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1.
Evolution of Comet Nucleus Rotation 总被引：1，自引：0，他引：1
The secular evolution of comet nucleus rotation states subject to outgassing torques is studied. The dynamical model assumes that the nucleus inertia ellipsoid is axially symmetric. The outgassing torques acting on the surface are modeled using standard cometary activity formulae. The general rotational equations of motion are derived and separately averaged over the fast rotational dynamics terms and the comet orbit. Special cases where the averaging assumptions cannot be applied are evaluated separately. The modification of the comet orbit due to comet outgassing is neglected. Resulting from this analysis is a system of secular differential equations that describes the dynamics of the comet nucleus angular momentum and rotation state. We find that the qualitative secular evolution of the rotation state is controlled by a single parameter that combines parameters related to the comet orbit and parameters related to the nucleus surface geometry and activity. From this solution, we find qualitatively different evolutionary paths for comet nuclei whose entire surface is active, as compared to nuclei with only a single active region. For surface activity models between these extremes, we show that certain evolutionary paths are more likely than others. Additionally, our solution indicates that a comet nucleus' rotational angular momentum will tend to increase over time, potentially contributing to the observed phenomenon of comet nucleus splitting. 相似文献
2.
3.
S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1983,30(1):71-83
New physical principles for an explanation of seasonal variations in the Earth's rate of rotation are proposed. It is thought that the variations are caused by a variation of the total energy of the Earth's atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. Jacobi's virial equation for the Earth's atmosphere is derived from the Eulerian equations. The virial theorem is obtained. The existence of the relationship between Jacobi's function and potential energy of the atmosphere is confirmed. In the framework of this relationship, Jacobi's equation is reduced to the equation of unperturbed virial oscillations. The solution of the above-mentioned equation expresses the periodic virial oscillations of Jacobi's function (moment of inertia) of the Earth's atmosphere with time. The solution of the perturbed virial oscillation problem of the atmosphere-solid Earth system is obtained. The perturbation term in Jacobi's virial equation regards, in explicit form, the energy changes occurring in the atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. The annual and semi-annual periodic variations in the Earth's rate of rotation can be considered as an astrometrical result following from the obtained solution. A satisfactory accord of the theoretical results with experimental data is shown. 相似文献
4.
Hans J. Sperling 《Celestial Mechanics and Dynamical Astronomy》1972,6(3):278-293
Let a rigid satellite move in a circular orbit about a spherically symmetric central body, taking into account only the main term of the gravitational torque. We shall investigate and find all solutions of the following problem: Let the satellite be permitted to spin about an axis that is fixed in the orbit frame; the satellite need not be symmetric, the spin not uniform, and the spin axis not a principal axis of inertia. The complete discussion of this type of spin reveals that the cases found by Lagrange and by Pringle - and the well-known spin about a principal axis of inertia orthogonal to the orbit plane — are essentially the only ones possible; the only further (degenerate) case is uniform spin of a two-dimensional, not necessarily symmetric satellite about certain axes that are orthogonal to the plane containing the body and to the orbit of the satellite around the central body. 相似文献
5.
A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is
given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar
radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape
and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous
orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the
energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation
pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be
averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology
is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are
presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their
evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise
models for their orbital evolution. 相似文献
6.
Marcello Romano 《Celestial Mechanics and Dynamical Astronomy》2008,101(4):375-390
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of
inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for
the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular
to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial
angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed
with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case
of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix
in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of
a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of
an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body
with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic
solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion
time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an
exact solution of the rotational motion of a rigid body exists. 相似文献
7.
Attitude dynamics of perturbed triaxial rigid bodies is a rather involved problem, due to the presence of elliptic functions even in the Euler equations for the free rotation of a triaxial rigid body. With the solution of the Euler–Poinsot problem, that will be taken as the unperturbed part, we expand the perturbation in Fourier series, which coefficients are rational functions of the Jacobian nome. These series converge very fast, and thus, with only few terms a good approximation is obtained. Once the expansion is performed, it is possible to apply to it a Lie-transformation. An application to a tri-axial rigid body moving in a Keplerian orbit is made. 相似文献
8.
