Exploiting Earth horseshoe orbits for space missions

We discuss the usefulness of unstable Earth horseshoe orbits to access interplanetary space, and in particular when low-velocity escape from Earth is involved. The application to a solar stereoscopic mission is described.     

Earth albedo and the orbit of Lageos

The long-period perturbations in the orbit of Lageos satellite due to the earth's albedo have been found using a new analytical formalism. The earth is assumed to be a sphere whose surface diffusely reflects sunlight according to Lambert's law. Specular reflection is not considered. The formalism is based on spherical harmonics; it produces equations which hold regardless of whether the terminator is seen by the satellite or not. Specializing in the case of a realistic zonal albedo shows that Lageos' orbital semimajor axis changes periodically by only about a centimeter and the eccentricity by two parts in 10⁵. The longitude of the node increases secularly by about 6×10^–4 arc sec yr^–1. The effect considered here can explain neither the secular decay of 1.1 mm day^–1 in the semimajor axis nor the observed along-track variations in acceleration of order 2×10^–12 ms^–2.     

The optimization of satellite orbit for Space-VLBI observation

By sending one or more telescopes into space,Space-VLBI(SVLBI)is able to achieve even higher angular resolution and is therefore the trend of the VLBI technique.For the SVLBI program,the design of satellite orbits plays an important role for the success of planned observation.In this paper,we present our orbit optimization scheme,so as to facilitate the design of satellite orbits for SVLBI observation.To achieve that,we characterize the uv coverage with a measure index and minimize it by finding out the corresponding orbit configuration.In this way,the design of satellite orbit is converted to an optimization problem.We can prove that,with an appropriate global minimization method,the best orbit configuration can be found within the reasonable time.Besides that,we demonstrate that this scheme can be used for the scheduling of SVLBI observations.     

Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.     

HIDDRA: a highly independent data distribution and retrieval architecture for space observation missions

Institutions such as NASA, ESA or JAXA find solutions to distribute data from their missions to the scientific community, and their long term archives. This is a complex problem, as it includes a vast amount of data, several geographically distributed archives, heterogeneous architectures with heterogeneous networks, and users spread around the world. We propose a novel architecture that solves this problem aiming to fulfill the requirements of the final user. Our architecture is a modular system that provides a highly efficient parallel multiprotocol download engine, using a publisher/subscriber policy which helps the final user to obtain data of interest transparently. We have evaluated a first prototype, in collaboration with the ESAC centre in Villafranca del Castillo (Spain) that shows a high scalability and performance, opening a wide spectrum of opportunities.     

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.     

Sequential filter design for precision orbit determination and physical constant refinement

Earth-based spacecraft tracking data have historically been processed with classical least squares filtering techniques both for navigation purposes and for physical constant determination. The small, stochastic non-gravitational forces acting on the spacecraft are described to motivate the use of sequential estimation as an alternative to the least squares fitting procedures. The stochastic forces are investigated both in terms of their effect on the tracking data and their influence on estimation accuracy. A flexiible sequential filter design which leaves the existing trajectory, variational equations, data observable and partial computations undisturbed is described. A detailed filter design is presented that meets the precision demands and flexibility requirements of deep space navigation and scientific problems, one which provides a high degree of numerical integrity and numerical analysis capability, facilitates the efficient computation of multiple solutions, and makes few demands on the supporting computational structure.This paper presents the results of one phase of research carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by NASA.     

Parallel initial orbit determination using angles-only observation pairs

We propose a type of admissible-region analysis for track initiation in multi-satellite problems when angles are the primary observable. Pairs of optical observations are used to calculate candidate orbits via a Lambert solver by hypothesizing range values. The method is attractive because it allows multiple levels of parallelization of the track-initiation process. Orbital element partitions are introduced to divide the admissible region into smaller search spaces to be processed on individual computer nodes. For a specified rectangular partition in the space of orbital elements, constraints are developed to bound the values of range that will lead to initial orbit hypotheses (data association hypotheses) associated with that partition. These bounds allow us to parallelize the generation of candidate orbits, because each element-space partition can be handled independently of the others. Several constraints are developed and shown to limit the range pair hypotheses effectively to the constrained admissible region based on the orbital element partitions. Examples are provided to highlight the topology of the proposed constraints.     

