Search Results (12)

The cislunar space navigation satellite system is essential infrastructure for lunar exploration in the next phase. It relies on high-precision orbit determination to provide the reference of time and space. This paper focuses on constructing a navigation constellation using special orbital locations such as Earth–Moon libration points and distant retrograde orbits (DRO), and it discusses the simplification of planetary perturbation models for their autonomous orbit determination on board. The gravitational perturbations exerted by major solar system bodies on spacecraft are first analyzed. The minimum perturbation required to maintain a precision of 10 m during a 30-day orbit extrapolation is calculated, followed by a simulation analysis. The results indicate that considering only gravitational perturbations from the Moon, Sun, Venus, Saturn, and Jupiter is sufficient to maintain orbital prediction accuracy within 10 m over 30 days. Based on these findings, a method for simplifying the ephemeris is proposed, which employs Hermite interpolation for the positions of the Sun and Moon at fixed time intervals, replacing the traditional Chebyshev polynomial fitting used in the JPL DE ephemeris. Several simplified schemes with varying time intervals and orders are designed. The simulation results of the inter-satellite links show that, with a 6-day orbit arc length, a 1-day lunar interpolation interval, and a 5-day solar interpolation interval, the accuracy loss for cislunar space navigation satellites remains within the meter level, while memory usage is reduced by approximately 60%. Full article

Since 1969, 55 years ago, Lunar Laser Ranging (LLR) has provided accurate and precise (down to ~1 cm RMS) measurements of the Moon’s orbit thanks to the Apollo and Lunokhod Cube Corner Retroreflector (CCR) Laser Retroreflector Arrays (LRAs) deployed on the Moon. Nowadays, the current level of precision of these measurements is largely limited by the lunar librations affecting the old generation of LRAs. To improve this situation, next-generation libration-free retroreflectors are necessary. To this end, the Satellite/lunar/GNSS laser ranging/altimetry and cube/microsat Characterization Facilities Laboratory (SCF_Lab) at the Istituto Nazionale di Fisica Nucleare—Laboratori Nazionali di Frascati (INFN-LNF), in collaboration with the University of Maryland (UMD) and supported by the Italian Space Agency (ASI), developed MoonLIGHT (Moon Laser Instrumentation for General relativity High-accuracy Tests), a single large CCR with a front face diameter of 100 mm, nominally unaffected by librations, and with optical performances comparable to the Apollo/Lunokhod LRAs of CCRs. Such a big CCR (hereafter, ML100) is mounted into a specifically devised, designed, and manufactured robotic actuator, funded by the European Space Agency (ESA), the so-called MoonLIGHT Pointing Actuator (MPAc), which, once its host craft has landed on the Moon, will finely align the front face of the ML100 towards the Earth. The (optical) performances of such a piece of hardware, MoonLIGHT+MPAc, were tested in/by the SCF_Lab in order to ensure that it was space flight ready before its integration onto the deck of the host craft. After its successful deployment on the Moon, additional and better-quality LLR data (down to ~ 1 mm RMS or better for the contribution of the laser retroreflector instrument, MoonLIGHT, to the total LLR error budget) will be available to the community for future and enhanced tests of gravitational theories. Full article

To observe lower-frequency gravitational waves (GWs), it is effective to utilize a large spacecraft formation baseline, spanning hundreds of thousands to millions of kilometers. To overcome the limitations of a gravitational-wave observatory (GWO) on specific orbits, a scientific observation mode and a non-scientific observation mode for GWOs are proposed. For the non-scientific observation mode, this paper designs equilateral triangle and equilateral tetrahedral array formations for a space-based GWO near a collinear libration point. A stable configuration is the prerequisite for a GWO; however, the motion near the collinear libration points is highly unstable. Therefore, the output regulation theory is applied. By leveraging the tracking aspect of the theory, the equilateral triangle and equilateral tetrahedral array formations are achieved. For an equilateral triangle array formation, two geometric configuration design methods are proposed, addressing the fuel consumption required for initialization and maintenance. To observe GWs in different directions and avoid configuration/reconfiguration, the multi-layer equilateral tetrahedral array formation is given. Additionally, the control errors are calculated. Finally, the effectiveness of the control method is demonstrated using the Sun–Earth circular-restricted three-body problem (CRTBP) and the ephemeris model located at Lagrange point $L_1$. Full article