Bruno Bertotti 《Celestial Mechanics and Dynamical Astronomy》2001,80(1):21-38
We show that, when a natural satellite like Titan is invisible (e.g., due to an opaque atmosphere) its planetary orbit and its mass can be determined by tracking a spacecraft in close flybys. This is an important problem in the Cassini mission to the Saturnian system, which will be greatly improved by a good astrometric model for all its main components; in particular, an accuracy of a few hundred meters for the orbit of Titan is necessary to allow a measurement of its moment of inertia. The orbit of the spacecraft is the union of elliptical arcs, joined by short hyperbolic transitions: a problem of singular perturbation theory, whose solution leads to a matching condition between the inner hyperbolic orbit and the elliptical orbital elements. Since the inner elements are given in terms of the relative position and velocity of the spacecraft, accurate Doppler measurements in both regions can provide a satisfactory determination of Titan's position and velocity, hence of its Keplerian elements. The errors in this determination are discussed on the basis of the expected Allan deviation of the Doppler method; it is found that the driving errors are those in the elliptical arcs; the fractional errors in Titan's orbital elements are expected to be 10–7. It is also possible to measure the mass of the satellite; however, when the eccentricity e of the flybys is large, the mass and a scaling transformation are highly correlated and the fractional error in the mass is expected to be e times worse. 相似文献
9.
Ming-Jiang Zhang Hong-Bo Wang Chang-Yin Zhao Jian-Ning Xiong Dong Wei Wei Zhang Sheng-Xian Yu 《Astrophysics and Space Science》2018,363(8):175
Taking the re-entry object CZ-3B R/B (COSPAR identifier 2012-018D, NORAD catalog number 38253) as an example, retrieval of atmospheric mass densities in lower thermosphere below 200 km from its rebuilt precise orbit is studied in this paper. Two methodologies, i.e. analytical and numerical methods, are adopted in the retrieval. Basic principles of these two methodologies are briefly introduced. Based on the short-arc sparse observational data accumulated in the high accuracy re-entry prediction, orbit determinations of re-entry object CZ-3B R/B are performed sectionally, and then its precise orbit is rebuilt. According to the orbit theory, the variation of orbital semi-major axis of re-entry object CZ-3B R/B induced by atmospheric drag perturbation only is derived from the rebuilt precise orbit. In the derivation of secular change of the orbital semi-major axis of re-entry object CZ-3B R/B induced by atmospheric drag perturbation only, the time-span is set as one minute tentatively. And then retrieval results of atmospheric mass densities in lower thermosphere below 200 km by analytical and numerical methods are presented, as well as their bias deviations from the calculated results of the NRLMSISE-00 empirical model of the atmosphere. Setting bias deviation bands, the corresponding ‘confidence coefficients’ of the retrieved atmospheric mass densities with respect to the model values are given. Average bias deviations of the retrieved atmospheric mass densities by analytical and numerical methods from the model values are also calculated respectively. On the whole, the retrieved atmospheric mass densities by numerical method approach to the model values more closely; the differences between the retrieved results and the model values are relatively smaller at the peaks of atmospheric mass densities than the other places. 相似文献
10.
A solution to the fixed-time minimum-fuel two-impulse rendezvous problem for the general non-coplanar elliptical orbits is
provided. The optimal transfer orbit is obtained using the constrained multiple-revolution Lambert solution. Constraints consist
of lower bound for perigee altitude and upper bound for apogee altitude. The optimal time-free two-impulse transfer problem
between two fixed endpoints implies finding the roots of an eighth order polynomial, which is done using a numerical iterative
technique. The set of feasible solutions is determined by using the constraints conditions to solve for the short-path and
long-path orbits semimajor axis ranges. Then, by comparing the optimal time-free solution with the feasible solutions, the
optimal semimajor axis for the two fixed-endpoints transfer is identified. Based on the proposed solution procedure for the
optimal two fixed-endpoints transfer, a contour of the minimum cost for different initial and final coasting parameters is
obtained. Finally, a numerical optimization algorithm (e.g., evolutionary algorithm) can be used to solve this global minimization
problem. A numerical example is provided to show how to apply the proposed technique. 相似文献
11.
R. A. Lyttleton 《Astrophysics and Space Science》1974,26(2):497-511
Owing to its extremely slow rotation, Venus must be regarded as a triaxial body with differences of all three principal moments of inertia comparable in magnitude, thus rendering it a body essentially different from a rapidly rotating planet. The dynamical problem then arises of how such a body, with a rotation-period comparable with its orbital period, would be affected by couples exerted upon it by the gravitational action of the Sun. Equations for the rotatory motion are set up in a form suitable for numerical solution by machine-calculations, but the problem so presented can be adequately investigated only for a hypothetical planet with far larger differences of principal moments than could hold for Venus. Results obtained on this limited basis nevertheless suggest that for the actual planet the direction of the rotation axis may move almost randomly between the two hemispheres defined by the orbital plane and thus that the present direction near the south celestial pole of the orbit may be only a temporary situation. Order-of-magnitude considerations based on the equations of motion suggest that a time-scale of order 107 to 108 yr may on average be required for large changes in direction of the rotation axis to take place. 相似文献
12.
Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9°±1.2°, placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape.Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries.The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images. 相似文献
13.
