Theory of motion of saturn's coorbiting satellites

A simple analytic theory describing the 1:1 orbital resonance is presented and applied to Saturn's coorbiting pair, 1980S1 and 1980S3. These satellites are very small and can approach to within 15,000 km, but are prevented from passing each other by their mutual gravitational interaction. The long-term stability of the S1–S3 orbital configuration is discussed in this paper, and a tie between the 1966 and 1980 observations is establised.     

Observations of Saturn's inner satellites and the orbit of Janus in 1980

Systematic observations of faint satellites were conducted at Pic-du-Midi with a focal coronograph from 1980 March 20 to 24, during which 150 exposures covering 17 hr were obtained; in addition, the 1966 discovery plates of satellites S10 Janus were reexamined together with other 1966 observations. Janus had its greatest eastern elongation on 1966 December 15.720 (±0.003) + light time, at a distance of 2.53R_eq. It is recognized that some of the observations thought to be 1966 S2 were in fact reobservations of Janus a few days after its discovery. Among the 1980 observations, differences in magnitudes indicate that is satellite 1980 S1 which corresponds to Janus; its greatest eastern elongation was observed on March 23.876 (±0.002) + light time. Subjected to corrections for librations, the mean period over the past 14 years has most probably one of three values: P₁ = 0.69458 day, P₂ = 06.9448 day or P₃ = 0.69438 day. The fainter satellite, S11, which is also 1980 S3, gravitates in an orbit similar to that of Janus and was leading it by +190° in March 1980; this difference of longitude was +224° in December 1966. An object of magnitude 15–16 was seen not detached from the ring; it could be a condensation in the external part of the rings or an additional faint inner satellite.     

A revaluation of the rotational speed of the upper atmosphere

In this paper the rotational speed of the upper atmosphere, mainly at heights of 200–300 km, is evaluated from the changes in the orbital inclinations of thirteen satellites. The values obtained represent the mean rotational speed over the latitudes covered by the satellites, at dates between late 1962 and early 1966, i.e. when solar activity was low.

If the angular velocity of the atmosphere is taken as Λ times that of the Earth, the values of Λ found are mostly between 1.0 and 1.6 with estimated S.D. between 0.1 and 0.25. If we exclude two values at heights above 300 km and one anomalous value, the mean of the remaining ten values of Λ obtained is 1.27, with r.m.s. scatter 0.18: this would correspond to an average west-to-east wind of about 100 m/sec in mid-latitudes.     

A possible satellite of 9 Metis

We attempted by means of photographic observations to search for satellites of asteroids in 1979 and 1980. An elongation of the image of 9 Metis has been detected on plates taken during 6 nights. The data suggest that there is a possible satellite with an orbital period of approximately 4.61 days and a mean distance of approximately 1100 km. We tabulate orbital parameters as well as predicted and observed position angles. A comparison with the secondary occultation results taken on 11.35 December 1979 is discussed.     

Saturn satellite observations and orbits from the 1980 ring plane crossing

The ground-based observations of the recently discovered Saturnian satellites, obtained during the 1980 apparition, have been collected from the IAU Circulars and identified with and fit to four orbital groups: (1) the inner pair of coorbital librating satellites, (2) the satellite known as “Dione B” near the L₄ point of Dione-Saturn, (3) the satellites associated with the L₄ and L₅ points of Tethys-Saturn or, alternatively, one satellite unconfortably near the orbit of Tethys, and (4) the F-ring satellites observed by Voyager I.     

On the gravitational fields of Pandora and Prometheus

Utilizing topographic models of Saturn's F-ring shepherd satellites Prometheus (S16 1980S27) and Pandora (S15 1980S26), derived by Stooke (1994), and supposing that their mass density is constant, we derived basic geometrical and dynamical characteristics of the moons. They include the volume and mass, the mean radii, the tensor of inertia, and Stokes coefficients of the harmonic expansions of external gravitational potential. The best fitting ellipsoid approximations of the topography were calculated. A simple method of determining the gravitational potential on the surface of an irregular satellite is presented. Examples of equipotential surfaces of the satellites are shown     

