共查询到20条相似文献，搜索用时 406 毫秒
1.
J. P. S. Carvalho R. Vilhena de Moraes A. F. B. A. Prado 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):371-388
In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites.
We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a
third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to
the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute
the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied
to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the
case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed,
considering that the perturbations are acting together or one at a time. 相似文献
2.
E. A. Roth 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):155-169
The third body perturbation of an orbiter of a planet or moon is considered. A very convenient form of the Lagrange equations is given allowing an easy derivation of the various terms of the expansion of the perturbed elements. A careful analysis of the order of magnitude of these terms indicates which ones are required for a consistent theory. It follows that in many practical cases the main term of the disturbing function has to be carried to the second order of the perturbation theory.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.Dedicated to V. Szebehely on the occasion of his 60th birthday 相似文献
3.
L. Sehnal 《Celestial Mechanics and Dynamical Astronomy》1981,25(2):169-179
The changes of the orbital motion of an artificial satellite caused by the terrestrial infrared radiation pressure are studied. The infrared radiation is described as a series of spherical harmonics and only the zero-th and second-order harmonics and taken into account. The expressions for the disturbing components and for the changes of the orbital elements are given together with numerical examples. The comparison of the computed magnitudes of the disturbing force with observed data shows good agreement. 相似文献
4.
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
5.
Bryan Brown 《Celestial Mechanics and Dynamical Astronomy》1977,16(2):229-259
Some of the results of an investigation into the long period behavior of the orbits of the Galilean satellites of Jupiter are presented. Special purpose computer programs were used to perform all the algebraic manipulations and series expansions that are necessary to describe the mutual interactions among the satellites.The disturbing function was expanded as a Poisson series in the modified Keplerian elements referred to a Jovicentric coordinate system. The differential equations for the modified Keplerian elements were then formed, and all short period perturbations were removed using Kamel's perturbation method. Approximate analytical solutions for these differential equations are derived, and the general form of the solutions are given. 相似文献
6.
Eric Bois 《Celestial Mechanics and Dynamical Astronomy》1986,39(4):309-327
This work aims at finding an analytic solution corresponding to the attitude evolution in space of a satellite submitted to disturbing torques. This paper presents a basic frame applicable to any perturbed rotation satellite, and a method of resolution leading to a formal solution which is given here to the first order. Thus, the main problem is the slow rotation of a body with three unequal axes of inertia, essentially submitted to a dominant solar radiation pressure torque, with the axis pointing far away from a position of equilibrium. The comparison of the results with a numerical integration based upon a HIPPARCOS model is convincing. 相似文献
7.
Ronald H. Estes 《Celestial Mechanics and Dynamical Astronomy》1974,10(3):253-276
The disturbing function of the Moon (Sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the Moon (Sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elementsl, l′, F, D and Γ of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements ω and Ω of the satellite so that analytic integration is simple and the results accurate over a long period of time. 相似文献
8.
S. Barcza 《Astrophysics and Space Science》1980,72(2):497-507
A new method is presented in a general form to solve the Schrödinger equation of helium-like ions. The wave function is expanded in terms of the eigenfunctions of a moving electron in the field of two Coulombic ions which are fixed in space. This makes the method similar to the Dirac perturbation theory (perturbation theory for time-dependent problems). In the present method an infinitely coupled system of infinitely many second-order ordinary differential equations must be solved instead of one second-order partial differential equation of three variables. The nature of the singular points and boundary conditions are discussed and some general relations are given which are useful for the numerical treatment. 相似文献
9.
J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):331-331
Some of the basic ideas of an analytical orbiter theory which is being developed by Hubert Claes in Namur are presented.The theory is based on the Lie transform technique and will be expressed in a closed form up to second order. The inclusion of additional terms of the third order (expanded in power series of the eccentricity) will be considered.Special attention is being given to the choice of the elements and to the final form of the theory. Three main criteria are used. The removal of the virtual singularities of small inclination and eccentricity. The simplicity of the final form of the theory once the elements have been given their numerical values. The numerical stability of the evaluation of the theory. 相似文献
10.
