On the Precession of Saturn

The precession of Saturn under the effect of the gravity of the Sun, Jupiter and planet’s satellites has been investigated. Saturn is considered to be an axisymmetric (A = B) solid body close to the dynamically spherical one. The orbits of Saturn and Jupiter are considered to be Keplerian ellipses in the inertial coordinate system. It has been shown that the entire set of small parameters of the problem can be reduced to two independent parameters. The averaged Hamiltonian function of the problem and the integrals of evolutionary equations are obtained disregarding the effect of satellites. Using the small parameter method, the expressions for the precession frequency and the nutation angle of the planet’s axis of rotation caused by the gravity of the Sun and Jupiter are obtained. Considering the planet with satellites as a whole preceding around the normal to the unmovable plane of Saturn’s orbit, the satellites effect on the Saturn rotation is taken into account via the corrections in the formula for the undisturbed precession frequency. The satellites are shown to have no effect on the nutation angle (in the framework of the accepted model), and the disturbances from Jupiter to make the main contribution to the nutation angle evolution. The effect of Jupiter on the nutation angle and the precession period is described with regard to the attraction of satellites.     

扰动引力场对远程火箭影响的分析及补偿方法研究进展

在分析扰动引力场影响机理的基础上,梳理了目前垂线偏差及扰动引力影响的分析方法。介绍了垂线偏差和扰动引力快速重构的主要研究进展。最后从弹道诸元、制导诸元和箭上实时三个方面评估了扰动引力场影响补偿的方法。本文的工作为提升扰动引力场下远程火箭的精度和快速反应能力提供了支持。     

On Saturn’s rotation relative to a center of mass under the action of the gravitational moments of the Sun and Jupiter

Saturn’s rotation relative to a center of mass is considered within an elliptic restricted three-body problem. It is assumed that Saturn is a solid under the action of gravity of the Sun and Jupiter. The motions of Saturn and Jupiter are considered elliptic with small eccentricities e_S and e_J, respectively; the mean motion of Jupiter n_J is also small. We obtain the averaged Hamiltonian function for a small parameter of ε = n_J and integrals of evolution equations. The main effects of the influence of Jupiter on Saturn’s rotation are described: (α) the evolution of the constant parameters of regular precession for the angular momentum vector I₂; (β) the occurrence of new libration zones of oscillations I₂ near the plane of the celestial equator parallel to the plane of the Jupiter’s orbit; (γ) the occurrence of additional unstable equilibria of vector I₂ at the points of the north and south poles of the celestial sphere and, as a result, the existence of homoclinic trajectories; and (δ) the existence of periodic trajectories with arbitrarily large periods near the homoclinic trajectory. It is shown that the effects of (β), (γ), and (δ) are caused by the eccentricity e of the Jupiter’s orbit and are practically independent of Jupiter’s mass (within satellite approximation).     

基于交叠视场亮度优选算法的导航星库构建方法

星敏感器导航星库直接影响星图识别效率和姿态解算精度。分析了参与姿态解算的星颗数和亮度对姿态精度影响,在此基础上,提出了一种基于交叠视场亮度优选算法的星敏感器导航星库构建方法。将精度较高的Hipparcos星表作为基础星表,分析了星等、双星、自行、变星等对姿态精度的影响,将星库筛选成一个备选星库,生成覆盖全天球的交叠视场。每个拥有较多星的视场,都按照亮度优先原则从视场内的扇形区域中选择导航星,从而得到分布均匀的导航星库。结果表明:该方法能有效减小星敏感器导航星库规模,实现导航星在全天球和局部天区的均匀分布。     

Recovery of long-wavelength mean gravity anomalies for the dedicated gravitational satellite (gravsat) mission

