月球重力场对绕月低轨卫星的长期影响

从解析形式出发,利用月球重力场模型JGL165P1,分析了月球重力场(带谐项)对绕月低轨卫星的长期影响。为了减少计算误差,保证计算精度,在分析解中使用循环公式来计算倾角函数。结果指出对于一个高度为100km的极月轨道卫星,冻结轨道存在的可能性不大,但是当轨道倾角在i=90°附近或者高度再高一些,则有可能存在冻结轨道;对于100km高的初始圆轨道,卫星在无控的情况下半年内将会坠落到月球表面,如果高度增加到200km,则不进行轨道控制也不会坠落到月面上。利用仿真软件GEODYN解算出来的结果证实了上述结论。     

Observations of forced oscillations of the magnetosphere by a geostationary satellite and an extensive ground magnetometer array

We present results from the analysis of magnetometer measurements of one of the clearest observations of a double resonance Pc4 pulsation to date. The Pc4, with a period of 55 s, was measured by 18 ground magnetometers and also on board the ATS-6 satellite at geostationary orbit. Using a subsequent observation of a second harmonic guided poloidal mode pulsation at ATS-6, we have been able to estimate the plasma density at geostationary orbit. We then calculated periods of theoretical cavity mode resonances in the plasmatrough and the eigenperiods of different wave modes and harmonics at geostationary orbit. We developed a model of the variation of plasma density, and hence eigenperiods, within the magnetosphere which is consistent with these calculations and with the amplitude, phase and ellipticity observations made over the array of ground observatories. In this model we suggest that hydromagnetic field line resonances occur in the plasmatrough and in the plasmasphcre, which are the second and fundamental harmonic guided toroidal mode resonances, respectively. The model also allows us to evaluate the damping experienced by hydromagnetic standing waves in the magnetosphere. The damping is found to be slightly higher than that previously suggested for daytime conditions.     

太阳同步卫星的控制现状及发展趋势

在介绍太阳同步轨道相关知识的基础上,着重分析了该轨道的高度因素,给出了当前在轨太阳同步卫星轨道高度的上下限,介绍了几种典型的低轨道太阳同步卫星,同时给出了太阳同步卫星轨道控制方法的发展状况及趋势,最后综述了当前国内外太阳同步轨道的轨控模式与维持策略。     

Normal modes of synchronous rotation

The dynamics of synchronous rotation and physical librations are revisited in order to establish a conceptually simple and general theoretical framework applicable to a variety of problems. Our motivation comes from disagreements between the results of numerical simulations and those of previous theoretical studies, and also because different theoretical studies disagree on basic features of the dynamics. We approach the problem by decomposing the orientation matrix of the body into perfectly synchronous rotation and deviation from the equilibrium state. The normal modes of the linearized equations are computed in the case of a circular satellite orbit, yielding both the periods and the eigenspaces of three librations. Libration in longitude decouples from the other two, vertical modes. There is a fast vertical mode with a period very close to the average rotational period. It corresponds to tilting the body around a horizontal axis while retaining nearly principal-axis rotation. In the inertial frame, this mode appears as nutation and free precession. The other vertical mode, a slow one, is the free wobble. The effects of the nodal precession of the orbit are investigated from the point of view of Cassini states. We test our theory using numerical simulations of the full equations of the dynamics and discuss the disagreements among our study and previous ones. The numerical simulations also reveal that in the case of eccentric orbits large departures from principal-axis rotation are possible due to a resonance between free precession and wobble. We also revisit the history of the Moon's rotational state and show that it switched from one Cassini state to another when it was at 46.2 Earth radii. This number disagrees with the value 34.2 derived in a previous study.     

A method of astronomical autonomous orbit and attitude determinations for satellites

A method of realtime autonomous orbit determination for earth satellites using the extended Kalman filtering is proposed. The observed quantities are: the satellite-sun direction vector measured by a sun sensor, the satellite-earth and satellite-moon direction vectors measured by an ultraviolet sensor, and the geocentric distance measured by a radar altimeter. At the same time the satellite attitude to the earth is also determined. Results of our simulation of the autonomous orbit determination show that the precision of the orbit determinations is better than 200 m. The effects of the sampling period, orbital inclination, orbital eccentricity and orbital altitude on the precision of orbit determination are analyzed and compared, and certain principles helpful for improving the precision of orbit determination are suggested.     