In the realm of precision space applications, improving the accuracy of orbit determination (OD) is a crucial and demanding task, primarily because of the presence of measurement noise. To address this issue, a novel machine learning method based on bidirectional long short-term memory (BiLSTM) is proposed in this research. In particular, the proposed method aims to improve the OD accuracy of Earth–Moon Libration orbits with angle-only measurements. The proposed BiLSTM network is designed to detect inaccurate measurements during an OD process, which is achieved by incorporating the least square method (LSM) as a basic estimation approach. The structure, inputs, and outputs of the modified BiLSTM network are meticulously crafted for the detection of inaccurate measurements. Following the detection of inaccurate measurements, a compensating strategy is devised to modify these detection results and thereby reduce their negative impact on OD accuracy. The modified measurements are then used to obtain a more accurate OD solution. The proposed method is applied to solve the OD problem of a 4:1 synodic resonant near-rectilinear halo orbit around the Earth–Moon L2 point. The training results reveal that the bidirectional network structure outperforms the regular unidirectional structures in terms of detection accuracy. Numerical simulations show that the proposed method can reduce the estimated error by approximately 10%. The proposed method holds significant potential for future missions in cislunar space. Full article

The NASA’s Artemis project intends to bring humans back to the Moon in the next decade. A key element of the project will be the Lunar Gateway, a space station placed in a peculiar, near rectilinear Halo orbit in the vicinity of a collinear libration point in the Earth–Moon system. This study focuses on the high-fidelity description of the relative orbit dynamics of a chaser spacecraft with respect to the Gateway, as well as on the design of a proper orbit control strategy for rendezvous maneuvers. A novel formulation of the Battin–Giorgi approach is introduced, in which the reference orbit is that traveled by the Gateway, i.e., it is a highly non-Keplerian, perturbed orbit. The modified Battin–Giorgi approach allows for the description of a relative orbit motion with no restrictive assumption, while including all the relevant orbit perturbations on both the chaser and the Gateway. Moreover, nonlinear hybrid predictive control is introduced as a feedback guidance strategy. This new technique is shown to outperform the classical, well-established feedback linearization in terms of success rate and accuracy on the final conditions. Moreover, a Monte Carlo analysis confirms that hybrid predictive control is also effective in the presence of the temporary unavailability of propulsion or thrust misalignment. Full article

Exploration of Venus is recently driven by the interest of the scientific community in understanding the evolution of Earth-size planets, and is leading the implementation of missions that can benefit from new design techniques and technology. In this work, we investigate the possibility to implement a microsatellite exploration mission to Venus, taking advantage of (i) weak capture, and (ii) nonlinear orbit control. This research considers the case of a microsatellite, equipped with a high-thrust and a low-thrust propulsion system, and placed in a highly elliptical Earth orbit, not specifically designed for the Earth-Venus mission of interest. In particular, to minimize the propellant mass, phase (i) of the mission was designed to inject the microsatellite into a low-energy capture around Venus, at the end of the interplanetary arc. The low-energy capture is designed in the dynamical framework of the circular restricted 3-body problem associated with the Sun-Venus system. Modeling the problem with the use of the Hamiltonian formalism, capture trajectories can be characterized based on their state while transiting in the equilibrium region about the collinear libration point L1. Low-energy capture orbits are identified that require the minimum velocity change to be established. These results are obtained using the General Mission Analysis Tool, which implements planetary ephemeris. After completing the ballistic capture, phase (ii) of the mission starts, and it is aimed at driving the microsatellite toward the operational orbit about Venus. The transfer maneuver is based on the use of low-thrust propulsion and nonlinear orbit control. Convergence toward the desired operational orbit is investigated and is proven analytically using the Lyapunov stability theory, in conjunction with the LaSalle invariance principle, under certain conditions related to the orbit perturbing accelerations and the low-thrust magnitude. The numerical results prove that the mission profile at hand, combining low-energy capture and low-thrust nonlinear orbit control, represents a viable and effective strategy for microsatellite missions to Venus. Full article

This paper is dedicated to identifying stable equilibrium positions of the tether systems attached to the L₁ or L₂ libration points of the Mars–Phobos system. The orbiting spacecraft deploying the tether is at the L₁ or L₂ libration point and is held at one of these unstable points by the low thrust of its engines. In this paper, the analysis is performed assuming that the tether length is constant. The equation of motion for the system in the polar reference frame is obtained. The stable equilibrium positions are found and the dependence of the tether angular oscillation period on the tether length is determined. An analytical solution in the vicinity of the stable equilibrium positions for small angles of deflection of the tether from the local vertical is obtained in Jacobi elliptic functions. The comparison of the numerical and analytical solutions for small angles of deflection is performed. The results show that the dependencies of the oscillation period on the length of the tether are fundamentally different for L₁ and L₂ points. Analytical expressions for the tether tension are derived, and the influence of system parameters on this force is investigated for static and dynamic cases. Full article