This paper describes a computer simulation study that was undertaken to determine how well long-wavelength variations in the Earth's gravitational field can be recovered using data from the Dedicated$\text{Grav}$itational $\text{Sat}$ellite (GRAVSAT) mission. This mission is to consist of two low altitude (160 km) spacecraft in essentially the same orbit but separated in phase by 100–300 km. Geodetic data are measurements of the relative range rate to an accuracy of about 1 μm/s at 4 sec intervals. Specifically, a Bayesian covariance simulation was used to investigate simultaneous recovery of the spacecraft ephemerides and a global distribution of 20° × 20° mean gravity anomaly blocks. Sources of errors considered were tracking station positions, gravitational constant, Earth body tides, tropospheric modeling and measurement noise. It should be noted that this simulation does not include as an error source variations in the gravity field that have a character different from what was modeled. Consequently, this study demonstrates the potential of the low-low system as configured to recover the long-wavelength variations in the gravity field.Using only one days worth of data, the mean of the standard deviations of the 162 20° × 20° gravity anomaly blocks is about 1 μgal. For a 6 month mission (assuming a reduction proportional to the square root of the data intervals) this projects to < 0.1 μgal. Because of the potential of increased measurement precision at shorter separation distances, and the relative insensitivity of the recovery process to separation distance, it should be possible to recover both long and short wavelength variations with a modest distribution of separation distances tailored primarily to the short wavelength recovery. Effects of the uncertainty in the gravitational constant and Love's numbers are negligible. In a simulation not reported on, increasing the altitude of the orbit to 200 km from 150 km, degraded, as expected, the accuracy of the recovered parameters by only 7%.     

State propagation in an uncertain asteroid gravity field

Various spacecraft have been and will be sent to asteroids to characterize them. Generally, an asteroid's gravity field is very irregular and not accurately known when compared to the gravity field of a major planet, Earth in particular. It has been well studied that the irregularity significantly affects the trajectory of an orbiting spacecraft, and causes it to impact or to escape from the asteroid. Complementary to that, this paper focuses on the influence of the limited knowledge of this gravity field on the evolution of the spacecraft's orbit. It develops a general method by which this influence can be quantified. This method comprises specific Monte Carlo simulations with a discrete set of low-altitude orbits, taking into account the uncertainties in the gravity-field parameters. For illustration purposes, it is applied to two different asteroids. Already after three revolutions, the gravity-field uncertainties propagate to significant position uncertainties; this specifically holds for prograde orbits, and around the smaller asteroid. Applying this robust and accurate method helps mission designers and planners to assess the risk posed by gravity uncertainties, and take appropriate measures such as choosing the most favorable orbital geometries and/or lowering the orbit more slowly.     

Concept of a space telescope able to see the planets and even the satellites around the nearest stars

The Space Telescope will be launched in 1986 and will improve considerably our observational possibilities, but not the visibility of outer planetary systems.The solar system as seen from Alpha Centauri is presented, as well as the nearest stars and the main cameras of the Space Telescope.As a possible improvement the action of a distant and star-shaped screen is described; that screen is 100 to 800 meters and placed 10⁵ to 10⁶ km in front of the telescope; it allows one to avoid the dazzling effect of the stars and to look for planets such as Jupiter and Saturn up to 20 to 40 light-years. Such planets as Earth and Venus are a little less visible.The visibility of satellites such as the Moon is discussed; it remains at the limit of our technical possibilities.This conceptual paper does not consider in detail the technical difficulties involved.     

Looking for planetary moons in the spectra of distant Jupiters

More than 100 nearby stars are known to have at least one Jupiter-sized planet. Whether any of these giant gaseous planets has moons is unknown, but here we suggest a possible way of detecting Earth-sized moons with future technology. The planned Terrestrial Planet Finder observatory, for example, will be able to detect objects comparable in size to Earth. Such Earth-sized objects might orbit their stars either as isolated planets or as moons to giant planets. Moons of Jovian-sized planets near the habitable zones of main-sequence stars should be noticeably brighter than their host planets in the near-infrared (1-4 microm) if their atmospheres contain methane, water, and water vapor, because of efficient absorption of starlight by these atmospheric components. By taking advantage of this spectral contrast, future space observatories will be able to discern which extrasolar giant planets have Earth-like moons capable of supporting life.     

