Exospheric zonal winds between 540 and 620 km from the orbit of Explorer 24

Data on the variation of the orbital inclination of the balloon satellite Explorer 24 (1964-76A) from 1964 to 1968 have been used to determine zonal winds between 540 and 620 km. In this height region the effect of zonal winds on the orbital inclination may become very small compared to other perturbations like accelerations due to the geopotential, lunisolar gravitation and the solar radiation pressure. It is demonstrated especially that the solar radiation pressure may become the most significant force changing the orbital inclination. The diurnal mean zonal winds derived from Explorer 24 point to an exospheric rotation rate which is about 6–10% less than the rotation rate of the Earth in the analyzed height region. Since the possible errors of the data analysis are of a similar order of magnitude, it can not be excluded that the exosphere corotates with the Earth. Furthermore, a local time dependence of the zonal winds could be detected. The diurnal varitation of the zonal wind is shown to be in good agreement with the theoretical model of Blum and Harris. Our results are discussed and compared with all previous investigations of orbital inclination changes of satellites above 350 km.     

The effects of diffuse solar radiation on the motion of an artificial satellite

Previous analyses of the orbits of spherical balloon satellites have attempted to satisfy residuals in observed perturbations in Keplerian elements, assumed to be caused by diffuse radiation pressure, by introducing small variations ins, the parameter representing the reflection characteristics of the satellite's surface. It is difficult to distinguish, however, between those perturbations caused by diffuse radiation and those caused by reflected radiation, as a result of the deformation of the assumed sphere. Following the derivation by Lucas of exact expressions for both incident and reflected radiation forces on a prolate spheroidal satellite, and the subsequent work of Aksnes pertaining to spherical satellites, the theory is extended to include the effects of diffuse radiation whilst at the same time qualifying the assumption that the radiation force acting along the Sun-satellite line can be taken as parallel to the Sun-Earth line.     

Perturbations of the orbit of Explorer 19 due to solar radiation

The orbit of the balloon satellite, Explorer 19, is analysed to determine the effects of direct solar radiation pressure over one revolution of the satellite (111 min) for MJD 42822 and MJD 42966. At the earlier date, the satellite entered the Earth's shadow, presenting an opportunity to examine the effectiveness of two different shadow models. The reflectivity of the surface of the satellite was estimated from analysis of the variations in orbital eccentricity over a period of 236 days.Although many of the parameters associated with the shape and orientation of the satellite are unknown, the theory for a non-spherical satellite is applied using trial and error methods to determine the parameters of best fit. The paper concludes with an examination of the perturbations in orbital eccentricity and inclination due to incident, specularly reflected, and diffusely reflected radiation.     

Orbital perturbations due to radiation pressure for a spacecraft of complex shape

We analyze the perturbations due to solar radiation pressure on the orbit of a high artificial satellite. The latter is modelled in a simplified way (axisymmetric body plus despun antenna emitting a radio beam), which seems suitable to describe the main effects for existing telecommunication satellites. We use the regularized general perturbation equations, by expressing the force in the moving Gauss' reference frame and by expanding the results in terms of some small parameters, referring both to the orbit (small eccentricity and inclination) and to the spacecraft's attitude. Some interesting results are derived, which assess the relative importance of different physical effects and of different parts of the spacecraft in determining the long-term evolution of the orbital elements.     

Thermal force effects on slowly rotating, spherical artificial satellites-I. Solar heating

The heating of a spinning artificial satellite by natural radiation sources such as the Sun and the Earth results in temperature gradients arising across the satellite's surface. The corresponding anisotropic emission of thermal radiation leads to a recoil force, commonly referred to as “thermal force”. A quantitative theory of this effect is developed, based on more general assumptions than used so far, to model such radiation forces on spherically symmetric LAGEOS-like satellites. In particular, the theory holds for any ratio of the three basic timescales of the problem: the rotation period of the satellite, the orbital period around the Earth, and the relaxation time for the thermal processes. Thus, the simplifying assumption of a comparatively fast rotational motion is avoided, which will fail for LAGEOS within the next decade, owing to magnetic dissipation effects. A number of predictions about the future behaviour of non-gravitational long-term orbital perturbations of LAGEOS become possible with the new theory. In particular the Yarkovsky-Schach thermal force effects are studied arising as a consequence of the solar radiation flux onto the satellite, periodically interrupted by eclipses. Starting on about year 2005, the orbital perturbation effects predicted by the new theory are substantially different from those inferred in the fast-rotation case. This holds not only for the long-term semimajor axis effects, but also for eccentricity and inclination perturbations.     

The Non-Gravitational Perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects

The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key rôle of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10^?6 m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about $10^{-9}\,m/s^{2}/\sqrt{Hz}The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key r?le of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10⁻⁶ m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about in the frequency band of 3·10⁻⁵–10⁻¹ Hz, guarantees a very significant reduction of the non-gravitational accelerations impact on the space mission accuracy, especially of the dominant direct solar radiation pressure.     