Tests and comparisons of gravity models

Optical observations of the GEOS satellites were used to obtain orbital solutions with different sets of geopotential coefficients. The solutions were compared before and after modification to high order terms (necessary because of resonance) and then analyzed by comparing subsequent observations with predicted trajectories. The most important source of error in orbit determination and prediction for the GEOS satellites is the effect of resonance found in most published sets of geopotential coefficients. Modifications to the sets yield greatly improved orbits in most cases.The sets of coefficients analyzed are APL 3.5, NWL5E-6, Köhnlein (1967), Rapp (1967), Kaula (1967), Smithsonian Astrophysical Observatory (SAO)M-1 (1966), SAO AGU (1969), SAO COSPAR (1969) and SAO 1969 Standard Earth. The SAO 1969 models generally give better orbital fits and prediction results than the other models above. However these models can be improved by corrections to resonant coefficients.The results of these comparisons suggest that with the best optical tracking systems and gravity models, satellite position error due to gravity model uncertainty can reach 50–100 m during a heavily observed 5–6 day orbital arc. If resonant coefficients are estimated, the uncertainty is reduced considerably.     

Photometric properties of outer planetary satellites

We present optical broadband photometry for the satellites J6, J7, J8, S7, S9, U3, U4, N1, and polarimetry for J6, obtained between 1970 and 1979. The outer Jovian satellites resemble C-type asteroids; J6 has a rotational lightcurve with period ～9.5 hr. The satellites beyond Jupiter also show C-like colors with the exception of S7 Hyperion. S9 Phoebe has a rotational lightcurve with period near either 11.25 or 21.1 hr. For U4 and N1 there is evidence for a lightcurve synchronous with the orbital revolution. The seven brighter Saturnian satellites show a regular relation between the ultraviolet dropoff and distance to the planet, probably related with differences in the rock component on their surfaces.     

The dynamics of tadpole and horseshoe orbits: II. The coorbital satellites of saturn

The recently discovered coorbital satellites of Saturn, 1980S1 and 1980S3, are shown to be librating in horseshoe orbits. By considering the effects of tangential forces on the semimajor axes of the satellite orbits, we derive an accurate relation between the sum of the satellite masses and (a) their minimum angular separation, (b) the variation of their angular separation with time and (c) the libration period. Observations of (b) and (c) are the most practical methods of determining the satellite masses. The orbits of the coorbital satellites of Dione and Tethys are discussed. We demonstrate the possibility of calculating a new value for the mass of Dione and we show that one of the coorbital satellites of Tethys could be moving in a horseshoe orbit even though another satellite is librating in a tadpole orbit about the leading Lagrangian equilibrium point L₄. The origin of coorbital satellites and the stability of their orbits are discussed.     

The Orbital Evolution of Two Sounding Satellites and Analysis of the Accuracy of Orbit Determination

The satellites TC-1 and TC-2 are the two Chinese satellites with great elliptical orbits which are still in orbit around the earth at present. Since the launch the orbits of the two satellites have continuously evolved, which has a certain effect on the orbit determination and prediction precision. The regularities of the orbital evolution of the two sounding satellites are qualitatively and quantitatively analyzed. Under the current tracking mode the corresponding prediction precision of orbit determination is analyzed based on the different stages of the orbital evolution, thereby providing the basis for the adjustment of planning mode by the satellite application departments and the guarantee of normal satellite payload. Finally, the orbital lifetimes of the two satellites are predicted through the trend of the orbital evolution.     

Mutual phenomena of Saturn's satellites in 1979–1980

Using two sets of orbital elements and the radii of the Saturnian satellites 1 (Mimas) through 7 (Hyperion), we find that from October 1979 until August 1980 nearly 300 mutual eclipses and occultations involving these bodies will occur. To allow for the expected errors in the satellite ephemerides, we repeat these calculations in order to obtain the additional events that occur when all satellite radii (save Titan's) are increased by 1000 km. A third listing predicts eclipses of satellites by (the shadow of) the ring. Photometric observations of a large number of these events will add much precise information to our knowledge of the Saturnian system at a critical time.     

Analytical description of physical librations of saturnian coorbital satellites Janus and Epimetheus

Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach.     

