Regional positioning using a low Earth orbit satellite constellation

Global and regional satellite navigation systems are constellations orbiting the Earth and transmitting radio signals for determining position and velocity of users around the globe. The state-of-the-art navigation satellite systems are located in medium Earth orbits and geosynchronous Earth orbits and are characterized by high launching, building and maintenance costs. For applications that require only regional coverage, the continuous and global coverage that existing systems provide may be unnecessary. Thus, a nano-satellites-based regional navigation satellite system in Low Earth Orbit (LEO), with significantly reduced launching, building and maintenance costs, can be considered. Thus, this paper is aimed at developing a LEO constellation optimization and design method, using genetic algorithms and gradient-based optimization. The preliminary results of this study include 268 LEO constellations, aimed at regional navigation in an approximately 1000 km \(\times \) 1000 km area centered at the geographic coordinates [30, 30] degrees. The constellations performance is examined using simulations, and the figures of merit include total coverage time, revisit time, and geometric dilution of precision (GDOP) percentiles. The GDOP is a quantity that determines the positioning solution accuracy and solely depends on the spatial geometry of the satellites. Whereas the optimization method takes into account only the Earth’s second zonal harmonic coefficient, the simulations include the Earth’s gravitational field with zonal and tesseral harmonics up to degree 10 and order 10, Solar radiation pressure, drag, and the lunisolar gravitational perturbation.     

Using space manifold dynamics to deploy a small satellite constellation around the Moon

The possibility of communicating with the far side of the Moon is essential for keeping a continuous radio link with lunar orbiting spacecraft, as well as with manned or unmanned surface facilities in locations characterized by poor coverage from Earth. If the exploration and the exploitation of the Moon must be sustainable in the medium/long term, we need to develop the capability to realize and service such facilities at an affordable cost. Minimizing the spacecraft mass and the number of launches is a driving parameter to this end. The aim of this study is to show how Space Manifold Dynamics can be profitably applied in order to launch three small spacecraft onboard the same launch vehicle and send them to different orbits around the Moon with no significant difference in the Delta-V budgets. Internal manifold transfers are considered to minimize also the transfer time. The approach used is the following: we used the linearized solution of the equations of motion in the Circular Restricted Three Body Problem to determine a first–guess state vector associated with the Weak Stability Boundary regions, either around the collinear Lagrangian point L1 or around the Moon. The resulting vector is then used as initial state in a numerical backward-integration sequence that outputs a trajectory on a manifold. The dynamical model used in the numerical integration is four-body and non-circular, i.e. the perturbations of the Sun and the lunar orbital eccentricity are accounted for. The trajectory found in this way is used as the principal segment of the lunar transfer. After separation, with minor maneuvers each satellite is injected into different orbits that lead to ballistic capture around the Moon. Finally, one or more circularization maneuvers are needed in order to achieve the final circular orbits. The whole mission profile, from launch to insertion into the final lunar orbits, is modeled numerically with the commercial software STK.     

Pitch angle and energy distributions of auroral electrons measured by the ESRO 4 satellite

Energy spectra and angular distributions of auroral electrons in the energy range 0.2–16 keV measured by the low-altitude polar orbiting satellite ESRO 4 are presented. The observations were made in the altitude range 800–1000 km near magnetic midnight. Energy-time spectrograms show inverted-V structures with peaked energy spectra. The inverted-V events are associated with anisotropic electron pitch angle distributions peaked at 0 deg. Frequently these distributions have a maximum also at 90 deg. Measurements of >43 keV electrons indicate that the acceleration probably occurs on closed field lines. It is found that many properties of the observed particle distributions can be explained by acceleration in an electric field parallel to the magnetic field lines, if trapping of particles under an increasing potential drop is included in the model.     

GEO卫星定轨可视化软件设计

介绍了基于Windows系统开发的GEO卫星定轨可视化软件,该软件是采用Microsoft Visual Studio 2005软件平台,利用Visual Basic.NET编程技术开发设计的,具有预处理观测数据资料、解算GEO卫星精密轨道、分析和图形化轨道解算结果等功能。该软件界面友好、可操作性强、方便省时,有效地提高了GEO卫星定轨工作效率。     

Mission-constrained design drivers and technical solutions for the MAGIA satellite

The Mission MAGIA (Missione Altimetrica Geofisica GeochImica lunAre) was proposed in the framework of the ??Bando per Piccole Missioni?? of ASI (Italian Space Agency) in 2007. The mission was selected for a phase A study by ASI on February 7th 2008. The tight budget allocation, combined with quite ambitious scientific objectives, set challenging requirements for the satellite design. The paper gives a fast overview of the payloads complement and of the mission-constrained design drivers, including cost minimization, risk reduction, and AIT flexibility. The spacecraft architecture is then outlined, along with an overview of the key subsystems and trade-offs. Some details are given of a Moon gravitometric experiment based on a mother?Cdaughter satellite configuration with the daughter being a subsatellite released from the MAGIA satellite and intended to circle the Moon at a very low altitude. Budgets are appended at the end of the paper showing the key study results.     