《大气一号》气球卫星轨道倾角变化分析

引起《大气一号》两颗气球卫星（ＤＱ－１Ａ和ＤＱ－１Ｂ）轨道倾角变化的摄动因素主要是太阳光压摄动、大气旋转和日月引力摄动。太阳光压摄动引起气球卫星轨道倾角增大，平均每天变化约０．００１７，大气旋转引起轨道倾角减小，平均每天变化不到０．０００１，但随着高度下降，变化量亦增大，陨落前达０．００２。本文根据卫星轨道摄动理论，给出气球卫星轨道倾角变化的一种定量分析方法，得到的分析结果为：（１）由太阳光压摄动     

The geomagnetic effects on the motion of an electrically charged artificial satellite

The orbital effects of the Lorentz force on the motion of an electrically charged artificial satellite moving in the Earth's magnetic field are determined. The geomagnetic field is considered as a multipole potential field and the satellite electrical charge is supposed to be constant. The relativistic perturbations of the main geomagnetic field are discussed briefly. The results are concentrated on the determination of the secular changes, and numerical values are computed for the case of the LAGEOS satellite. The results are discussed in the context of a possible detection of the Lense-Thirring effect analyzing the orbital perturbations of the LAGEOS and LAGEOS X satellites.     

Time distributions in satellite constellation design

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.     

Libration dynamics and stability of electrodynamic tethers in satellite deorbit

This paper studies libration dynamics and stability of deorbiting nano-satellites by short and bare electrodynamic tethers. A critical aspect of satellite deorbit by an electrodynamic tether is to maintain the tether aligned with the local vertical and stable while subjected to external perturbations. The dynamics of electrodynamic tether system in deorbit application is divided into the orbital motion of the center of system’s mass and the tether libration motion relative to that center. Major space environmental perturbations including the current-induced electrodynamic force, atmospheric drag, oblateness effect of the Earth, irregularity of geomagnetic field, variable plasma density, solar radiation pressure, and lunisolar gravitational attractions are considered in the dynamic analysis. Quantitative analyses are provided in order to characterize the order of the perturbative torques during the deorbit process. A single index is derived from the libration energy to stabilize the libration motion by regulating the current in the tether through simple on-off switching. Numerical results show that the libration dynamics of an electrodynamic tether has significant impacts on the deorbit process and the electrodynamic tether cannot effectively deorbit satellites without libration stability control. The proposed current regulation strategy is simple and very effective in stabilizing libration motion of an electrodynamic tether.     

Satellite orbits perturbed by direct solar radiation pressure: General expansion of the disturbing function

An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method. The Kaula inclination functions are replaced by an equivalent set of modified Allan inclination functions.The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, 1976), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonsnce with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure.     

Approximate Analytical Theory of Satellite Orbit Prediction Presented in Spherical Coordinates Frame

A comparative review of analytic theories for the motion of Earth satellites in quasi-circular orbits written in the spherical coordinate frame is presented. The theory of motion is developed for satellites in quasi-circular and quasi-equatorial orbits subjected to geopotential, luni-solar and solar radiation pressure force perturbations. The intermediate orbit is Keplerian and the equations of motion are solved by the Lyapunov–Poincaré small parameter method. Both resonant and non-resonant cases are considered. The results can be useful for the development of a complete theory of weakly eccentric orbits.     

Dust on the Outskirts of the Jovian System

The outer region of the jovian system between ∼50 and 300 jovian radii from the planet is found to be the host of a previously unknown dust population. We used the data from the dust detector aboard the Galileo spacecraft collected from December 1995 to April 2001 during Galileo's numerous traverses of the outer jovian system. Analyzing the ion amplitudes, calibrated masses and speeds of grains, and impact directions, we found about 100 individual events fully compatible with impacts of grains moving around Jupiter in bound orbits. These grains have moderate eccentricities and a wide range of inclinations—from prograde to retrograde ones. The radial number density profile of the micrometer-sized dust is nearly flat between about 50 and 300 jovian radii. The absolute number density level (∼10 km⁻³ with a factor of 2 or 3 uncertainty) surpasses by an order of magnitude that of the interplanetary background. We identify the sources of the bound grains with outer irregular satellites of Jupiter. Six outer tiny moons are orbiting the planet in prograde and fourteen in retrograde orbits. These moons are subject to continuous bombardment by interplanetary micrometeoroids. Hypervelocity impacts create ejecta, nearly all of which get injected into circumjovian space. Our analytic and numerical study of the ejecta dynamics shows that micrometer-sized particles from both satellite families, although strongly perturbed by solar tidal gravity and radiation pressure, would stay in bound orbits for hundreds of thousands of years as do a fraction of smaller grains, several tenths of a micrometer in radius, ejected from the prograde moons. Different-sized ejecta remain confined to spheroidal clouds embracing the orbits of the parent moons, with appreciable asymmetries created by the radiation pressure and solar gravity perturbations. Spatial location of the impacts, mass distribution, speeds, orbital inclinations, and number density of dust derived from the data are all consistent with the dynamical model.     

