Asteroids with large secular orbital variations

In this paper, using the expansion of the true anomaly, we examine how the time variation of the gravitational constant influences the variation of the orbital elements of planets. The theoretical results show that the semimajor axis exhibits secular and periodic variation in the first order for u G/G. The eccentricity exhibits periodic variation, but there is no secular variation in the first and second orders for u G/G. The longitude of perihelion and the mean longitude at the epoch exhibit periodic variation but no secular variation in the first order for u G/G. However, they do exhibit secular variation in the second order for u G/G. The inclination and ascending node exhibit no variation. The bounds on the values of the secular variation of the semimajor axis and the orbital period, which result from the time variation of the gravitational constant, are estimated for five planets. The results are discussed and conclusions are made.

Asteroid proper elements and secular resonances

We report results from long term numerical integrations and analytical studies of particular orbits in the circular restricted three-body problem. These are mostly high-inclination trajectories in 1 : 1 resonance starting at or near the triangular Lagrangian L5 point. In some intervals of inclination these orbits have short Lyapunov times, from 100 to a few hundred periods, yet the osculating semi-major axis shows only relatively small fluctuations and there are no escapes from the 1 : 1 resonance. The eccentricity of these chaotic orbits varies in an erratic manner, some of the orbits becoming temporarily almost rectilinear. Similarly the inclination experiences large variations due to the conservation of the Jacobi constant. We studied such orbits for up to 109 periods in two cases and for 106 periods in all others, for inclinations varying from 0° to 180°. Thus our integrations extend from thousands to 10 million Lyapunov times without escapes of the massless particle. Since there are no zero-velocity curves restricting the motion this opens questions concerning the reason for the persistence of the 1 : 1 resonant motion. In the theory sections we consider the mechanism responsible for the observed behavior. We derive the averaged 1 : 1 resonance disturbing function, to second order in eccentricity, to calculate a critical inclination found in the numerical experiment, and examine motion close to this inclination. The cause of the chaos observed in the numerical experiments appears to be the emergence of saddle points in the averaged disturbing potential. We determine the location of several such saddle points in the (φ, ω) plane, with φ being the mean longitude difference and ω the argument of pericentre. Some of the saddle points are illustrated with the aid of contour plots of the disturbing function. Motion close to these saddles is sensitive to initial conditions, thus causing chaos.

The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. Specifically, two steps organize the contribution of this study. First, combined with functional approximations, a set of analytical expressions for the variation maxima of orbital elements over one orbital revolution are derived. Second, the secular approximations for the variation maxima of the inclination and the right ascension of the ascending node are derived and expressed explicitly. An iterative algorithm is given to obtain the secular variation maxima of the other orbital elements the orbital elements other than the inclination and right ascension of the ascending node. Numerical simulations for approximating the variation maxima and a preliminary application in estimation of the velocity increment are given to demonstrate the efficiency and accuracy of the proposed method. Compared with the indirect method used alone for low-thrust trajectory optimization, the computation burden of the proposed method is reduced by over five orders of magnitude, and the computational accuracy is still high.

An impulsive feedback control is developed to establish specie c relative orbits for spacecraft formation e ying. The relative orbit tracking errors are expressed in terms of mean orbit elements. The feedback control, based on Gauss’ s variational equations of motion, allows specie c orbit elements or orbit element sets to be controlled with minimal impact on the remaining osculating orbit elements. This is advantageous when J2-invariant orbits are to be controlled, where only the argument of perigee and mean anomaly will drift apart at equal and opposite rates. The advantage of this impulsive feedback control, compared to optimal control solutions, is that it can operate with little computational effort and in a near-optimal manner, whilerequiring only a marginal penalty in fuel cost. When applied to the spacecraft formation e ying problem, this control could also be used to perform general orbit corrections. Formulas are developed providing accurate estimates of the sensitivities of the mean semimajor axis and mean eccentricity with respect to the osculating inclination angle. With these sensitivities, the tracking error in semimajor axis, eccentricity, and inclination angle can be canceled within one orbit.