Radiation environment detected by a proportional counter in Earth orbit

We present the measured cosmic ray- and electron-induced background detected by a proportional counter in Earth orbit. The data were obtained by the Hard X-ray Experiment on board the Astronomical Netherlands Satellite. The data are presented as a function of satellite position above the Earth, i.e. geographical longitude and latitude, with the altitude varying between 200 and 1100 km.     

Placing Venus in an orbit similar to that of the Earth

Motivated by the recent proposals of A. Abian, we introduce the physical and dynamical considerations for producing a second Earth-like planet on which life sustaining conditions may exist, and hence we acquire multiplication of the cosmic resources of the human race. We investigate the perturbations in our solar system after alteration, through a third order Hamiltonian planetary theory for the eight principal planets. The Hori-Lie theorem, the Jacobi-Radau coordinates, and the canonical variables of H. Poincaré are adopted.     

Simulations of ultra-long wavelength interferometers in Earth orbit and on the lunar surface

We present simulations of interferometers in Earth orbit and on the lunar surface to guide the design and optimization of space-based ultra-long wavelength missions, such as those pioneered by China’s Chang’e Program. We choose parameters and present simulations using simulated data to identify inter-dependencies and constraints on science and engineering parameters. A regolith model is created for the lunar surface array simulation, and the results show that the lunar regolith will have an undesirable effect on the observations. We estimate data transmission requirements,calculate sensitivities for both cases, and discuss the trade-off between brightness temperature sensitivity and angular resolution for the Earth orbit array case.     

Reducing inter-satellite drift of low Earth orbit constellations using short-periodic corrections

Celestial Mechanics and Dynamical Astronomy - Quasi-satellite orbits (QSOs) are considered by JAXA’s MMX mission, in which CNES is involved, for the scientific observation of the Martian moon...     

The relativistic equations of motion for a satellite in orbit about a finite-size,rotating Earth

The relativistic equations of motion are derived for N self-gravitating, rotating finite bodies. These equations are then applied to the near-Earth satellite orbit determination problem. The apparent change of the shape of the Earth from the Earth centered frame to the Solar System barycentric frame changes the value of the Newtonian potential term in the metric. This in turn leads to a simplification of the equations of motion in the barycentric frame.     

Millimeter-wave experiments for cometary space missions

Predicted brightness temperatures for a variety of cometary nucleus models, consisting of homogeneous layers comprised of mixtures of water ice and refractory grains, are presented as functions of wavelength. These illustrative spectra are computed using simple radiative transfer techniques adapted from modeling of terrestrial ice and snow fields. The computed millimeter-wave spectra are sensitive to the values of physically significant nucleus parameters such as crust thickness, the subsurface temperature gradient, and the boundary temperature of the sublimating surface. It appears that millimeter-wave sensing from an interplanetary spacecraft is an effective means for distinguishing between alternate models of the nucleus and for inferring the rough physical state of substrata; modern theories on the nature of the nucleus indicate that sublimation from the substrata provides the gas phase cometary volatiles that are actually observed from ground-based and Earth-orbiting instruments. Antenna beam dilution is a major obstacle for ground-based molecular spectral line radio observations (e.g., water and ammonia) of comets but a modest millimeter-wave radiometer system in the near vicinity of the comet would not be subject to this problem. Such a system can make definitivebservations of several candidate parent molecules in the gas phase and should contribute to the understanding of the physics of the inner coma.     