Long-Period Variations of the Eccentricity Vector Valid also for Near Circular Orbits around a Non-Spherical Body

This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity. We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis, inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations or librations around an equilibrium point.     

Satellite resonance with longitude-dependent gravity—II Effects involving the eccentricity

For a satellite in a nominally circular orbit at arbitrary inclination whose mean motion is commensurable with the Earth's rotation, the dependence of gravity on longitude leads to a resonant variation in eccentricity as well as the long-period oscillation in longitude. Provided forces capable of processing perigee are present, it is shown that the change in eccentricity for a satellite captured in librational resonance is not secular but periodic.

There are corresponding resonance effects for a satellite in a nominally equatorial but eccentric orbit. Here the commensurability condition is that the longitudes of the apses shall be nearly repetitive relative to the rotating Earth. There will be a long-period oscillation in longitude which can take the form of either a libration (trapped) or a circulation (free), and there will also be an oscillation of the orbital plane having the same period as the precession of perigee relative to inertial space.     

Analysis of the orbit of 1968-90A (Cosmos 248)

The satellite 1968-90A (Cosmos 248), was launched in October 1968 into an orbit inclined at 62.25° to the equator, with an initial perigee height of 475 km, apogee height 543 km, and orbital period 94.8 min. The orbit has been determined at 57 epochs over nearly one and a quarter cycles of the argument of perigee from January 1972 until December 1975 with the aid of the RAE orbit refinement program PROP, using nearly 3000 observations. For most of these orbits the standard deviations in inclination are less than 0.0009° (corresponding to about 100m in cross-track distance). The values of eccentricity give perigee heights accurate to between 30 and 120m.The main purpose of the orbit determination was to provide accurate values of the eccentricity for use in determining the odd zonal harmonics in the Earth's gravitational potential. These values have been analysed to determine the amplitude of the oscillation in eccentricity, which is found to be 0.00433 ± 0.00001.     

GIM在LEO卫星单频GPS定轨中的应用

电离层延迟误差是单频GPS(Global Positioning System)数据最主要的误差源,为提高基于单频GPS数据的LEO(Low Earth Orbiting)卫星定轨精度,必须消除/减弱GPS观测数据中电离层延迟影响.研究了全球电离层模型GIM(Global IonosphericMaps)在基于单频GPS伪距数据的低轨卫星运动学和动力学定轨中的应用,并通过估算电离层尺度因子的方法消除C/A码伪距观测量中电离层延迟影响.由于LEO卫星星载GPS信号受电离层延迟影响与卫星轨道高度相关,选取了轨道高度在300～800 km的CHAMP(CHAllenging Mini-satellite Payload)、GRACE(Gravity Recovery AndClimate Experiment)、TerraSAR-X及SAC-C等LEO卫星C/A码伪距观测量作为试算数据.CHAMP等卫星实测数据计算结果表明:以JPL(Jet Propulsion Laboratory)发布的GIM模型作为背景模型,通过电离层比例因子法能很好地消除C/A码伪距观测量中电离层延迟影响,提高LEO卫星运动学和动力学定轨精度,其中,CHAMP卫星轨道最低,受电离层延迟影响最严重,定轨精度提高最显著,分别为55.6%和47.6%;SAC-C卫星轨道高度最高,受电离层延迟影响最小,相应的定轨精度提高幅度也最低,分别为47.8%和38.2%.     

A tidal explanation for the Titan haze layers

Though Titan is in synchronous rotation around Saturn, it experiences gravitational tides as a consequence of its eccentric orbit. It is proposed that the vertical transport of aerosols by these tides produces the haze layers in Titan's upper atmosphere. Analysis shows that the zonal winds in Titan's superrotating atmosphere have a profound influence on which tidal components are effective in establishing the multiple detached-haze layers. If the Huygens Doppler winds are representative of the equatorial global superrotation, then the westward propagating s=2 mode is the responsible tidal component even though its forcing is significantly weaker than that of the s=0 and eastward s=2 components. The eastward s=2 tidal mode is eliminated by critical levels while the s=0 mode is viscously damped in the strong high altitude winds. At polar latitudes, however, the gravest s=0 mode is the one most likely to produce layering. It is also suggested that the atmospheric gravitational tides could be responsible for decelerating the superrotating atmosphere as seen in the Huygens Doppler wind velocity profile at about 80 km altitude.     