Preferred design and error analysis for the future dedicated deep-space Mars-SST satellite gravity mission

Because the precise measurement of the Martian gravitational field plays a significant role in the future Mars exploration program, the future dedicated Mars satellite-to-satellite tracking (Mars-SST) gravity mission in China is investigated in detail for producing the next generation of the Mars gravity field model with high accuracy. Firstly, a new semi-numerical synthetical error model of the cumulative Martian geoid height influenced by the major error sources of the space-borne instruments is precisely established and efficiently verified. Secondly, the deep space network in combination with the satellite-to-satellite tracking in the low-low (DSN-SST-LL) mode is a preferred design owing to the high precision determination of the gravity maps, the low technical complexity of the satellite system and the successful experiences with the Earth’s Gravity Recovery and Climate Experiment (GRACE) projects and the lunar Gravity Recovery and Interior Laboratory (GRAIL) program. Finally, the future twin Mars-SST satellites plan to adopt the optimal matching accuracy indices of the satellite-equipped sensors (e.g., \(10^{-7}\) m/s in the inter-satellite range-rate from the interferometric laser ranging system (ILRS), 35 m in the orbital position tracked by the DSN and \(3\times 10^{-11}\) m/s² in the non-conservative force from the drag-free control system (DFCS)) and the preferred orbital parameters (e.g., the orbital altitude of \(100\pm 50\) km and the inter-satellite range of \(50\pm 10\) km).     

Effects of interplanetary dust on the LISA drag-free constellation

The analysis of non-radiative sources of static or time-dependent gravitational fields in the Solar System is crucial to accurately estimate the free-fall orbits of the LISA space mission. In particular, we take into account the gravitational effects of Interplanetary Dust (ID) on the spacecraft trajectories. The perturbing gravitational field has been calculated for some ID density distributions that fit the observed zodiacal light. Then we integrated the Gauss planetary equations to get the deviations from the LISA Keplerian orbits around the Sun. This analysis can be eventually extended to Local Dark Matter (LDM), as gravitational fields are expected to be similar for ID and LDM distributions. Under some strong assumptions on the displacement noise at very low frequency, the Doppler data collected during the whole LISA mission could provide upper limits on ID and LDM densities.     

Neutral hydrogen distributions and probable magnetic field distributions in nearby spiral galaxies

Six spiral galaxies (NGC 253, NGC 2903, M 106, M 63, M 51, and M 83) are studied in their HI and magnetic field distributions. There is a possible link between the two distributions, such that a spiral-galaxy with a regularly shaped (VA = 1) or moderately arched (VA = 2) disk of neutral hydrogen seems to have a regular axisymmetric azimuthal magnetic field (m _azim = 0). Conversely, a spiral galaxy with a strongly arched (VA = 3) or extremely arched (VA = 4) disk of neutral hydrogen seems to have a beautifully-shaped bisymmetric azimuthal magnetic field (m _azim = 1).     

Oscillating gyroscopes in a satellite

It is shown that a set of three gyroscopes in a satellite can test vital aspects of general relativity in a period of a few days.     

Suprathermal particle distributions in space physics: Kappa distributions and entropy

The energization of a charged test-particle of mass m in contact with a large ensemble of charged particles of mass M at equilibrium is studied with the Fokker-Planck equation for Coulomb collisions and a quasi-linear diffusion operator for wave-particle interactions. The features of the nonequilibrium steady state velocity distribution of the test-particle system is studied as a function of the mass ratio m/M, and the relative strengths of the wave-particle interactions and Coulomb collisions. It is shown that the steady distribution function is not necessarily a Kappa distribution. The temperature of heavy minor ions given by the model is shown to vary linearly with the mass ratio as observed in the solar wind. The time evolution of the distribution function with and without the energization by wave-particle interactions is calculated and it is demonstrated that the Kullback relative entropy rather than the Tsallis nonextensive entropy rationalizes the results obtained.     

