Kamel 《Earth, Moon, and Planets》1982,26(1):47-60
We review in this part the outline of a third-order general planetary theory established through Von Zeipel's method and in terms of Poincaré's canonical variables We consider our system to consist of the Sun as the primary body, one disturbed planet, and one disturbing planet. 相似文献
16.
Osman M. Kamel 《Earth, Moon, and Planets》1992,57(1):23-64
In this paper we eliminate in a first order U-N theory the 1 : 2 critical terms up to the third degree with respect to eccentricity — inclination in both parts, main and indirect of the U-N planetary Hamiltonian. We operate the Von Zeipel technique. We adopt, in this theory, the Jacobi-Radau coordinates, and the Poincaré canonical variables. We neglect powers higher than the third in the eccentricity-inclination. This paper is related to the two previous articles (Kamel, 1982; 1983). 相似文献
17.
Jean Meffroy 《Earth, Moon, and Planets》1982,26(2):143-169
We solve the first order non-linear differential equation and we calculate the two quadratures to which are reduced the canonical differential equations resulting from the elimination of the short period terms in a second order planetary theory carried out through Hori's method and slow Delaunay canonical variables when powers of eccentricities and the sines of semi-inclinations which are >3 are neglected and the eccentricity of the disturbing planet is identically equal to zero. The procedure can be extended to the case when the eccentricity of the disturbing planet is not identically equal to zero. In this latter general case, we calculatedthe two quadratures expressing angular slow Delaunay canonical variable
1
of the disturbed planet and angular slow Delaunay canonical variable
2
of the disturbing planet in terms of timet. 相似文献
18.
Xavier James Raj 《Planetary and Space Science》2009,57(11):1312-1320
A new non-singular analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of uniformly regular KS canonical elements. Diurnally varying oblate atmosphere is considered with variation in density scale height dependent on altitude. The series expansion method is utilized to generate the analytical solutions and terms up to fourth-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere) are retained. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The important drag perturbed orbital parameters: semi-major axis and eccentricity are obtained up to 500 revolutions, with the present analytical theory and by numerical integration over a wide range of perigee height, eccentricity and inclination. The differences between the two are found to be very less. A comparison between the theories generated with terms up to third- and fourth-order terms in c and e shows an improvement in the computation of the orbital parameters semi-major axis and eccentricity, up to 9%. The theory can be effectively used for the re-entry of the near-Earth objects, which mainly decay due to atmospheric drag. 相似文献
19.
Osman M. Kamel 《Earth, Moon, and Planets》1992,59(2):111-140
We eliminate the 1:2 critical terms — after a previous elimination of the short period terms — in the Hamiltonian of a first order U-N theory. We take into account terms of degree 0, 1, 2, 3, 4 in the eccentricity-inclination. We apply for this elimination the Hori-Lie technique through the Poincaré canonical variables and the Jacobi coordinates. The purely principal first order secular U-N Hamiltonian admits a complete solution. We obtained the U-N equations of motion generated by the principal first order long period U-N Hamiltonian which will be solved later. This part III is closely related to the two previous papers (Kamel, 1982, 1983). 相似文献
20.
M. Xavier James Raj 《Planetary and Space Science》2009,57(1):34-41
A new non-singular analytical theory for the contraction of near-Earth satellite orbits under the influence of air drag is developed in terms of uniformly regular Kustaanheimo and Stiefel (KS) canonical elements using an oblate atmosphere with variation of density scale height with altitude. The series expansions include up to fourth power in terms of eccentricity and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. It is observed that the analytically computed values of the semi-major axis and eccentricity are consistent with the numerically integrated values up to 500 revolutions over a wide range of the drag-perturbed orbital parameters. The theory can be effectively used for re-entry of near-Earth objects. 相似文献