Time distributions in satellite constellation design     

David Arnas  Daniel Casanova  Eva Tresaco 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):197-219

The aim of the time distribution methodology presented in this paper is to generate constellations whose satellites share a set of relative trajectories in a given time, and maintain that property over time without orbit corrections. The model takes into account a series of orbital perturbations such as the gravitational potential of the Earth, the atmospheric drag, the Sun and the Moon as disturbing third bodies and the solar radiation pressure. These perturbations are included in the design process of the constellation. Moreover, the whole methodology allows to design constellations with multiple relative trajectories that can be distributed in a minimum number of inertial orbits.  相似文献   

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited     

Alexandre Pousse  Philippe Robutel  Alain Vienne 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):383-407

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.  相似文献   

Libration of arguments of circumbinary-planet orbits at resonance     

Joachim Schubart 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):295-301

The paper refers to fictitious resonant orbits of planet type that surround both components of a binary system. In case of 16 studied examples a suitable choice of the starting values leads to a process of libration of special angular arguments and to an evolution with an at least temporary stay of the planet in the resonant orbit. The ratio of the periods of revolution of the binary and a planet is equal to 1:5. Eight orbits depend on the ratio 1:5 of the masses of the binary components, but two other ratios appear as well. The basis of this study is the planar, elliptic or circular restricted problem of three bodies, but remarks at the end of the text refer to a four-body problem.  相似文献   

High-precision repeat-groundtrack orbit design and maintenance for Earth observation missions     

Yanchao He  Ming Xu  Xianghua Jia  Roberto Armellin 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):275-294

The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to \(J_{15}\). A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.  相似文献   

A vectorial approach to determine frozen orbital conditions     

Christian Circi  Ennio Condoleo  Emiliano Ortore 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):361-382

Taking into consideration a probe moving in an elliptical orbit around a celestial body, the possibility of determining conditions which lead to constant values on average of all the orbit elements has been investigated here, considering the influence of the planetary oblateness and the long-term effects deriving from the attraction of several perturbing bodies. To this end, three equations describing the variation of orbit eccentricity, apsidal line and angular momentum unit vector have been first retrieved, starting from a vectorial expression of the Lagrange planetary equations and considering for the third-body perturbation the gravity-gradient approximation, and then exploited to demonstrate the feasibility of achieving the above-mentioned goal. The study has led to the determination of two families of solutions at constant mean orbit elements, both characterised by a co-planarity condition between the eccentricity vector, the angular momentum and a vector resulting from the combination of the orbital poles of the perturbing bodies. As a practical case, the problem of a probe orbiting the Moon has been faced, taking into account the temporal evolution of the perturbing poles of the Sun and Earth, and frozen solutions at argument of pericentre 0\(^{\circ }\) or 180\(^{\circ }\) have been found.  相似文献   

On the period of the periodic orbits of the restricted three body problem     

Oscar Perdomo 《Celestial Mechanics and Dynamical Astronomy》2017,129(1-2):89-104

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).  相似文献   

Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory     

Julien Frouard  Michael Efroimsky 《Celestial Mechanics and Dynamical Astronomy》2017,129(1-2):177-214

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.  相似文献   

Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth     

Melaine Saillenfest  Marc Fouchard  Giacomo Tommei  Giovanni B. Valsecchi 《Celestial Mechanics and Dynamical Astronomy》2017,129(3):329-358

We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-Earth-mass perturber. The secular dynamics is analogous to an “eccentric Kozai mechanism” but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for \(a>150\) AU, large-amplitude orbital flips become possible, and for \(a>200\) AU, the Kozai libration islands at \(\omega =\pi /2\) and \(3\pi /2\) are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated with apsidal alignments or anti-alignments with the orbit of the distant perturber.  相似文献   

Improvements on a unified dark matter model     

A. Del Popolo  Xi-Guo Lee 《Astronomy Letters》2017,43(10):635-643

We study, by means of a spherical collapse model, the effect of shear, rotation, and baryons on a generalized Chaplygin gas (gCg) dominated universes. We show that shear, rotation, and the baryon presence slow down the collapse with respect to the simple spherical collapse model. The slowing down in the growth of density perturbation is able to solve the instability of the unified dark matter (UDM) models described in previous papers (e.g., Sandvik et al. 2004) at the linear perturbation level, as also shown by a direct comparison of our model with previous results.  相似文献   

The subsistence patterns of the Shengedaliang site (~4,000 yr BP) revealed by stable carbon and nitrogen isotopes in northern Shaanxi,China     

XiangLong Chen  XiaoNing Guo  WeiLin Wang  SongMei Hu  MiaoMiao Yang  Yan Wu  YaoWu Hu 《中国科学:地球科学(英文版)》2017,60(2):268-276

In order to explore subsistence patterns in northern Shaanxi Province around 4,000 yr BP,28 human and 24 animal bones from the Shengedaliang site were sampled for stable carbon and nitrogen isotope ratio analysis.The results show that most people primarily subsisted on C_4 resources,e.g.millet and millet-related animal products,despite the fact that there was some intake of C_3 plants by some individuals.Stable nitrogen isotope values indicate that there were differences in meat consumption between individuals at the site.Pigs were mainly foddered with millet and millet byproducts,as well as some cattle,according to their highδ~(13)C values.However,most cattle and the sheep/goats consumed wild C_3 plants at Shengedaliang.Our above findings indicates that subsistence patterns in northern Shaanxi around 4,000 yr BP were characterized by millet farming,while the grassland animal husbandry,e.g.cattle and sheep/goats raising,displayed very little contribution to local economy.The intensive millet farming in northern Shaanxi provided enough food for population growth,ensured the accumulation of wealth,and consequently accelerated social differentiation and complexity.  相似文献