Orogenic gold deposits formed in various terranes of most ages since the Paleoarchean and generally consist of quartz veins hosted in shear zones formed at the ductile brittle transition under greenschist to lower amphibolite metamorphic conditions. Vein mineralogy is dominated by quartz with various amounts of silicates, carbonates, phyllosilicates, borates, tungstates, sulfides, and oxides. The isotopic composition of these minerals and fluid inclusions has been investigated since the 1960s to constrain the characteristics of orogenic fluid systems involved in the formation of gold deposits worldwide. This review is based on 8580 stable isotope analyses, including δ18O, δD, δ13C, δ34S δ15N, δ11B, and δ30Si values, from 5478 samples from 558 orogenic gold deposits reported in the literature from 1960 to 2010. This contribution describes the variability of the light stable isotopic systems as function of the minerals, the age of the deposits, their regional setting, and their country rocks. The temperature of isotopic equilibrium of orogenic gold veins is estimated from mineral pairs for oxygen and sulfur isotopes. Based on these temperatures, and on fractionation between mineral and fluid components (H2O, CO2 and H2S), the isotopic composition of fluids is estimated to better constrain the main parameters shared by most of auriferous orogenic fluid systems. Orogenic gold deposits display similar isotopic features through time, suggesting that fluid conditions and sources leading to the formation of orogenic gold deposits did not change significantly from the Archean to the Cenozoic. No consistent secular variations of mineral isotope composition for oxygen (−8.1‰ ≤ δ18O ≤ 33‰, n = 4011), hydrogen (−187‰ ≤ δD ≤ −4‰, n = 246), carbon (−26.7‰ ≤ δ13C ≤ 12.3‰, n = 1179), boron (−21.6‰ ≤ δ11B ≤ 9‰, n = 119), and silicon (−0.5‰ ≤ δ30Si ≤ 0.8‰, n = 33) are documented. Only nitrogen (1.6‰ ≤ δ15N ≤ 23.7‰, n = 258) and sulfide sulfur from deposits hosted in sedimentary rocks (−27.2‰ ≤ δ34S ≤ 25‰, n = 717) display secular variations. For nitrogen, the change in composition is interpreted to record the variation of δ15N values of sediments devolatilized during metamorphism. For sulfur, secular variations reflect incorporation of local sedimentary sulfur of ultimate seawater origin. No significant variation of temperature of vein formation is documented for orogenic gold deposits of different ages. Quartz-silicate, quartz-carbonate and sulfide-sulfide mineral pairs display consistent temperatures of 360 ± 76 °C (1σ; n = 332), in agreement with the more common greenschist facies hostrocks and fluid inclusion microthermometry. Fluid sources for orogenic gold deposits are complex but the isotopic systems (hydrogen, boron, carbon, nitrogen, oxygen, sulfur) are most consistent with contributions from metamorphic fluids released by devolatilization of igneous, volcano-sedimentary and/or sedimentary rocks. The contribution of magmatic water exsolved from magma during crystallization is not a necessary component, even if permissible in specific cases. Isotopic data arrays can be interpreted as the result of fluid mixing between a high T (~550 °C)—high δ18O (~10‰)—low δD (~−60‰) deep-seated (metamorphic) fluid reservoir and a low T (~200 °C)—low δ18O (~2‰)—high δD (~0‰) upper crustal fluid reservoir in a number of orogenic gold deposits. The origin of the upper crustal fluid is most likely sea- or meteoric water filling the host rock porosity, with a long history of water–rock isotope exchange. Mixing of deep-seated and upper crustal fluids also explains the large variation of tourmaline δ11B values from orogenic gold veins. Regional spatial variations of oxygen and hydrogen isotope compositions of deep-seated fluid reservoirs are documented between orogenic gold districts. This is the case for the Val-d’Or (Abitibi), Coolgardie and Kalgoorlie (Yilgarn) where the oxygen isotope composition of the deep-seated fluid end-member is 4‰ lower compared to that from the Timmins, Larder Lake, and Kirkland Lake districts (Abitibi). However, both mixing trends converge towards a common, low δ18O upper crustal fluid end-member. Such variations cannot be related to fluid buffering at the site of deposition and suggest provinciality of the fluid source. The contribution of meteoric water is mainly recorded by fluid inclusions from Mesozoic and Cenozoic age deposits, but micas are not systematically in isotopic equilibrium with fluid inclusions trapped in quartz from the same vein. This suggests late involvement of meteoric water unrelated to deposit formation. Yet, a number of deposits with low δD mica may record infiltration of meteoric water in orogenic gold deposits. Isotope exchange between mineralizing fluid and country rocks is documented for oxygen, carbon, sulfur and silicon isotopes. Large variations (> 10‰) of sulfide δ34S values at the deposit scale are likely related to evolving redox conditions of the mineralizing fluid during reaction with country rocks. Deposits hosted in sedimentary rocks show a shift to higher δ18O values as a result of fluid/rock oxygen exchange with the regional sedimentary country rocks.

