Long-term perturbations due to a disturbing body in elliptic inclined orbit

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.     

Approximate analysis for relative motion of satellite formation flying in elliptical orbits

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.     

The influence of obliquity on europan cycloid formation

Tectonic patterns on Europa are influenced by tidal stress. An important well-recognized component is associated with the orbital eccentricity, which produces a diurnally varying stress as Jupiter's apparent position in Europa's sky oscillates in longitude. Cycloidal lineaments seem to have formed as cracks propagated in this diurnally varying stress field. Maps of theoretical cycloid patterns capture many of the characteristics of the observed distribution on Europa. However, a few details of the observed cycloid distribution have not been reproduced by previous models. Recently, it has been shown that Europa has a finite forced obliquity, so Jupiter's apparent position in Europa's sky will also oscillate in latitude. We explore this new type of diurnal effect on cycloid formation. We find that stress from obliquity may be the key to explaining several characteristics of observed cycloids such as the shape of equator-crossing cycloids and the shift in the crack patterns in the Argadnel Regio region. All of these improvements of the fit between observation and theory seem to require Jupiter crossing Europa's equatorial plane 45° to 180° after perijove passage, suggestive of complex orbital dynamics that locks the direction of Europa's pericenter with the direction of the ascending node at the time these cycloids were formed.     

On error bounds and initialization in satellite orbit theories

The order of magnitude of the error is investigated for a first-order von Zeipel theory of satellite orbits in an axisymmetric force field, i.e., first-order long period and short-period effects are included along with second order secular rates. The treatment is valid for zero eccentricity and/or inclination. In the case where initial position and velocity vectors are known, the in-track position error over time intervals of order 1/J ₂ is kept at 0(J ₂ ²), like the other position errors and velocity errors, by calibration of the mean motion with the aid of the energy integral. The results are specifically applicable to accuracy comparisons of the Brouwer orbit prediction method with numerical integration. A modified calibration is presented for the general asymmetric force field which includes tesseral harmonics.     

Feedback and late star formation in elliptical galaxies

We present a one-zone model of star formation in elliptical galaxies that includes thermal feedback from supernovae and a temperature dependent star formation efficiency. The modulation of feedback with the total mass results in the triggering of late episodes of star formation in low-mass galaxies. These small `bursts' can occur as late as at redshifts z ∼ 0.5 but they do not change significantly the optical and NIR color-magnitude relation (CMR) of cluster galaxies, both locally and out to moderate redshifts, in agreement with the observations. However, they introduce a large scatter at the faint end of the NUV-Optical CMR, as recently found in cluster Abell 851 (z = 0.41). This revised version was published online in August 2006 with corrections to the Cover Date.     

e-VLBI技术及其在卫星定轨中的应用概况

e-VLBI技术继承了VLBI本身具有的极高角分辨率,且其利用高速通讯网络传送观测数据,能够快速得到观测结果,这些优点对于卫星的快速测定轨和提高卫星现有的定轨精度是十分有利的。通过对e-VLBI技术特点的分析及其发展历程的回顾,并结合卫星的差分VLBI观测原理,重点阐述和讨论了e-VLBI技术在我国的应用现状、发展及要求,展望了我国未来e-VLBI的发展前景。     

Potential effects of obliquity change on gas hydrate stability zones on Mars

Methane hydrate dissociation due to obliquity-driven temperature change has been suggested as a potential source of atmospheric methane plumes recently observed on Mars. This work uses both equilibrium and time-dependent models to determine how geothermal gradients change on Mars as a result of obliquity and predict how these changes affect gas hydrate stability zones (HSZs). The models predict that the depth to the HSZ decreases with increasing latitude for both CO₂ and CH₄ hydrate, with CO₂ hydrate occurring at shallower depths than CH₄ hydrate over all latitudes. The depth of the HSZ increases as surface temperatures warm and decreases as surface temperatures cool with changing obliquity, with the largest change in HSZ volume predicted near the equator and the poles. Therefore, changes in the depth to the HSZ may cause hydrate dissociation near the equator and poles as the geothermal gradient moves in and out of the hydrate stability field over hundreds of thousands of years. Sublimation of overlying ice containing diffused methane could account for recent observations of seasonal methane plumes on Mars. In addition, near-surface gas hydrate reservoirs may be preserved at mid-latitudes due to minimal changes in surface temperature with obliquity over geologic time scales. Comparisons of the predicted changes in the HSZ with hydrate dissociation and diffusion rates reveal that metastable hydrate may also remain in the near subsurface, especially at high latitudes, for millions to billions of years. The presence of methane hydrate in the near subsurface at midlatitudes could be an important analytical target for future Mars missions, as well as serving as a source of fuel for future spacecraft.     

Dissipationless collapse and the formation of elliptical galaxies

Summary A brief review of previous work and the present situation in the problem of formation of elliptical galaxies via dissipationless collapse are presented, as well as the results of a new set of numerical experiments. It is shown that collapses started from cold initial conditions are different from warmer collapses, due to the presence of a dynamical instability associated with radial orbits. This instability leads to triaxial final configurations, regardless of the initial amount of random kinetic energy, rotational kinetic energy, or shape of the initial conditions, as long as2T/W0.1, whereT is the total (rotational plus thermal) kinetic energy andW is the potential energy of the initial conditions. Warmer initial conditions preserve their initial shape, or become oblate if initially rotating. Cold initial conditions produce equilibrium systems with realistic density profiles, as opposed to collapses from warmer conditions that result in core-halo profiles, unlike the observed surface brightness profiles of elliptical galaxies. Although the same cold collapses that result in triaxial shapes produce realistic density profiles, it is shown that these two effects are not directly connected: cold collapses simulated with anN-body code that enforces spherical symmetry result in realistic density profiles too.Invited Talk at the 18th meeting of the Division on Dynamical Astronomy of the American Astronomical Society held in Braintree, Massachussetts, May 7–9, 1987.     