基于Broyden方法的不对称与对称周期解延拓算法与应用

考虑周期解的数值延拓问题并提出基于Broyden拟牛顿法来延拓周期解的一种有效算法,先后以布鲁塞尔振子、平面圆型限制性三体问题(Planar Circular Restricted Three-Body Problem, PCRTBP)的周期解为例进行了验证.这里的Broyden方法包含线性搜索、正交三角分解求线性方程组的步骤.对一般的周期解,周期性条件方程组中含有周期作为待延拓参数,可用周期来决定积分时长,将解代入周期性条件得到积分型的非线性方程组,利用Broyden方法迭代延拓直至初值收敛.根据两次垂直通过一个超平面的轨道是对称周期轨道的性质,可采用插值的方法求得再次抵达超平面的解分量,得到周期性条件方程组,再用Broyden方法求解.结合哈密顿系统的对称性和PCRTBP周期轨道的一些分类,对2/1、3/1的内共振周期解族进行了数值研究.最后,对算法和计算结果做了总结和讨论.     

Numerical verification of analytic expressions for the perturbations due to an arbitrary zonal harmonic of the geopotential

Expressions are given for the first order node-to-node perturbations in the orbital elements of a satellite due to an arbitrary zonal harmonic of the geopotential. Accurate and efficient procedures for computing such perturbations are necessary for orbit determination methods which will fully utilize the highly accurate observations now available.Comparison with a double precision numerical integration is made for an intermediate altitude satellite, TELSTAR I. (Second order perturbations due to the second harmonic, derived elsewhere, are included, as are the first order perturbations due to the zonals through fourteenth order.) Discrepancies in semi-major axis after 1 period are of the order of 0.1 mm. Discrepancies in timing are of the order of 0.03 msec. A detailed discussion of computational efficiency is included.     

The Application of GIM in Precise Orbit Determination for LEO Satellites with Single-Frequency GPS Measurements

With the precise GPS ephemeris and clock error available, the iono- spheric delay is left as the dominant error source in the single-frequency GPS data. Thus, the removal of ionospheric effects is a ma jor prerequisite for an improved orbit reconstruction of LEO satellites based on the single-frequency GPS data. In this paper, the use of Global Ionospheric Maps (GIM) in kine- matic and dynamic orbit determinations for LEO satellites with single-frequency GPS pseudorange measurements is discussed first, and then, estimating the iono- spheric scale factor to remove the ionospheric effects from the C/A-code pseu- dorange measurements for both kinematic and dynamic orbit determinations is addressed. As it is known that the ionospheric delay of space-borne GPS sig- nals is strongly dependent on the orbit altitudes of LEO satellites, we select the real C/A-code pseudorange measurement data of the CHAMP, GRACE, TerraSAR-X and SAC-C satellites with altitudes between 300 km and 800 km as sample data in this paper. It is demonstrated that the approach to eliminating ionospheric effects in C/A-code pseudorange measurements by estimating the ionospheric scale factor is highly effective. Employing this approach, the accu- racy of both kinematic and dynamic orbits can be improved notably. Among those five LEO satellites, CHAMP with the lowest orbit altitude has the most remarkable improvements in orbit accuracy, which are 55.6% and 47.6% for kine- matic and dynamic orbits, respectively. SAC-C with the highest orbit altitude has the least improvements in orbit accuracy accordingly, which are 47.8% and 38.2%, respectively.     

Tidal friction in triple stars

Tidal friction in close binaries, with periods of a few days, is expected to circularize the orbit on a time-scale long compared with human observation but shorter than, or comparable to, the lifetimes of main-sequence stars. In a hierarchical triple star, however, the perturbing effect of the distant third star may decircularize the inner orbit significantly on a time-scale of the order of days (as in λ Tau) or centuries (as in β Per). If the inner pair is observed to be semidetached, however, it is plausible to assume that the eccentricity is small. This may be because tidal friction is operating on a comparably short time-scale, and so it is in principle amenable to observation. We attempt to determine a lower limit to the strength of tidal friction in λ Tau and β Per, on the basis of this consideration. Tidal friction will also lead to a secular transfer of angular momentum from the inner orbit to the outer orbit. Too rapid a transfer may lead to orbital shrinkage that is fast compared with the nuclear time-scales of the inner systems, and this can also be ruled out on observational grounds. Thus we may be able to set an upper as well as a lower limit to the strength of tidal friction, on the basis of observations. In a young hierarchical triple, provided that the orbits are fairly nearly orthogonal, tidal friction can serve to reduce the inner orbital period from months to days within a fairly short period of time, of order P ²_out/ P _in. This may be a significant mechanism for producing young short-period binaries.     