Galilean satellite eclipse studies I. Observations and satellite characteristics

Spectrophotometric light curves of 12 Galilean satellite eclipses are reported. The observations were made in 20 to 30 channels over the wavelength range 3240 to 10,500 Å using the 200-in. telescope. The initial data processing is described. These data measure the Jovian aerosol content in the lower stratosphere and uppermost troposhere and the methane abundance in the lower stratosphere. The data are consistent with a lack of limb darkening on the Galilean satellites. The orbit of Callisto is shown to be inclined 0.08 ± 0.02° to the equatorial plane of Jupiter.     

Predicting satellite visibility

An Earth satellite can only be observed by optical methods when it is illuminated by sunlight and the observing station is in darkness, with the result that the satellite is in general only visible on two fairly small arcs of its orbit.

In this paper, a graphical method has been developed for predicting the latitudes from which a satellite in a circular orbit is visible, with the particular aim of discovering periods when a satellite may be observed in mid-latitudes in both the northern and southern hemispheres. For near-polar orbits the occurrence of such periods depends critically on the position of the ascending node of the orbit; but for lower inclinations, the periods of visibility become shorter and more frequent, and the orientation of the orbit is less significant.     

Post-Newtonian satellite orbits

The first post-Newtonian approximation of general relativity is used to account for the motion of solar system bodies and near-Earth objects which are slow moving and produce weak gravitational fields. The \(n\)-body relativistic equations of motion are given by the Einstein-Infeld-Hoffmann equations. For \(n=2\), we investigate the associated dynamics of two-body systems in the first post-Newtonian approximation. By direct integration of the associated planar equations of motion, we deduce a new expression that characterises the orbit of test particles in the first post-Newtonian regime generalising the well-known Binet equation for Newtonian mechanics. The expression so obtained does not appear to have been given in the literature and is consistent with classical orbiting theory in the Newtonian limit. Further, the accuracy of the post-Newtonian Binet equation is numerically verified by comparing secular variations of known expression with the full general relativistic orbit equation.     

Jovian satellite nomenclature

A brief review of the history of Jovian satellite nomenclature is given to indicate the background for the names proposed for the numbered satellites. The new names are consistent with established tradition and should cause minimal confusion with other named objects in the solar system.     

Inversions of satellite to satellite electron content: Simulation studies with NeUoG-plas

The signals of Global Navigation Satellites have found a large number of uses in atmospheric and ionospheric research. Reception of the signals from a satellite in a Low Earth Orbit (LEO) leads regularly to occultation of the signals by the surface of the Earth. Before an occultation the signals traverse the ionosphere with rays with decreasing height of their perigees. Satellite electron content observed prior to ‘setting’ occultations or after `rising' occultations can be used as input data for inversion. The inversion procedure gives horizontally averaged height profiles of electron density.Assessment studies are needed to find out under which conditions the profiles from inversions are representative for ‘true’ electron density profiles above the Earth occultation point.A great number of such studies have been carried out using the ionosphere/plasmasphere model NeUOG-plas for forward and backward modelling. Different transmitter-receiver scenarios have been investigated.We describe the assessment procedure and report on results showing the most interesting cases and statistics.     

Approximations of satellite stability

Modifications of a previous paper by one of the authors (V. S.) are presented and approximations to sharper stability conditions are given.     

Ringlet–satellite interactions

We study the interaction of a satellite and a nearby ringlet on eccentric and inclined orbits. Secular torques originate from mean motion resonances and the secular interaction potential which represents the m  = 1 global modes of the ring. The torques act on the relative eccentricity and inclination. The resonances damp the relative eccentricity. The inclination instability owing to the resonances is turned off by a finite differential eccentricity of the order of 0.27 for nearly coplanar systems. The secular potential torque damps the eccentricity and inclination and does not affect the relative semi-major axis; also, it suppresses the inclination instability that persists at small differential eccentricities. The damping of the relative eccentricity and inclination forces an initially circular and planar small mass ringlet to reach the eccentricity and inclination of the satellite. When the planet is oblate, the interaction of the satellite damps the proper precession of a small mass ringlet so that it precesses at the satellite's rate independently of their relative distance. The oblateness of the primary modifies the long-term eccentricity and inclination magnitudes and introduces a constant shift in the apsidal and nodal lines of the ringlet with respect to those of the satellite. These results are applied to Saturn's F-ring, which orbits between the moons Prometheus and Pandora.