Satellite constellations can provide communication and navigation services to support future lunar missions, and are attracting growing interest from both the scientific community and industry. The deployment of satellites in orbital planes that can have significantly different inclinations and right ascension of the ascending node requires dedicated launches and represents a non-trivial issue for lunar constellations, due to the complexity and low accessibility of launches to the Moon. In this work, a strategy to deploy multiple satellites in different orbital planes around the Moon in a single launch is examined. The launch vehicle moves along a conventional lunar escape trajectory, with parameters selected to take advantage of gravity-braking upon encountering the Moon. A maneuver at the periselenium allows the transfer of the spacecraft along a trajectory converging to the equilibrium region about the Earth–Moon libration point $L_1$, where the satellites are deployed. Providing a small $\Delta V$, each satellite is transferred into a low-energy trajectory with the desired inclination, right ascension of the ascending node, and periselenium radius. A final maneuver, if required, allows the adjustment of the semimajor axis and the eccentricity. The method is verified using numerical integration using high-fidelity orbit propagators. The results indicate that the deployment could be accomplished within one sidereal month with a modest $\Delta V$ budget. Full article

The aim of this study is to analyze lunar trajectories with the optimal junction point of geocentric and selenocentric segments. The major motivation of this research is to answer two questions: (1) how much of the junction of the trajectory segments at the libration point between the Earth and the Moon is non-optimal? and (2) how much can the trajectory be improved by optimizing the junction point of the two segments? The formulation of the end-to-end optimization problem of power-limited trajectories to the Moon and a description of the method of its solution are given. The proposed method is based on the application of the maximum principle and continuation method. Canonical transformation is used to transform the costate variables between geocentric and selenocentric coordinate systems. For the initial guess, a collinear libration point between the Earth and the Moon is used as a junction point, and the transformation to the optimal junction of these segments is carried out using the continuation method. The developed approach does not require any user-supplied initial guesses. It provides the computation of the optimal transfer duration for trajectories with a given angular distance and facilitates the incorporation of the perturbing accelerations in the mathematical model. Numerical examples of low-thrust trajectories from an elliptical Earth orbit to a circular lunar orbit considering a four-body ephemeris model are given, and a comparison is made between the trajectories with an optimal junction point and the trajectories with a junction of geocentric and selenocentric segments at the libration point. Full article

Deep space missions are recently gaining increasing interest from space agencies and industry, their maximum exponent being the establishment of a permanent station in cis-lunar orbit within this decade. To that end, autonomous rendezvous and docking in multi-body dynamical environments have been defined as crucial technologies to expand and maintain human space activities beyond near Earth orbit. Based on analytical and numerical formulations of the relative dynamics in the Circular Restricted Three Body Problem (CR3BP), a family of optimal, linear and nonlinear, continuous and impulsive, guidance and control techniques are developed for the design of end-to-end rendezvous trajectories between co-orbiting spacecraft in this multi-body dynamical environment. To this end, several modern control techniques are effectively designed and adapted to this problem, with particular emphasis on the design of low cost rendezvous manoeuvres. Finally, the designed hybrid rendezvous strategies, combining both discrete and continuous control techniques, are effectively tested and validated under several start-to-end deep space testbench mission scenarios, where their performance is compared and quantitatively assessed with a set of performance indices. Full article

In this work, we investigate the behavior of low-energy trajectories in the dynamical framework of the spatial elliptic restricted 4-body problem, developed using the Hamiltonian formalism. Introducing canonical transformations, the Hamiltonian function in the neighborhood of the collinear libration point $L_1$ (or $L_2$), can be expressed as a sum of three second order local integrals of motion, which provide a compact topological description of low-energy transits, captures and quasiperiodic libration point orbits, plus higher order terms that represent perturbations. The problem of small denominators is then applied to the order three of the transformed Hamiltonian function, to identify the effects of orbital resonance of the primaries onto quasiperiodic orbits. Stationary solutions for these resonant terms are determined, corresponding to quasiperiodic orbits existing in the presence of orbital resonance. The proposed model is applied to the Jupiter-Europa-Io system, determining quasiperiodic orbits in the surrounding of Jupiter-Europa $L_1$ considering the 2:1 orbital resonance between Europa and Io. Full article

The nonlinear orbital dynamics of a class of the perturbed restricted three-body problem is studied. The two primaries considered here refer to the binary system HD 191408. The third particle moves under the gravity of the binary system, whose triaxial rate and radiation factor are also considered. Based on the dynamic governing equation of the third particle in the binary HD 191408 system, the motion state manifold is given. By plotting bifurcation diagrams of the system, the effects of various perturbation factors on the dynamic behavior of the third particle are discussed in detail. In addition, the relationship between the geometric configuration and the Jacobian constant is discussed by analyzing the zero-velocity surface and zero-velocity curve of the system. Then, using the Poincaré–Lindsted method and numerical simulation, the second- and third-order periodic orbits of the third particle around the collinear libration point in two- and three-dimensional spaces are analytically and numerically presented. This paper complements the results by Singh et al. [Singh et al., AMC, 2018]. It contains not only higher-order analytical periodic solutions in the vicinity of the collinear equilibrium points but also conducts extensive numerical research on the bifurcation of the binary system. Full article