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1.
Peter Musen 《Celestial Mechanics and Dynamical Astronomy》1971,4(3-4):378-396
This paper derives the contributionF
2
* by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. An earlier solution suggested by Hill is based on Leverrier's equations for the variation of elements of Jupiter and Saturn and on the semi-empirical adjustment of the coefficients in the secular disturbing function. Nowadays there are several modern methods of eliminating periodic terms from the Hamiltonian and deriving a purely secular disturbing function. Von Zeipel's method is especially suitable. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations.The Krylov-Bogolubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing functionF
2
* derived in this paper can be included in existing theories of the secular effects of principal planets. A better approach would be to preserve the homogeneity of the theory and rederive all the secular perturbations of principal planets using Andoyer's symbolism, including the part produced by the great inequality. 相似文献
2.
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
3.
Zoran Knežević 《Celestial Mechanics and Dynamical Astronomy》1989,46(2):147-158
The Hamiltonian of the second order with respect to the disturbing mass, as defined in the higher order-higher degree theory of asteroid secular perturbations by Yuasa (1973), is expressed in the heliocentric, ecliptic coordinate system. Errors found in the original paper with terms coming from the principal part of the disturbing function are removed, and corrected values of the coefficients are computed. The importance of second-order perturbations and the improvement in the accuracy of proper element determination, achieved by using the newly-obtained coefficients, are demonstrated. Finally, a table of the secular frequencies as functions of the semimajor axis is given, and compared with the analogous one by Kozai (1979). 相似文献
4.
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
5.
A second order atmospheric drag theory based on the usage of TD88 model is constructed. It is developed to the second order
in terms of TD88 small parameters K
n,j
. The short periodic perturbations, of all orbital elements, are evaluated. The secular perturbations of the semi-major axis
and of the eccentricity are obtained. The theory is applied to determine the lifetime of the satellites ROHINI (1980 62A),
and to predict the lifetime of the microsatellite MIMOSA. The secular perturbations of the nodal longitude and of the argument
of perigee due to the Earth’s gravity are taken into account up to the second order in Earth’s oblateness. 相似文献
6.
In this part we calculate the secular and critical terms arising from the indirect part of the classical planetary Hamiltonian for Uranus and Neptune. We neglect in our expansions powers higher than the second in the eccentricity-inclination. Our required results, are expressed in terms of Poincaré variables. 相似文献
7.
Giorgio E. O. Giacaglia James P. Murphy Theodore L. Felsentreger 《Celestial Mechanics and Dynamical Astronomy》1970,3(1):3-66
A semi-analytical solution to the problem of the motion of a satellite of the moon is presented. Perturbative effects which are considered include those due to the attraction of the moon, earth, and sun, the non-sphericity of the moon's gravitational field, coupling of lower-order terms, solar radiation pressure, and physical libration. Short-period terms and intermediate-period terms, terms with the period of the moon's longitude, are produced by means of von Zeipel's method; it is proposed to obtain the secular perturbations, and those depending only on the argument of perilune, by numerical integration of the equations of motions. The short-period terms and intermediate-period terms are developed up to second order, where first order is 10–2. The secular perturbations and perturbations dependent on the argument of perilune are obtained to third order. 相似文献
8.
M. Burša 《Earth, Moon, and Planets》1988,42(1):49-53
A dynamic homogeneous model of Phobos is used: its boundary is an equipotential surface specified by the second zonal and the second sectorial harmonics plus the constant part of the tidal potential due to Mars. The principal moments of inertia, the hydrostatic second zonal harmonic and the secular Love number of Phobos have been estimated. They support the hypothesis that Phobos is formed out of primordial matter by accretion in orbit. 相似文献
9.
We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the secular Hamiltonian, we use angular momentum and eccentricity vectors as elements. The method of variation of constants then leads to a set of equations of motion that are simple and regular, thus allowing efficient numerical integration. Some possible applications are briefly described. 相似文献
10.
Maxim Varfolomeev 《Planetary and Space Science》2008,56(14):1773-1777
An attempt to build a new theory of the main Uranian satellites is being made at the Sternberg Astronomical Institute. The main difference compared to GUST86 theory is that the new theory is planned to be completely analytical. To do this, the secular frequencies of the satellites should be calculated taking into account the secular perturbations of the second order and, partly, of the third order. This allows to improve the secular frequencies and make them more close to those obtained from numerical integration. Nevertheless, discrepancies remain, which indicate that more terms in the analytical development are needed. Some other advantages of the new theory are also discussed. 相似文献
11.
Nikolaos Georgakarakos 《Monthly notices of the Royal Astronomical Society》2009,392(3):1253-1263
In a series of papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. However, for certain combinations of the masses and the orbital elements, the secular part of the solution failed. In this paper, we derive a new solution for the secular part of the inner eccentricity, which corrects the previous weakness. The derivation applies to hierarchical triple systems with coplanar and initially circular orbits. The new formula is tested numerically by integrating the full equations of motion for systems with mass ratios from 10−3 to 103 . We also present more numerical results for short-term eccentricity evolution, in order to get a better picture of the behaviour of the inner eccentricity. 相似文献
12.