Evidence-based robust design of deflection actions for near Earth objects

This paper presents a novel approach to the robust design of deflection actions for near Earth objects (NEO). In particular, the case of deflection by means of solar-pumped laser ablation is studied here in detail. The basic idea behind laser ablation is that of inducing a sublimation of the NEO surface, which produces a low thrust thereby slowly deviating the asteroid from its initial Earth threatening trajectory. This work investigates the integrated design of the space-based laser system and the deflection action generated by laser ablation under uncertainty. The integrated design is formulated as a multi-objective optimisation problem in which the deviation is maximised and the total system mass is minimised. Both the model for the estimation of the thrust produced by surface laser ablation and the spacecraft system model are assumed to be affected by epistemic uncertainties (partial or complete lack of knowledge). Evidence Theory is used to quantify these uncertainties and introduce them in the optimisation process. The propagation of the trajectory of the NEO under the laser-ablation action is performed with a novel approach based on an approximated analytical solution of Gauss’ variational equations. An example of design of the deflection of asteroid Apophis with a swarm of spacecraft is presented.     

Doubly averaged effect of the Moon and Sun on a high altitude Earth satellite orbit

Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI _ab, whereI _b=180°–I _a andI _a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature a semi-major axis - A _lk coefficient defined in Equation (11) - B _lk coefficient defined in Equation (24) - C _km coefficient defined in Equation (25) - D, E, F coefficients in Equations (38), (39) - e eccentricity - H _k expression defined in Equation (34) - expression defined in Equation (35) - I inclination of satellite orbit on lunar (or solar) ring plane - J ₂ coefficient of second harmonic of Earth's gravitational potential (1082.637×10^–6 R _E ² ) - K _k, L_k, M_k expressions in Section 4 - expressions in Section 4 - p=a(1–e ²) semi-latus rectum - P _l Legendre polynomial of degreel - q argument of Legendre polynomial - radial distance of satellite - R _E Earth equatorial radius (6378.16 km) - R, S, W perturbing accelerations in the radial, tangential and orbit normal directions - syn synchronous orbit radius (42 164.2 km=6.6107R _E) - t time - T satellite orbital period - T orbital period of perturbing body (Moon) - T _e period of long periodic oscillations ine for |I|<I _a - T _s synodic period - U gravitational potential of lunar (or solar) ring - x, y, z Cartesian coordinates of a satellite with (x, y) being the ring plane - coefficient defined in Equation (20) - average change in orbital element over one orbit (=a, e, I, , ) - ₁,₂₃ unit vectors in thex, y, z coordinate directions - _r , _s , _w unit vectors in the radial, tangential and orbit normal directions - =+ angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite - angle around the ring - gravitational constant times mass of Earth (3.986 013×10⁵ km s^–2) - gravitational constant times mass of Moon (or Sun) - _m gravitational constant times mass of Moon (/81.301) - _s gravitational constant time mass of Sun (332 946 ) - ratio of the circumference of a circle to its diameter - radius of lunar (or solar) ring - _m radius of lunar ring (60.2665R _E) - _s radius of solar ring (23455R _E) - true anomaly - argument of perigee - ₀ initial value of - _i critical value of in quadranti(i=1, 2, 3, 4) - longitude of ascending node on ring plane This work was sponsored by the Department of the Air Force.     

Long-term capture orbits for low-energy space missions

This research aims at ascertaining the existence and characteristics of natural long-term capture orbits around a celestial body of potential interest. The problem is investigated in the dynamical framework of the three-dimensional circular restricted three-body problem. Previous numerical work on two-dimensional trajectories provided numerical evidence of Conley’s theorem, proving that long-term capture orbits are topologically located near trajectories asymptotic to periodic libration point orbits. This work intends to extend the previous investigations to three-dimensional paths. In this dynamical context, several special trajectories exist, such as quasiperiodic orbits. These can be found as special solutions to the linear expansion of the dynamics equations and have already been proven to exist even using the nonlinear equations of motion. The nature of long-term capture orbits is thus investigated in relation to the dynamical conditions that correspond to asymptotic trajectories converging into quasiperiodic orbits. The analysis results in the definition of two parameters characterizing capture condition and the design of a capture strategy, guiding a spacecraft into long-term capture orbits around one of the primaries. Both the results are validated through numerical simulations of the three-dimensional nonlinear dynamics, including fourth-body perturbation, with special focus on the Jupiter–Ganymede system and the Earth–Moon system.