By linear perturbation theory, a sensitivity study is presented to calculate the contribution of the Mars gravity field to the orbital perturbations in velocity for spacecrafts in both low eccentricity Mars orbits and high eccentricity orbits(HEOs). In order to improve the solution of some low degree/order gravity coefficients, a method of choosing an appropriate semimajor axis is often used to calculate an expected orbital resonance, which will significantly amplify the magnitude of the position and velocity perturbations produced by certain gravity coefficients. We can then assess to what degree/order gravity coefficients can be recovered from the tracking data of the spacecraft. However, this existing method can only be applied to a low eccentricity orbit, and is not valid for an HEO. A new approach to choosing an appropriate semimajor axis is proposed here to analyze an orbital resonance. This approach can be applied to both low eccentricity orbits and HEOs. This small adjustment in the semimajor axis can improve the precision of gravity field coefficients and does not affect other scientific objectives. 相似文献
14.
Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2014,118(3):221-234
A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part of this Hamiltonian via the Hamilton–Jacobi equation provides the action-angle variables that ease the construction of a perturbation solution by Lie transforms. The lowest orders of the transformation equations of the perturbation solution are checked to agree with Kinoshita’s corresponding expansions for the exact solution of the free rigid body problem. For approximately axisymmetric bodies rotating close to the principal axis of maximum inertia, the common case of major solar system bodies, the new approach is advantageous over classical expansions based on a small triaxiality parameter. 相似文献
15.
Larry A. Lebofsky 《Icarus》1975,25(2):205-217
Calculations on the stability of various frosts (against evaporation) for solar system objects in circular and elliptical orbits are made. It is found that the stability of these frosts is dependent on the rate of rotation of the object, the latitude of the area on the object being considered, and the eccentricity of the orbit as well as its mean distance from the Sun. These factors greatly influence the amount of solar radiation incident and reradiated from a given area on the object. The likelihood of finding these frosts on the surfaces of objects and the lifetimes of objects composed of these frosts is discussed. 相似文献
16.
《New Astronomy》2021
In our previous paper (hereafter, paper I) we presented analytical results on the non-planar motion of a planet around a binary star for the cases of the circular orbits of the components of the binary. We found that the orbital plane of the planet (the plane containing the “unperturbed” elliptical orbit of the planet), in addition to precessing about the angular momentum of the binary, undergoes simultaneously the precession within the orbital plane. We demonstrated that the analytically calculated frequency of this additional precession is not the same as the frequency of the precession of the orbital plane about the angular momentum of the binary, though the frequencies of both precessions are of the same order of magnitude. In the present paper we extend the analytical results from paper I by relaxing the assumption that the binary is circular – by allowing for a relatively small eccentricity ε of the stars orbits in the binary. We obtain an additional, ε-dependent term in the effective potential for the motion of the planet. By analytical calculations we demonstrate that in the particular case of the planar geometry (where the planetary orbit is in the plane of the stars orbits), it leads to an additional contribution to the frequency of the precession of the planetary orbit. We show that this additional, ε-dependent contribution to the precession frequency of the planetary orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Besides, we also obtain analytical results for another type of the non-planar configuration corresponding to the linear oscillatory motion of the planet along the axis of the symmetry of the circular orbits of the stars. We show that as the absolute value of the energy increases, the period of the oscillations decreases. 相似文献
17.
Samuel P. Altman 《Celestial Mechanics and Dynamical Astronomy》1972,6(4):425-446
The trajectory and attitude dynamics of an orbital spacecraft are defined by a unified state model, which enables efficient and rapid machine computation for mission analysis, orbit determination and prediction, satellite geodesy and reentry analysis. The state variables are momenta — a general form for attitude, and a parametric form for orbital motion. The orbital parameters are the velocity state characteristics of the orbital hodograph. The coordinate variables are sets of four Euler parameters, which define the rotation transformation by the quaternion algebra. The unified state model possesses many analytical properties which are invaluable for dynamical system synthesis, numerical analysis and machine solution: regularization, unified matrix algebra, state graphs and transforms. The analytic partials of position and velocity with the state and coordinate variables are presented, as well as representative perturbation functions such as air drag, gravitational potential harmonics, and propulsion thrust. 相似文献
18.
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
19.
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
20.
Adrian Brunini 《Celestial Mechanics and Dynamical Astronomy》1992,53(2):129-143
In this paper we apply a numerical method to determine unmodeled perturbations in an attempt to explain the observed discrepancies in the motion of Uranus. We find that the estimated perturbation shows some significant periods that could be attributed to insufficient knowledge of the perturbations from some of the known planets. On the assumption that the gravitational attraction of an unknown planet is the origin of the deviations, the best planar solution of the inverse problem is a planet of 0.6 Earth masses, with true longitude of 133° (1990.5), semi major axis a = 44 AU and eccentricity e = 0.007. 相似文献