Starting from the analytical theory of perturbed circular motions presented in Celestial Mechanics (Bois, 1994), this paper presents an extended resolution valid also for small eccentricity orbits. The solution is of the first order of a small parameter characterizing the magnitude of disturbing forces. The solution has the form of Fourier series with the coefficients given by iterative formation laws. The solution is free from singularities due to small eccentricity or inclination. As an example of numerical application the equatorial artificial satellite orbits are analyzed. For some high satellite orbits with small eccentricity the difference between the numerical integration and the analytical model does not exceed few centimeters per one revolution.On leave from Astronomical Observatory of A. Mickiewicz University, Soneczna 36, PL60-286 Pozna, Poland. 相似文献
11.
This paper deals with the perturbations which rotation can produce to the orbital elements of a close binary system. The rectangular components,R, S andW of the disturbing accelerations due to rotation have been substituted to the Gauss form of Lagrange's planetary equations to yield the first order approximation. The results obtained are exact for any value of orbital eccentricity between the values 0<e<1 and for arbitrary inclinations of the rotational axes to the orbital plane.First and second order approximations are given for the special case when equators are coplanar to the orbit. 相似文献
12.
G. Antonacopoulos 《Astrophysics and Space Science》1972,17(2):267-276
The secular terms of the planetary disturbing function are given, after elimination of short period terms by von Zeipel's
transformation.
The adequacy of this expansion up to terms of eighth order in the inclination and eccentricity is investigated by numerical
processes, as a function of the Keplerian elementsa, e andi. The eccentricityé of the outer planet, is taken equal to zero.
It is concluded that for values ofi which are not small the inclusion of additional terms in the expression for the disturbing function, results to drastic changes
in its values, while larger values ofe do not have an equaly large effect on the disturbing function. 相似文献
13.
David R. Cok 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):459-479
The lunar disturbing function for a close-Earth satellite is expressed as a sum of products of harmonics of the satellite's position and harmonics of the Moon's position, and the latter are expanded about a rotating and precessing elliptic orbit inclined to the ecliptic. The deviations of the Moon from this approximate orbit are computed from Brown's lunar theory andthe perturbations in satellite orbital elements due to these inequalities are derived. Numerical calculations indicate that several perturbations in the position of the satellite's node and perigee have magnitudes on the order of one meter.The author is supported in part by a National Science Foundation Graduate Fellowship. 相似文献
14.
This paper studies the relative motion of satellite formation flying in arbitrary elliptical orbits with no perturbation.
The trajectories of the leader and follower satellites are projected onto the celestial sphere. These two projections and
celestial equator intersect each other to form a spherical triangle, in which the vertex angles and arc-distances are used
to describe the relative motion equations. This method is entitled the reference orbital element approach. Here the dimensionless
distance is defined as the ratio of the maximal distance between the leader and follower satellites to the semi-major axis
of the leader satellite. In close formations, this dimensionless distance, as well as some vertex angles and arc-distances
of this spherical triangle, and the orbital element differences are small quantities. A series of order-of-magnitude analyses
about these quantities are conducted. Consequently, the relative motion equations are approximated by expansions truncated
to the second order, i.e. square of the dimensionless distance. In order to study the problem of periodicity of relative motion,
the semi-major axis of the follower is expanded as Taylor series around that of the leader, by regarding relative position
and velocity as small quantities. Using this expansion, it is proved that the periodicity condition derived from Lawden’s
equations is equivalent to the condition that the Taylor series of order one is zero. The first-order relative motion equations,
simplified from the second-order ones, possess the same forms as the periodic solutions of Lawden’s equations. It is presented
that the latter are further first-order approximations to the former; and moreover, compared with the latter more suitable
to research spacecraft rendezvous and docking, the former are more suitable to research relative orbit configurations. The
first-order relative motion equations are expanded as trigonometric series with eccentric anomaly as the angle variable. Except
the terms of order one, the trigonometric series’ amplitudes are geometric series, and corresponding phases are constant both
in the radial and in-track directions. When the trajectory of the in-plane relative motion is similar to an ellipse, a method
to seek this ellipse is presented. The advantage of this method is shown by an example. 相似文献
15.