关于星座小卫星的编队飞行问题

从轨道力学角度来看星座小卫星编队飞行和星星跟踪中的伴飞，遵循着如下动力学机制：(1)在各小卫星绕地球运动过程中轨道摄动变化的主要特征决定了星-星之间的空间构形，(2)当星星之间相互距离较近时，在退化的限制性三体问题(实为限制性二体问题)中，共线秤动点附近的条件周期运动亦可在一定时间内制约星-星之间的空间构形．将具体阐明这两种动力学机制的原理和相应的星星之间的相对构形，并用仿真计算来证实这两种动力学机制的适用范围，为星座小卫星编队飞行和在伴飞运动过程中进行轨控提供理论依据和具体的轨控条件．     

土星卫星的精密定轨方案

由于星际探测事业的发展,对土星卫星的定位精度要求愈来愈高,经典的分析法定轨方法已难以适应,在当今计算技术条件高度发展的背景下,本文给出了土星卫星的数值法定轨方案,采用了土星卫星运动的高精度力学模型,并运用１８７４－１９８９这１００多年间的观测资料,引用现代最小二乘估计,对土星卫生进行精密定轨。该方案可以在引用同样的力学模型的前提下,对土星各颗卫星进行定轨,亦可同时进行多颗卫星的定轨。相应的软件比较     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.     

Orbital evolution of Jupiter’s new outer satellites

Data on recently discovered outer satellites of Jupiter are used to analyze their long-period orbital evolution. We determine the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. The satellite orbital elements are plotted against time. The methods of analysis are identical to those that we used to analyze the orbital evolution of Uranus’s and Saturn’s new outer satellites.     

Two problems about the motion of low-moon-orbit satellites

A detailed theoretical analysis on the orbital lifetime and frozen orbit of low-moon-orbit satellites (LMOS) is carried out, and their relationships with the orbital inclination, as well as some mutual relationships are presented. Taking account of the main perturbing sources of low-orbit satellites, we carried out numerical simulations under a comprehensive force model, and the results not only confirm the correctness of the theoretical analysis, but also provide some valuable insights on the orbital design of LMOS.     

Some simple formulas for latitude effects and lifetimes of satellites

An analysis is made of the effect which manifests itself in the orbital period of a satellite because of the latitudinal shifting of the perigee. The American satellites Discoverer V and Discoverer VI (both in 1959) offered good opportunities for such an analysis, especially after elimination of the normal aperiodic decrease of the orbital period. Hereby, the latitude effect has turned out to mean deflections in the decrease of the orbital period about 20 per cent from the average. Some consequences as to air pressure and lifetimes of satellites are implied.     

Role of the solar wind parameters in changing orbital motion of the Earth’s satellites

The investigation of the solar wind and geomagnetic activity parameters' effect on variations of the orbital motion periods of artificial satellites has been continued. The periods of orbital motion of uncontrolled satellites from the database of the Ukrainian network of optical stations (UNOS) for 2012–2014 was used. The data have been compared with the values of geomagnetic planetary index K and the energy spectra of protons and electrons obtained by the GEOS satellites in events during which the orbital periods have changed. It is shown that, in the energy spectra of the proton and electron fluxes, there is no effect of softening the spectrum with time at the time of the flare appearance. This indicates the possibility of particle accumulation above the active region (AR), which entails further continuous energy emission of the solar flare from AR. Dependences have been obtained between the geomagnetic activity and the solar wind speed at a given interplanetary magnetic field strength during the periods under study for the changes in the orbital motion periods of satellites. The corresponding correlation coefficients are 0.93–0.96.     

Theory of the rotation of Janus and Epimetheus

The saturnian coorbital satellites Janus and Epimetheus present a unique dynamical configuration in the Solar System, because of high-amplitude horseshoe orbits, due to a mass ratio of order unity. As a consequence, they swap their orbits every 4 years, while their orbital periods is about 0.695 days. Recently, Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) got observational informations on the shapes and the rotational states of these satellites. In particular, they detected an offset in the expected equilibrium position of Janus, and a large libration of Epimetheus.We here propose to give a three-dimensional theory of the rotation of these satellites in using these observed data, and to compare it to the observed rotations. We consider the two satellites as triaxial rigid bodies, and we perform numerical integrations of the system in assuming the free librations as damped.The periods of the three free librations we get, associated with the three dimensions, are respectively 1.267, 2.179 and 2.098 days for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of 0.747 days to the orbital period causes a high sensitivity of the librations of Epimetheus to the moments of inertia. Our theory explains the amplitude of the librations of Janus and the error bars of the librations of Epimetheus, but not an observed offset in the orientation of Janus.