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
13.
The secular effect of YORP torque on the rotational dynamics of an asteroid in non-principal axis rotation is studied. The
general rotational equations of motion are derived and approximated with an illumination function expanded up to second order.
The resulting equations of motion can be averaged over the fast rotation angles to yield secular equations for the angular
momentum, dynamic inertia and obliquity. We study the properties of these secular equations and compare results to previous
research. Finally, an application to several real asteroid shapes is made, in particular we study the predicted rotational
dynamics of the asteroid Toutatis, which is known to be in a non-principal axis state. 相似文献
14.
Anne-Sophie Libert Marco Sansottera 《Celestial Mechanics and Dynamical Astronomy》2013,117(2):149-168
We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincaré canonical variables, we determine the fundamental frequencies of the motion and compute analytically the long-term evolution of the Keplerian elements. Our study clearly shows that, for systems close to a mean-motion resonance, the second order approximation describes their secular evolution more accurately than the usually adopted first order one. Moreover, this approach takes into account the influence of the mean anomalies on the secular dynamics. Finally, we set up a simple criterion that is useful to discriminate between three different categories of planetary systems: (i) secular systems (HD 11964, HD 74156, HD 134987, HD 163607, HD 12661 and HD 147018); (ii) systems near a mean-motion resonance (HD 11506, HD 177830, HD 9446, HD 169830 and $\upsilon $ υ Andromedae); (iii) systems really close to or in a mean-motion resonance (HD 108874, HD 128311 and HD 183263). 相似文献
15.
In this paper we investigate the influence of a varying gravitation constant on the orbits of celestial bodies. Regarding the eccentric anomaly as an independent variable, we find the solutions to the perturbed equations of motion. In the first order solutions, we find the secular and periodic variations in semi-major axis. For the other orbital elements only periodic variations exhibit. However in the second order solutions, the longitude of periastron and the mean longitude have secular terms. Applying the calculations to six selected binaries, we give the numerical estimations of the variations of orbits. These results are then carefully compared and discussed. 相似文献
16.
Zdeněk Kopal 《Astrophysics and Space Science》1974,27(2):389-418
The aim of the present paper will be to develop a theory which should make it possible to investigate secular stability of close binary systems, consisting of tidally-distorted components of arbitrary internal structure, by a minimization of the potential energy of the system as a whole. In the second section which follows brief introductory remarks, appropriate expressions for the total potential energy of a close binary will be formulated. Section 3 will be concerned mainly with the nature of the tide-generating potential, and its effects on the shape of each star. In Section 4, the amplitudes of partial tides raised by this potential will be specified, for stars of arbitrary structure, correctly to terms of second order in superficial distortion; and in Section 5 we shall investigate the effects of interaction between rotation and tides to the same degree of approximation. The concluding Section 6 will then contain an explicit formulation of different constituents adding up to the total potential energy of the system, which can be used as a basis for its secular stability by the methods outlined already in our previous investigation (Kopal, 1973). 相似文献
17.
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
18.
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
19.
The secular terms of the first-order planetary Hamiltonian is determined, by two methods, in terms of the variables of H. Poincaré, neglecting powers higher than the second in the eccentricity-inclination. 相似文献
20.
Michael Efroimsky 《Celestial Mechanics and Dynamical Astronomy》2005,91(1-2):75-108
It was believed until very recently that a near-equatorial satellite would always keep up with the planet’s equator (with
oscillations in inclination, but without a secular drift). As explained in Efroimsky and Goldreich [Astronomy & Astrophysics (2004) Vol. 415, pp. 1187–1199], this misconception originated from a wrong interpretation of a (mathematically correct)
result obtained in terms of non-osculating orbital elements. A similar analysis carried out in the language of osculating
elements will endow the planetary equations with some extra terms caused by the planet’s obliquity change. Some of these terms
will be non-trivial, in that they will not be amendments to the disturbing function. Due to the extra terms, the variations
of a planet’s obliquity may cause a secular drift of its satellite orbit inclination. In this article we set out the analytical
formalism for our study of this drift. We demonstrate that, in the case of uniform precession, the drift will be extremely
slow, because the first-order terms responsible for the drift will be short-period and, thus, will have vanishing orbital
averages (as anticipated 40 years ago by Peter Goldreich), while the secular terms will be of the second order only. However,
it turns out that variations of the planetary precession make the first-order terms secular. For example, the planetary nutations
will resonate with the satellite’s orbital frequency and, thereby, may instigate a secular drift. A detailed study of this
process will be offered in a subsequent publication, while here we work out the required mathematical formalism and point
out the key aspects of the dynamics.
In this article, as well as in (Efroimsky 2004), we use the word ‘‘precession’’ in its most general sense which embraces the
entire spectrum of changes of the spin-axis orientation -- from the long-term variations down to the Chandler Wobble down
to nutations and to the polar wonder. 相似文献