Sun-synchronous orbits near critical inclination

The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated.     

The effect of aerodynamic lift on near-circular satellite orbits

Theory is developed to evaluate the effect of aerodynamic lift on near circular satellite orbits for: (i) flat surfaces at constant attitude to the velocity vector and (ii) sun-oriented plates. In both cases, the gas-surface interaction is restricted to diffuse or specular reflection; the former being particularly relevant to the height band where atomic oxygen predominates.An order of magnitude study is undertaken to determine the effect of lift on the solar panels of the ERS 1 satellite, due for launch around 1990. Calculations reveal radial perturbations of order 1 cm over a 5-day period for low to moderate solar activity. High solar activity, however, leads to a 10-fold increase in the order of this effect. Effects on stabilised satellites at lower altitudes are illustrated by a hypothetical study of the orbital inclination of Skylab 1.     

A method for averaging the perturbing function in Hill’s problem

A modified method for averaging the perturbing function in Hill’s problem is suggested. The averaging is performed in the revolution period of the satellite over the mean anomaly of its motion with a full allowance for a variation in the position of the perturbing body. At its fixed position, the semimajor axis of the satellite orbit during the revolution of the satellite is constant in view of the evolution equations, while the remaining orbital elements undergo secular and long-period perturbations. Therefore, when the motion of the perturbing body is taken into account, the semimajor axis of the satellite orbit undergoes the strongest perturbations. The suggested approach generalizes the averaging method in which only the linear (in time) term is included in the perturbing function. This method requires no expansion in powers of time. The described method is illustrated by calculating the perturbations of the semimajor axes for two distant satellites of Saturn, S/2000 S 1 and S/2000 S5. An approximate analytic solution is compared with the results of numerical integration of the averaged system of equations of motion for these satellites.     

北斗三号卫星精密定轨中的光压模型研究

对于在轨运行的BDS (BeiDou Navigation Satellite System)卫星, 太阳光压是作用在卫星上主要的非引力摄动. 受多种因素的影响, 太阳光压摄动力难以精确建模, 是BDS卫星精密定轨和轨道预报过程中重要的误差来源. 由于ECOMC (Empirical CODE Orbit Model 1 and 2 Combined)模型兼顾了ECOM1 (Empirical CODE Orbit Model 1)和ECOM2 (Empirical CODE Orbit Model 2)模型的特点, 在模型中引入了较多的待估参数, 使得参数之间存在强相关性. 针对ECOMC模型的这一缺陷, 文中收集了2019年1月至2022年4月武汉大学分析中心提供的BDS-3卫星精密星历, 采用动力学轨道拟合方法得到了ECOMC模型的13个光压参数. 通过对该模型的光压参数进行时间序列分析, 分别给出了BDS-3 IGSO (Inclined Geosynchronous Orbit)和MEO (Medium Earth Orbit)卫星光压模型的参数选择策略. 并利用轨道拟合和轨道预报试验, 验证了光压模型参数选择策略的合理性. 结果表明, 采用改进型ECOMC模型进行BDS-3 IGSO和MEO卫星轨道拟合的效果最佳, 同时, 也能够提升BDS-3 IGSO和MEO卫星中长期轨道预报的精度.     

Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth’s satellites

We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth’s satellites. We describe parameters of the motion model used for the artificial Earth’s satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.     

A numerical solution for lageos thermal thrust: The rapid-spin case

We report the results of detailed numerical calculations of the thermal thrust on the rapidly-spinning LAGEOS spacecraft. This thrust results from anisotropic emission of thermal radiation from its surface. LAGEOS is a good test case for such calculations because of its relatively simple structure and because precise orbit determinations based on laser ranging give observed thrust effects for comparison.The numerical integration includes the varying heating over spacecraft-surface latitude from earth infrared radiation (for the earth-Yarkovsky force) and the varying solar heating as the spacecraft moves in and out of the earth's shadow (for the solar-Yarkovsky force). The computation allows for the poor thermal coupling between the spacecraft structure and individual surface elements (the fused-silica cube-corner reflectors and their aluminum retainer rings), and the poor conduction between structural hemispheres.A Fourier analysis of the computed force with respect to orbital longitude gives the important frequency components for the computation of long-term orbit perturbations. Empirical formulas fit to the numerical results accurately express the component amplitudes as simple functions of spin axis orbital latitude, the sun aspect angle from the spin axis, and the fraction of the orbit period spent in the earth's shadow. These results. based on first principles, are similar to those from simplified theories of the thermal thrust. but add the following new feature: The decrease in orbit-averaged satellite temperature when the orbit intersects the earth's shadow decreases the earth-Yarkovsky drag by 0.14 pm/s² from the no-eclipse value.The development of spacecraft-element thermal parameters is the most difficult part of the analysis; the paper tabulates the parameters that should be directly measured before the launch of future geodynamic satellites.