Juan Getino José M. Ferrándiz 《Monthly notices of the Royal Astronomical Society》2001,322(4):785-799
In this paper we present a theory of the Earth rotation for a model composed of an inelastic mantle and a liquid core, including the dissipation in the core–mantle boundary (CMB). The main features of the theory are: (i) to be Hamiltonian, therefore the computation of some complex inner torques can be avoided; (ii) to be self-consistent and non-dependent on a previous rigid Earth theory, so there is no need to use transfer functions; (iii) to be analytical, the solution being derived by perturbation methods. Numerical nutation series deduced from the theory are compared with the IERS 96 empirical series, an accuracy better than 0.8 mas in providing celestial ephemeris pole (CEP) offsets . 相似文献
16.
We study the effects of a non-singular gravitational potential on satellite orbits by deriving the corresponding time rates
of change of its orbital elements. This is achieved by expanding the non-singular potential into power series up to second
order. This series contains three terms, the first been the Newtonian potential and the other two, here R
1 (first order term) and R
2 (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian
potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change
of the orbital elements of a satellite in a non-singular gravitational field. We split these effects into secular, low and
high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate
Experiment (GRACE). We show that the secular effect of the second-order disturbing term R
2 on the perigee and the mean anomaly are 4″.307×10−9/a, and −2″.533×10−15/a, respectively. These effects are far too small and most likely cannot easily be observed with today’s technology. Numerical
evaluation of the low and high frequency effects of the disturbing term R
2 on low Earth orbiters like GRACE are very small and undetectable by current observational means. 相似文献
17.
E. Bois 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):125-138
This paper presents a basic frame applicable to any perturbed circular motion in any orbital inclination, and a method of resolution leading to a formal solution given here to the first order. The main advantage of the solution, expanded in Fourier series and non-singular variables, is the presence of iterative formation laws for its coefficients. The theory is then particularly accurate and suitable for various periodic perturbations. The comparison of the results with a numerical integration is convincing. 相似文献
18.
Eddy current torques,air torques,and the spin decay of cylindrical rocket bodies in orbit 总被引：1，自引：0，他引：1
This paper considers the torques causing spin decay in cylindrical rocket bodies in orbit. Eddy current torques, due to the Earth's magnetic field, are estimated using Smith's (1962) model—a hollow cylindrical conducting shell, tumbling about a transverse axis. Air torques are estimated by numerical integration of aerodynamic moments over the rocket surface. It is shown that for Cosmos rockets, 7.4 m long and 2.4 m in diameter, eddy current torques outweigh air torques by several orders of magnitude at altitudes near 500 km, and that they are dominant at altitudes down to 160 km. Visual observations of several such rockets illustrate a variation of spin decay time with altitude which supports this conclusion. The same observations suggest that a few Cosmos rockets may be special cases, different from the rest in construction. 相似文献
19.
Dieter S. Schmidt 《Earth, Moon, and Planets》1980,23(2):135-164
Brown's method for solving the main problem of lunar theory has been adapted for the computation by machine with the help of an algebraic processor. Brown's results are first recovered and refined. The solution is then expanded to include most terms of order nine. The terms in the series for the longitude and latitude are listed with an accuracy of 0.000 01 and of 0.000 001 for the parallax.This research was supported in parts by the National Science Foundation grant MCS 78-01425. 相似文献
20.
In the current study, a double-averaged analytical model including the action of the perturbing body’s inclination is developed
to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to
the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of
the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous
study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body’s inclination, and
illustrate that the lunar obliquity with the value 6.68∘ is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity
of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude
Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial
systems. 相似文献