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1.
The orbit of the balloon satellite, Explorer 19, is analysed to determine the effects of direct solar radiation pressure over one revolution of the satellite (111 min) for MJD 42822 and MJD 42966. At the earlier date, the satellite entered the Earth's shadow, presenting an opportunity to examine the effectiveness of two different shadow models. The reflectivity of the surface of the satellite was estimated from analysis of the variations in orbital eccentricity over a period of 236 days.Although many of the parameters associated with the shape and orientation of the satellite are unknown, the theory for a non-spherical satellite is applied using trial and error methods to determine the parameters of best fit. The paper concludes with an examination of the perturbations in orbital eccentricity and inclination due to incident, specularly reflected, and diffusely reflected radiation. 相似文献
2.
D. V. Nikonchuk 《Astronomy Letters》2012,38(12):813-828
Anonlinear analytical theory of secular perturbations in the problem of the motion of a systemof small bodies around a major attractive center has been developed. Themutual perturbations of the satellites and the influence of the oblateness of the central body are taken into account in the model. In contrast to the classical Laplace-Lagrange theory based on linear equations for Lagrange elements, the third-degree terms in orbital eccentricities and inclinations are taken into account in the equations. The corresponding improvement of the solution turns out to be essential in studying the evolution of orbits over long time intervals. A program inC has been written to calculate the corrections to the fundamental frequencies of the solution and the third-degree secular perturbations in orbital eccentricities and inclinations. The proposed method has been applied to investigate the motion of the major Uranian satellites. Over time intervals longer than 100 years, allowance for the nonlinear terms in the equations is shown to give corrections to the coordinates of Miranda on the order of the orbital eccentricity, which is several thousand kilometers in linear measure. For other satellites, the effect of allowance for the nonlinear terms turns out to be smaller. Obviously, when a general analytical theory of motion for the major Uranian satellites is constructed, the nonlinear terms in the equations for the secular perturbations should be taken into account. 相似文献
3.
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
4.
A new nonsingular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed for long term motion in terms of the KS uniformly regular canonical elements by a series expansion method, by assuming the atmosphere to be symmetrically spherical with constant density scale height. The series expansions include up to third order terms in eccentricity. 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. Numerical comparisons of the important orbital parameters semi major axis and eccentricity up to 1000 revolutions, obtained with the present solution, with KS elements analytical solution and Cook, King-Hele and Walker's theory with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination. 相似文献
5.
M. A. Vashkov’yak 《Astronomy Letters》2003,29(6):416-423
A modified method for averaging the perturbing function in Hill’s problem is suggested. The averaging is performed in the revolution period of the satellite over the mean anomaly of its motion with a full allowance for a variation in the position of the perturbing body. At its fixed position, the semimajor axis of the satellite orbit during the revolution of the satellite is constant in view of the evolution equations, while the remaining orbital elements undergo secular and long-period perturbations. Therefore, when the motion of the perturbing body is taken into account, the semimajor axis of the satellite orbit undergoes the strongest perturbations. The suggested approach generalizes the averaging method in which only the linear (in time) term is included in the perturbing function. This method requires no expansion in powers of time. The described method is illustrated by calculating the perturbations of the semimajor axes for two distant satellites of Saturn, S/2000 S 1 and S/2000 S5. An approximate analytic solution is compared with the results of numerical integration of the averaged system of equations of motion for these satellites. 相似文献
6.
The equations describing the disturbed motion of an artificial Earth satellite in the atmosphere are integrated by using a new variable instead of the true anomaly. The atmospheric flattening and rotation, the linear variation of the density scale height with the altitude, the symmetrical diurnal effect and the variation of its amplitude with the heigth are taken into account. Approximate formulae for the perturbations in all the orbital elements over a revolution of the satellite are given. 相似文献
7.
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
8.
《Planetary and Space Science》2007,55(10):1388-1397
A new non-singular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed in terms of the Kustaanheimo and Stiefel (KS) uniformly regular canonical elements, by assuming the atmosphere to be oblate diurnally varying with constant density scale height. The series expansions include up to third-order terms in 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. Numerical comparisons of the important orbital parameters semimajor axis and eccentricity up to 1000 revolutions, obtained with the present solution, with the third-order analytical theories of Swinerd and Boulton and in terms of the KS elements, with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination. 相似文献
9.
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
10.