Selected Accelerations and Orbital Elements of the Goce Satellite in the Time Domain

view Abstract Citations (100) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS An analysis of the variable radial velocity of Alpha Cygni. Lucy, L. B. Abstract On the basis of 447 radial velocities obtained at the Lick Observatory in the years 1927-1935, an attempt is made to discover the nature of the semiregular variability of alpha Cygni. Harmonic analysis of the 144 velocities obtained in 1931 suggests that this variability is due to the simultaneous excitation of many discrete pulsation modes. The amplitudes and periods of these modes are then determined by least-squares obtaining a solution that comprises 16 terms. All terms are found to have highly significant amplitudes, and most terms also pass a test of the stability of their amplitudes and phases. Reasons are given for believing that most terms represent nonradial oscillations, leading to the suggestion that the resulting surface motions are to be identified with macroturbulence. An argument is given for believing that the pulsational instability persists down to periods at which atmospheric oscillations become progressive, possibly giving rise to the observed mass loss. Publication: The Astrophysical Journal Pub Date: June 1976 DOI: 10.1086/154405 Bibcode: 1976ApJ...206..499L Keywords: A Stars; Radial Velocity; Supergiant Stars; Variable Stars; Binary Stars; Orbital Elements; Photographic Plates; Secular Variations; Stellar Mass Ejection; Astrophysics full text sources ADS | data products SIMBAD (2)

A closed form solution is presented for the coplanar transfer between nearby circular orbits for spacecraft using their own blow down propulsion system. The decaying thrust is applied along the local horizontal and the linearized equation of motion in the orbital elements formulation are used to describe the transfer which consists of a thrust-coast-relight program. Sensitivity partials are also presented analytically in order to study the effect of maneuver execution errors and various other parameters affecting the blow down propulsion system characteristics on the transfer. This strategy is applied to study the transfer of the TOPEX spacecraft from the Shuttle parking orbit to its final operational orbit.

The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly eccentric. In these cases, in order for close encounters, which destabilize the planetary systems, to be avoided, phase protection mechanisms should be considered. Additionally, since the GTBP is a non-integrable system, chaos may also cause the destabilization of the system after a long time interval. By computing dynamical maps, based on Fast Lyapunov Indicator, we reveal regions in phase space with stable orbits even for very high eccentricities (e>0.5). Such regions are present in mean motion resonances (MMR). We can determine the position of the exact MMR through the computation of families of periodic orbits in a rotating frame. Elliptic periodic orbits are associated with the presence of apsidal corotation resonances (ACR). When such solutions are stable, they are associated with neighbouring domains of initial conditions that provide long-term stability. We apply our methodology so that the evolution of planetary systems of highly eccentric orbits is assigned to the existence of such stable domains. Particularly, we study the orbital evolution of the extrasolar systems HD 82943, HD 3651, HD 7449, HD 89744 and HD 102272 and discuss the consistency between the orbital elements provided by the observations and the dynamical stability.

The recently discovered super-Earth Gl 514 b, orbiting a nearby M0.5-1.0 star at 7.6 pc, is one of the best benchmark exoplanets for understanding the potential climate states of eccentric planets. The elongated (e = 0.45$^{+0.15}_{-0.14}$) orbit of Gl 514 b, which only partially lies in the Conservative Habitable Zone, suggests a dynamically young system, where the spin-orbit tidal synchronization may not have yet occurred up to the present time. In the present work, we use a seasonal-latitudinal energy balance model, EOS-ESTM, to explore the potential impact of both constrained and unconstrained planetary, orbital, and atmospheric parameters on the Gl 514 b habitability, mapped in terms of surface temperature. We test three distinct CO2-dominated atmospheres by varying the CH4 concentration values (0 per cent, 0.1 per cent, and 1 per cent) and the total surface pressure. As a general trend, we find that habitable conditions are favoured by high-CH4 and high-pressure regimes. Habitability also increases for high-axis obliquities (at least until the appearance of an icebelt), long-rotation periods, and high-ocean fractional coverage. If the ocean fraction is low, then also the argument of periastron becomes relevant. Our results are robust against changes of the continental distribution. Thus, we conclude that Gl 514 b can potentially maintain temperate surface conditions with modest seasonal temperature variations under a wide variety of planetary, orbital, and atmospheric conditions. Despite no transit have been detected yet, the results found in this work should motivate the community to invest time in future observations.