The determination of the satellite orbit of Mariner 9

This paper presents a comprehensive analysis of the Mars orbital phase of the Mariner 9 trajectory as determined from Earth based radio data. Both the method and accuracy of the orbit determination process are reviewed. Analysis is presented to show the effects of Mars gravity model and node in the plane of the sky errors on the accuracy of orbit determination. In addition the long term evolution of the orbit from insertion through the first 500 revolutions is presented, and decomposed into effects from the Mars garvity field,n-body perturbations, and solar radiation pressure. Since the orbit period is nearly commensurable with the Mars rotational period, the orbit experiences significant resonance perturbations. The primary perturbation is in-track with a maximum amplitude of 1000 km and a wavelength of 39 spacecraft revolutions.This paper was presented at the AIAA/AAS Astrodynamics Conference, Palo Alto, California, September 11 and 12, 1972. At this time Mariner 9 operations were still underway. The operational life of Mariner 9 ended October 27, 1972, when the supply of nitrogen gas, used for attitude stabilization, was depleted. This paper represents one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, under NASA Contract No. NAS 7-100.     

AKARI: space infrared cooled telescope

AKARI, formerly known as ASTRO-F, is the second Japanese space mission to perform infrared astronomical observations. AKARI was launched on 21 February 2006 (UT) and brought into a sun-synchronous polar orbit at an altitude of 700 km by a JAXA M-V rocket. AKARI has a telescope with a primary-mirror aperture size of 685 mm together with two focal-plane instruments on board: the Infrared Camera (IRC), which covers the spectral range 2–26 μm and the Far-Infrared Surveyor (FIS), which operates in the range 50–180 μm. The telescope mirrors are made of sandwich-type silicon carbide, specially developed for AKARI. The focal-plane instruments and the telescope are cooled by a unique cryogenic system that kept the telescope at 6K for 550 days with 180 l super-fluid liquid Helium (LHe) with the help of mechanical coolers on board. Despite the small telescope size, the cold environment and the state-of-the-art detectors enable very sensitive observations at infrared wavelengths. To take advantage of the characteristics of the sun-synchronous polar orbit, AKARI performed an all-sky survey during the LHe holding period in four far-infrared bands with FIS and two mid-infrared bands with IRC, which surpasses the IRAS survey made in 1983 in sensitivity, spatial resolution, and spectral coverage. AKARI also made over 5,000 pointing observations at given targets in the sky for approximately 10 min each, for deep imaging and spectroscopy from 2 to 180 μm during the LHe holding period. The LHe ran out on 26 August 2007, since which date the telescope and instrument are still kept around 40K by the mechanical cooler on board, and near-infrared imaging and spectroscopic observations with IRC are now being continued in pointing mode.     

The spectroscopic orbit of the K‐giant binary γ Canis Minoris

We have determined an improved orbit for the bright, evolved, double lined binary γ Canis Minoris. The system has an orbital period of 389.31 days and an eccentricity of 0.2586. We have revised the secondary to primary mass ratio to 0.987. The spectral types of the primary and secondary are K4 III and K1: III, respectively, and the components have a V magnitude difference of 2.2. Orbital fits to the Hipparcos astrometry are not definitive, but they suggest an orbital inclination of ∼ 66°, which produces masses of 1.88 and 1.85 M_⊙ for the components. A comparison with evolutionary tracks results in an age of 1.3 Gyr. STELLA very low amplitude radial velocity residuals of the secondary indicate a period of 278 days. We interpret this as the rotation period of the secondary, detectable because of star spots rotating in and out of view. This period is nearly identical to the pseudosynchronous rotation period of the star. The primary is rotating more slowly than its pseudosynchronous rate. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy fluxes of the (1,1,1) atmospheric oscillation

The global mean vertical energy flux of the (1,1,1) mode of atmospheric oscillation is evaluated at 80 km altitude by classical tidal theory for mean January, April, July and October conditions using revised profiles of water vapour and ozone heating. Fluxes calculated for January and July are lower than those for April and October due to seasonal changes in water vapour, solar declination and Sun-Earth distance. Flux values obtained are compared with a previously stated requirement for maintaining the residual thermosphere and are adequate unless damping, which is ignored in the present calculations, introduces a factor of more than an order of 10 in magnitude. The relative changes of flux between the above four months are noted to be similar in form to the semi-annual variation of thermospheric air densities.