Cassini Saturn-escape trajectories to Jupiter,Uranus, and Neptune

Potential encore-mission scenarios have been considered for the Cassini mission. In this paper we discuss one of the end-of-life scenarios in which the Cassini spacecraft could perform a Saturn escape via gravity assists from Titan. It is shown that such satellite-aided escape requires a small deterministic maneuver (e.g., Δv<50 m/s), but provides enough energy for the Cassini spacecraft to reach a range of targets in our Solar System, as close to the Sun as the asteroid belt or as far as the Kuiper belt. The escape sequence could be initiated from an arbitrary point during the on-going Cassini mission. Example tours are presented in which the final Titan flyby places the spacecraft into ballistic trajectories that reach Jupiter, Uranus, and Neptune. After years of heliocentric flight, the spacecraft could impact on the target gas giant or perform a flyby to escape from the Solar System (if not to another destination). The concept can be generalized to a new kind of missions, including nested-grand tours, which may involve satellite-aided captures and escapes at more than one planet.     

基于形状的火卫一重力场研究

介绍基于形状对不规则小天体重力场建模的原理和方法,并通过解析法和数值法对火卫一的重力场进行正演建模。相比之前的重力场模型,基于解析算法获得的17阶次球谐展开形式重力场模型,在分辨率上有显著提高。进一步结合火卫一动力学参数,分析了火卫一表面加速度。结果显示,火卫一因其轨道十分接近火星,导致表面离心力和潮汐力十分显著,在某些区域与自引力相当,造成火卫一的特殊表面重力环境。这些结果可为未来的火卫一探测和科学研究提供基本输入物理场模型,也可为其他小天体探测中的类似问题提供方法参考。     

An alternative approach to solar system exploration planning

Planning for the future exploration of the solar system has involved the structuring of a series of missions that address major scientific objectives at a minimum runout cost for the entire endeavor. In many cases, however, the optimal structuring of a program that would minimize the runout cost would entail an unacceptable high annual funding. Our actual planning must consider the planning wedge imposed on the National Aeronautics and Space Administration. It is vital that a plan be structured that copes with the annual restraint. If we do not recognize this, our plan will not be realized and a queing problem will result, thus negating all of our planning efforts.This paper presents ideas as to how planetary initiatives can be structured, wherein the peak annual funding is minimized. One vital aspect in the plan is to have a transportation capability that can launch a mission in any planetary opportunity. Solar electric propulsion can provide this capability. Another cost reduction approach would be to structure a mission set in a time sequenced fashion that could utilize essentially the same spacecraft for the implementation of several missions. This opportunity does exist. A third technique would be to fulfill a scientific objective in several sequential missions rather than attempt to accomplish all of the objectives with one mission. This approach might be applied to a mission currently in the planning stage designated the Saturn Orbiter Dual Probe mission. The current concept involves the delivery of a Saturn probe, a Titan probe, and a Saturn Orbiter by a one Shuttle launch. In this case, the orbiter must serve as a relay station for both probes; map the magnetosphere of Saturn; conduct a survey of Saturn's major satellites; and perform the planetological observation of Saturn itself. This mission entails the development of a complex spacecraft that would be required to have a fairly long life due to the extended mission operations at the benefit of accomplishing the mission with one launch. An alternate approach would be to break the mission into two separate elements. We could, for example, launch a Saturn orbiter carrying a Saturn entry probe. After serving as a communications relay system for the Saturn probe, the orbiter would then be specialized to map the magnetosphere of Saturn. A second launch would involve the delivery of a Titan probe by another orbiter where after delivery the orbiter would conduct the planetological observation of Saturn and its satellites. For the split-launch option, the runout cost for the two missions would be greater than the single launch option. However, optimum structuring of the two missions could materially reduce the peak annual funding.This paper presents data on the estimated cost on a year by year basis of a mission set structured to minimize the runout cost with no concern as to the peak annual funding as compared to a mission set that would yield the same scientific objectives in a slightly longer time span wherein the annual peak funding would be minimized. The consequences of this revised plan are analyzed.     