The technique now regularly in use for the generation of orbital elements for the TELSTAR communications satellites is described using angle-only and/or angle-range data versus time as input information. It is found that secular perturbation considerations are sufficient to permit trajectory prediction with pointing errors of about 0.05° over 100 orbits from a single set of elements. Modified orbital elements are chosen as the orbit description, since they explicitly express the secular rates and thereby simplify and reduce the cost of drive tape generations for the Andover ground station. The rates are derived both from perturbation theory and from direct measurement. The size and shape accuracy of the predicted orbit ellipse is improved by statistical means using trajectory data from a number of passes over a particular ground station. This permits better round-the-world predictions. Finally the computer-operator ensemble presently used for generating the orbits of the TELSTAR satellites is described.

Minimum-fuel rendezvous of two power-limited spacecraft is investigated. Both vehicles are active and provide thrust to complete the rendezvous. Total propellant consumption is minimized. A direct-minimization method, direct collocation with nonlinear programming, is used to obtain cooperative rendezvous solutions in an inverse- square gravitational field. Unconstrained and constrained circular terminal orbits are considered. The optimal solutions depend upon the power-to-mass ratios of the spacecraft, the initial orbits, and the specified transfer time. Optimal cooperative rendezvous solutions are compared with optimal active-passive solutions and with previously reported linearized solutions. ISTORICALLY, spacecraft rendezvous has involved one thrusting (active) vehicle and one coasting (passive) vehicle. A cooperative power-limited (PL) rendezvous is an orbital maneuver in which two PL spacecraft are active. With both vehicles thrust- ing, a reduction in total propellant consumption is obtained when compared to the traditional active-passive rendezvous. The practical application of cooperative rendezvous occurs if both vehicles have comparable size and propulsive capability. It would make no sense to consider cooperative rendezvous between a small spacecraft and a space station. Early studies of cooperative control considered general linear or nonlinear systems with various performance indices.14 Recently, cooperative rendezvous methodology has been applied to spacecraft maneuvering. Prussing and Conway5 determined the optimal termi- nal maneuver for a cooperative impulsive rendezvous. Mirfakhraie6 and Mirfakhraie and Conway7 developed a method for determin- ing fuel-optimal trajectories for the fixed-time impulsive cooper- ative rendezvous. Coverstone-Carroll and Prussing8 obtained an- alytical solutions for fixed-time PL cooperative rendezvous using the Hill-Clohessy-Wiltshire linearized gravity field to approximate the inverse-square gravity field. In this article, fixed-time cooper- ative and active-passive (noncooperative) rendezvous solutions are obtained for two PL spacecraft in an inverse-square gravity field. Transfer times, maximum exhaust powers, and the initial orbits of the spacecraft are varied to determine their influence on the optimal cooperative solution. Optimal solutions subject to circular terminal- orbit constraints are also examined. Necessary Conditions for Optimal Solution

Lunar frozen orbits, characterized by constant orbital elements on average, have been previously found using various dynamical models, incorporating the gravitational field of the Moon and the third-body perturbation exerted by the Earth. The resulting mean orbital elements must be converted to osculating elements to initialize the orbiter position and velocity in the lunar frame. Thus far, however, there has not been an explicit transformation from mean to osculating elements, which includes the zonal harmonic $$J_2$$ , the sectorial harmonic $$C_{22}$$ , and the Earth third-body effect. In the current paper, we derive the dynamics of a lunar orbiter under the mentioned perturbations, which are shown to be dominant for the evolution of circumlunar orbits, and use von Zeipel’s method to obtain a transformation between mean and osculating elements. Whereas the dynamics of the mean elements do not include $$C_{22}$$ , and hence does not affect the equilibria leading to frozen orbits, $$C_{22}$$ is present in the mean-to-osculating transformation, hence affecting the initialization of the physical circumlunar orbit. Simulations show that by using the newly-derived transformation, frozen orbits exhibit better behavior in terms of long-term stability about the mean values of eccentricity and argument of periapsis, especially for high orbits.

In this paper, the feasibility of exploiting the Sun’s gravitational force to design the final phase (capture and orbit circularisation) to Mercury with a low propellant consumption has been investigated. The initial conditions, on the eccentricity and argument of pericentre, for the circularisation phase are obtained from a prime integral of motion, which takes place when the probe moves over a polar orbit. A numerical analysis has highlighted how these initial conditions allow, under the third-body effect, an optimal reduction of eccentricity (circularisation phase) with limited variations of the other orbit elements, without requiring orbital manoeuvres. Then, by introducing a small velocity variation, the phase of ballistic capture has been joined to the circularisation phase. The obtained results can encourage the exploitation of this phenomenon in future missions for the exploration of Mercury.