Secondary episodes of star formation in elliptical galaxies

We put upper limits on the secondary burst of star formation in elliptical galaxies of the González sample, based on the colour dispersion around the U  −  V versus central velocity dispersion relation, and the equivalent width of Hβ absorption. Note that most of these galaxies locate in small groups. There is a significant number of Hβ strong galaxies that have EW(Hβ) > 2 Å, but they do not always have bluer colours in U  −  V . To be consistent with the small colour dispersion of U  −  V , the mass fraction of the secondary burst to the total mass should be less than 10 per cent at the maximum within the most recent 2 Gyr. This result suggests that even if recent galaxy merging has produced some ellipticals, it should not have been accompanied by an intensive starburst, and hence it could not involve large gas-rich systems. The capture of a dwarf galaxy is more likely to explain the dynamical disturbances observed in some elliptical galaxies. The above analysis, based on the U  −  V , is not compatible with the one based on the line indices, which requires that more than 10 per cent of mass is present in a 2-Gyr-old starburst to cover the full range of the observed Hβ (de Jong &38; Davies). The discrepancy might be partly explained by the internal extinction localized at the region where young stars form. However, considering that the Hβ index might have great uncertainties both in models and in observational data, we basically rely on U − V analysis.     

Regular precessions of a gyrostatic satellite in a circular orbit

In the present paper, the regular precessions about the mass center are studied, for a Volterra-type gyrostatic satellite in a circular orbit under a Newtonian force field. All the possible regular precessions are determined.     

A note on the tidally induced potential of a satellite in eccentric orbit

A planetary body moving on an eccentric orbit around the primary is subject to a periodic perturbing potential, affecting its internal mass distribution. In a previous paper (Rappaport et al., 1997, Icarus 126, 313), we have calculated the periodic modulation of the gravity coefficients of degree 2, for a body on a synchronous orbit. Here, the previous analysis is extended by considering also non-synchronous orbits, and by properly accounting for the apparent motion of the primary due to the non uniform motion along the elliptical orbit. The cases of Titan and Mercury are briefly discussed.     

The variations in eccentricity and apse precession rate of a narrow ring perturbed by a close satellite

We derive a Hamiltonian which describes the first-order perturbations of orbital eccentricity and apse precession rate of a narrow ring due to a close satellite whose orbit is also eccentric. Our treatment covers cases in which the satellite crosses the ring. The level curves of the Hamiltonian are displayed for several values of the parameters. We apply our results to the interaction of Saturn's F ring with its inner shepherd satellite.     

The general equilibria of a spinning satellite in a circular orbit

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.     

The effect of solar radiation pressure on the orbit of a cylindrical satellite

The effect of solar radiation pressure on the orbits of cylindrical satellites is considered. The cylinder is assumed to reflect radiation both specularly and diffusely. The resultant forces on a stationary cylindrical satellite are given. The evolution of the satellite's orbit is described for two particular modes of rotation. In both cases the satellites are assumed to be in circular Sun-synchronous orbits.     

Effect of solar pressure on the motion and stability of the system of two inter-connected satellites in an elliptical orbit

The effect of solar pressure on the two-dimensional motion of two cable-connected satellites in the Earth's central gravitational field of force for the elliptical orbit of the centre-of-mass of the system has been analysed. The equations of motion obtianed are nonlinear and non-autonomous.It is concluded with the aid of non-resonant solution that the system experiences resonance main as well as parametric. If the eccentricity is small, the system will always oscillate about the position of equilibrium with tight string like dumb-bell satellite with changing phase and constant amplitude.     

Dynamical friction on a satellite of a disk galaxy: The circular orbit

In a previous paper, we have studied dynamical friction during a parabolic passage of a companion galaxy past a disk galaxy. This paper continues with the study of satellites in circular orbits around the disk galaxy. Simulations of orbit decay in a self gravitating disk are compared with estimates based on two-body scattering theories; the theories are found to give a satisfactory explanation of the orbital changes. The disk friction is strongly dependent on the sense of rotation of the companion relative to the rotation of the disk galaxy as well as on the amount of mass in a spherical halo. The greatest amount of dynamical friction occurs in direct motion if no spherical halo is present. Then the infall time from the edge of the disk is about one half of the orbital period of the disk edge. A halo twice as massive as the disk increases the infall time four fold. The results of Quinn and Goodman, obtained with a non-self-gravitating method, agree well with our experiments with massive halos (Q ₀ 1.5), but are not usable in a more general case. We give analytic expressions for calculating the disk friction in galaxies of different disk/halo mass ratios.     

Attitude stability of a spinning symmetric satellite in a planar periodic orbit

This paper contains an analysis of the attitude stability of a spinning axisymmetric satellite whose mass center moves in any known planar periodic orbit of the restricted three-body problem while the spin axis remains normal to the orbit plane. A procedure based on Floquet theory is developed for constructing attitude instability charts, and examples of these are presented for two stable periodic orbits of the Earth-Moon system—one direct and one retrograde. The physical significance of these instability predictions is then explored by means of numerical integration of the full nonlinear equations of motion. Finally, an analysis based on averaging is performed, leading to approximate instability charts and indicating a possible connection between certain orbital-attitude resonance conditions and unstable attitude motions.     

Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration

Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, we extend this technique to mass points and mass discs in the gravity field. This required the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.