Tides and the evolution of planetary habitability

Tides raised on a planet by the gravity of its host star can reduce the planet's orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close in, and tides can alter the orbits of planets in these locations. We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars ( less or similar to 0.35 M(circle)). Such migration may have important implications for the evolution of the atmosphere, internal heating, and the Gaia hypothesis. Similarly, a planet that is detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently discovered, approximately 5 M(circle) planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago. However, when constraints derived from the additional companions are included, most parameter choices that indicate past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable.     

深空探测器多次引力辅助转移轨道全局搜索

介绍行星引力辅助近似模型,包括近行星点无动力和有动力两种方式;采用开普勒轨道拼接法与双脉冲Lambert算法,建立多次引力辅助转移轨道的参数优化模型;通过广度优先搜索算法对引力辅助行星序列进行穷举,对发射窗口和天体间转移时间进行离散化网格搜索,每一步网格搜索后均采用合理的定界剪枝方法,减少后续计算量。这种全局搜索方法不需要提前指定引力辅助行星序列,并可得到对应不同飞行时间以及不同引力辅助次数的搜索结果,获得若干多天体引力辅助转移轨道初步结果,为进一步局部优化设计奠定基础。文章给出几组全局搜索算例,得到从地球到火星、木星和土星的多次引力辅助转移轨道,验证了全局搜索方法的有效性。     

卫星跟踪卫星应用于月球重力场探测的模拟研究

月球卫星跟踪卫星技术作为月球和行星重力场探测的一种解决方案已经初步研究和讨论。文章引入已有的解析方法在理论上分析卫星间精密测距与月球重力场信号的频率响应关系,并通过模拟计算,以分析月球卫星跟踪卫星方法应用于月球重力场探测的可行性和恢复重力场的能力。由于月球卫星跟踪卫星方法是目前解决远月面重力探测最有潜力的方法之一,且已为一些月球探测计划采用,而我国的月球探测计划也同样面,临远月面探测的难题,文章的研究成果可为我国月球和行星重力场的探测提供参考。     

Ares V launch vehicle: An enabling capability for future space science missions

NASA's planned Ares V cargo launch vehicle offers the potential to completely change the paradigm of future space science mission architectures. Future space science telescopes desire increasingly larger telescope collecting aperture. But, current launch vehicle mass and volume constraints are a severe limit. The Ares V greatly relaxes these constraints. For example, while current launch vehicles have the ability to place a 4.5 m diameter payload with a mass of 9400 kg on to a Sun-Earth L2 transfer trajectory, the Ares V is projected to have the ability to place an 8.8 m diameter payload with a mass of approximately 60,000 kg on to the same trajectory, or 180,000 kg into Low Earth Orbit. Also the Ares V could place approximately 3000 kg (13,000 kg with a Centaur upper stage) on to a trajectory with a C3 of 106 km²/s², arriving at Saturn in 6.1 years without the use of gravity assists. This paper summarizes the current planned Ares V payload launch capability.     

一种多星分离的姿控联合仿真方法

现阶段仅依据多体动力学,难以准确分析和评估多星分离时含调姿过程的近远场分离过程。因此针对一箭多星任务的分离安全性设计需求,提出了一种姿控联合仿真方法,实现了近远场分离的实时调姿仿真。计算结果表明,该方法与专业弹道软件相比,计算误差不超过5%。同时为了进一步研究结构参数、动力学参数和调姿算法等变量对分离方案的影响,结合拉丁超立方采样和蒙特卡罗打靶法,优化了采样空间,从而可以快速分析变量偏差、采样方式对不同分离工况的影响,进而准确判定分离方案的安全性。该方法实现了参数的自动化设置,可有效提高仿真效率,能为一箭多星发射任务的快速论证及分离安全性设计需求提供有力支撑。     