Paul C. Joss 《Icarus》1973,19(1):147-153
The statistical significance of anisotropies in the distribution of orbital orientations among the long-period and nearly parabolic comets is evaluated. It is suggested that these anisotropies are not the result of observational selection effects. A numerical model for the distribution of orbital orientations is constructed, based on Oort's theory of comet origin and the assumption that the observed anisotropies are caused by multiple planetary perturbations over the course of many perihelion passages. The model, which is restricted to comets with peri-helion distances less than 0.3AU, does not predict any significant anisotropies. 相似文献
11.
K. Aksnes 《Celestial Mechanics and Dynamical Astronomy》1976,13(1):89-104
On the basis of expressions derived by Kozai, and new ones developed here, a detailed, semianalytic algorithm is presented for calculating radiation-pressure perturbations in the Keplerian elements. Through some simple modifications, the algorithm is also made to hold whene=0 and/ori=0. The perturbations are obtained by summing over the sunlit segment of the satellite's orbit during each revolution or part thereof. The end points of this segment are evaluated numerically once per revolution. The effect of the inherent uncertainties in the boundaries of the Earth's shadow is discussed. The algorithm is tested by means of numerical integration of the equations of motion and through comparisons with observations of the balloon satellite 1963 30D during a 200-day interval. 相似文献
12.
P. Moore 《Celestial Mechanics and Dynamical Astronomy》1979,20(2):125-142
The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime. 相似文献
13.
D. A. Lautman 《Celestial Mechanics and Dynamical Astronomy》1977,15(4):387-420
A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomalyv. The perturbations within a given revolution can be obtained analytically by integrating with respect tov while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution. 相似文献
14.
Variations in satellite orbital elements are derived due to perturbations in the external gravitational field of the central body caused by mass deformations of the body occurring from variations in its rotation; the central body is assumed to be perfectly elastic. General theory derived is applied to the actual Earth, as an example; possible resonances are discussed. 相似文献
15.
Julien Dufey Anne Lemaître Nicolas Rambaux 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):141-157
Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR. 相似文献
16.
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss’ equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the “adiabatic” approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request. 相似文献
17.
《New Astronomy》2007,12(6):490-496
To explore the dynamics of a test particle in the near-Mercury’s environment, the orbital motion of an orbiter around Mercury is considered. Different perturbing forces, namely the Mercurian gravity field, the solar radiation pressure, the solar wind and the coronal mass ejections, are taken into account. The order of magnitude of each perturbing term is assessed. The equations of motion in canonical representation are obtained. The Hamiltonian in terms of Hansen coefficients is expressed. A procedure for solution is presented. The short and long periodic terms are removed from the Hamiltonian and the solution is obtained. Long periodic perturbations on the orbital dynamics of an orbiter around Mercury due to the solar events are found as revealed by Eq. (26) in the text. Resonance cases are discussed and the different resonant inclinations are obtained. A procedure for the computation of the position and velocity is presented. 相似文献
18.
Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1978,18(2):141-161
The problem is considered within the framework of the elliptic restricted three-body problem. The asymptotic solution is derived by a three-variable expansion procedure. The variables of the expansion represent three time-scales of the asteroids: the revolution around the Sun, the libration around the triangular Lagrangian pointsL
4,L
5, and the motion of the perihelion. The solution is obtained completely in the first order and partly in the second order. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter. As an example for the perturbations of the orbital elements the main perturbations of the eccentricity, the perihelion longitude and the longitude of the ascending node are given. Conditions for the libration of the perihelion are also discussed. 相似文献
19.
Ram Krishan Sharma 《Celestial Mechanics and Dynamical Astronomy》1993,56(4):503-521
Analytical theory for short-term orbit motion of satellite orbits with Earth's zonal harmonicsJ
3 andJ
4 is developed in terms of KS elements. Due to symmetry in KS element equations, only two of the nine equations are integrated analytically. The series expansions include terms of third power in the eccentricity. Numerical studies with two test cases reveal that orbital elements obtained from the analytical expressions match quite well with numerically integrated values during a revolution. Typically for an orbit with perigee height, eccentricity and inclination of 421.9 km, 0.17524 and 30 degrees, respectively, maximum differences of 27 and 25 cm in semimajor axis computation are noted withJ
3 andJ
4 term during a revolution. For application purposes, the analytical solutions can be used for accurate onboard computation of state vector in navigation and guidance packages. 相似文献
20.
Stefano Casotto 《Celestial Mechanics and Dynamical Astronomy》1993,55(3):223-241
Kaula's celebrated solution to the problem of satellite motion in the gravitational field of a rigid body is transformed to give the perturbation spectra in both position and velocity in the radial, transverse and normal directions of the orbital reference frame. This work is an extension and a refinement of the theory of orbital perturbations due to the geopotential previously published by Rosborough and Tapley (1987). 相似文献