A method for determination of internal gravity wave parameters from a vertical temperature or density profile measurement in the Earth’s atmosphere

A method for determination of internal gravity wave (IGW) parameters from a single vertical temperature or density profile measurement in the Earth’s atmosphere has been developed. This method may be used for the analysis of profiles measured by any techniques in which the accuracy is enough to measure small (∼1%) amplitudes of the temperature or density fluctuations in the atmosphere. The criterion for the IGW identification has been formulated and argued. In the case when this criterion is satisfied then analyzed fluctuations can be considered as wave-induced. The method is based upon the analysis of relative amplitude thresholds of the temperature or density wave field and upon linear IGW saturation theory in which amplitude thresholds are restricted by dynamical instability processes in the atmosphere. In order to approbate the method we have used data of simultaneous radiosonde measurements of the temperature and wind velocity in the Earth’s stratosphere where the saturated IGW propagation has been detected. It is shown that the application of the method to radio occultation temperature data gives the possibility to identify IGWs in the Earth’s lower stratosphere and to determine values of key wave parameters.     

一种新的全天自主星图识别算法

在星图识别领域三角形算法得到了广泛的应用，但是在星对角距很小的情况下，其识别率严重降低。字符匹配算法可以解决这个问题，但是它无法识别由于相机在拍摄瞬问的平移和旋转而产生位移的星图。为了克服这一缺陷，提出了一种有效的星图识别算法，该算法在生成导航星数据库时以一些一定范围内的亮星为中心，把整个天球分为很多个四方形区域，然后根据被拍摄星图的特点从这些四方形区域内选取子区域参与星图识别。仿真结果表明该算法不但继承了字符匹配算法的优点，而且对星图位移有很强的鲁棒性。     

Net electric power of concentrating solar mirror systems for application in space as a function of the distance to the sun

The use of solar radiation by means of concentrating solar mirror systems, such as parabolic and spheric configurations, mainly is an engineering problem. A decisive characteristic for the optimisation of a complete system with turboelectric power conversion is the thermal cycle applied. Besides the Carnot process, here taken up into the study as an ideal comparative process, suitable processes for the technological realisation are the Brayton process and the Rankine process. The Brayton process is a typical gas turbine process using only the gaseous phase. The Rankine process is a steam engine process using liquid and gaseous phase.The work in hand shows how such solar systems with turboelectric conversion are optimised with respect to their specific weight (kg/kW_e) and how the distance to the sun as well as technological data enter into the analysis.As expected, the Carnot cycle as an ideal comparative process for both types of systems shows the best results for the optimum specific mass of the system. Regarding the real processes, the Rankine cycle shows more favourable characteristics than the Brayton cycle. The difference of the specific masses of the real processes mainly results from the different thermal conditions at the radiator.The influence of the distance to the sun is as expected. The nearer to the sun the solar power system operates, the better is the optimum specific mass of the system. For distances to the sun between 0.3 and 1.0 AU the spheric system shows a better behaviour than the parabolic system. For distances to the sun greater than 2.0 AU the parabolic system shows better behaviour of the specific weight. In the region between 1 and 2 AU the better optimum specific mass of the system belongs to the technological data used in the analysis.     

On reliability of determining the orbital parameters of exoplanets by the Doppler method

As a part of the program of searching for exoplanets, the hypothetical influence of changeable velocity of light (due to parameters of motion of a radiation source) on the results of spectrometric measurements of stars is considered. Accelerations of stars relative to the barycenter of a system star-planet (planets) are taken into account. It is shown that the dependence of velocity of light on the barycentric radial velocity and on the component of barycentric radial acceleration of stars should result in significant increase (up to an order of magnitude) of semimajor axes of the found candidates for exoplanets. Consequently, a correct comparison of the spectral method with other known modern methods of finding exoplanets would allow one to use the results obtained in this paper as a reliable test for inspection of invariance of the velocity of light.