Search Results (37)

Moons tidally interact with their host planets and stars. A close moon is quickly synchronised by the planet or becomes captured in a higher spin–orbit resonance. However, the planet requires much more time to significantly alter its rotation rate under the influence of moon-generated tides. The situation becomes more complex for close-in planets, as star-generated tides come into play and compete with moon-generated tides. The synchronisation of the planet by its moon changes the tidal dynamics of the entire star–planet–moon system and can lead to long-term stable configurations. In this paper, we demonstrate that a certain initial condition must be met for this to occur. Based on the angular momentum conservation, the derived condition is universal and bears no dependence upon the planet’s internal structure or tidal dissipation model. It is applicable to dwindling systems as well as to tidally expanding orbits and cases of initially retrograde motion. We present calculations for specific planet–moon systems (Earth and the Moon; Neptune and Triton; Venus and its hypothetical presently extinct moon Neith; Mars, Phobos, and Deimos; and Pluto and Charon) to constrain dynamically plausible formation and evolution scenarios. Among other things, our analysis prompts the question of whether Pluto and Charon evolved into their current state from an initially more compact configuration (as is commonly assumed) or from a wider orbit—a topic that will be discussed at length elsewhere. Our results are equally applicable to exoplanets. For example, if asynchronous close-in exoplanets are detected, the possibility of tidal synchronisation by an exomoon should be considered. Full article

This study presents a novel conceptual model to explain the differential rotation within Earth’s layers, a phenomenon observed through seismic wave studies but not fully understood. While geodynamo theory and electromagnetic coupling models have been proposed to explain this phenomenon, our model offers an alternative perspective focusing on the Moon’s tidal forces. Our model proposes that the Moon’s tidal forces play a crucial role in this process, acting as a braking mechanism on Earth’s rotation. We hypothesize that these tidal forces initially decelerate the Earth’s crust and mantle, with this effect sequentially transmitted to deeper layers. A key aspect of our model is the role of the liquid outer core in mediating this process. We suggest that the liquid state of the outer core delays the transmission of tidal friction, resulting in differential rotation between layers in contact with it. This delay mechanism provides a potential explanation for the observed rotational differences between the mantle and core. Our model demonstrates that about 66,000 years after the Moon’s formation, the tidal force slowed the crust–mantle rotation by approximately 5.5 degrees per year more than the core. Furthermore, we estimate that the frictional heat generated at the boundaries of differential rotation is about 0.3478 TW. At this rate, the outer core temperature would increase by approximately 13.4 K per billion years. This thermal effect may have significant implications for the long-term evolution of Earth’s core, potentially slowing its cooling rate and maintaining its liquid state. Our model thus provides a new perspective on the interplay between lunar tidal forces, Earth’s internal structure, and its thermal evolution, offering insights into the complex dynamics of our planet’s interior. Full article

This paper investigates the design of optimal low-thrust transfers between relative planar and spatial quasi-satellite orbits (QSOs) in the Earth–Moon system under the Circular Restricted Three-Body Problem (CR3BP). A key contribution is the adaptation of a trajectory optimization framework, previously applied to halo orbit transfers, to accommodate the unique challenges of QSO families, especially the transition between planar and spatial configurations. The method employs a refined beam search strategy to construct diverse initial guess chains, which are then optimized via a successive convexification algorithm tailored for the spatial dynamics of QSOs. Additionally, a linear–quadratic regulator (LQR)-based control scheme is implemented to ensure long-term station-keeping of the final 3D-QSO. Simulation results demonstrate the feasibility of connecting planar and spatial QSOs with minimum-fuel trajectories while maintaining bounded terminal deviations, offering new tools for future Earth–Moon logistics and navigation infrastructure. Key findings include the successful design of low-thrust transfer trajectories between planar QSOs and 1:5 3D-QSOs, with a minimum total $\mathsf{\Delta }V$ of 195.576 m/s over a time of flight (ToF) of 261 days, and a minimum ToF of 41 days with a total $\mathsf{\Delta }V$ of 270.507 m/s. Additionally, the application of LQR control demonstrated the ability to maintain 1:5 3D-QSO families around the Moon with less than 12 mm/s $\mathsf{\Delta }V$ over two months. This research provides valuable insights into the optimization of low-thrust transfer trajectories and the application of advanced control techniques for space missions, particularly those targeting lunar and planetary satellite exploration. Full article

In the Moon–Earth elliptic restricted three-body problem, near-polar and near-circular lunar-type periodic orbits are numerically continued from Keplerian circular orbits using Broyden’s method with line search. The Hamiltonian system, expressed in Cartesian coordinates, is treated via the symplectic scaling method. The radii of the initial Keplerian circular orbits are then scaled and normalized. For cases in which the integer ratios $\{j/k\}$ of the mean motions between the inner and outer orbits are within the range $[9,150]$, some periodic orbits of the elliptic restricted three-body problem are investigated. For the middle-altitude cases with $j/k\in [38,70]$, the perturbations due to $J_2$ and $C_{22}$ are incorporated, and some new near-polar periodic orbits are computed. The orbital dynamics of these near-polar, near-circular periodic orbits are well characterized by the first-order double-averaged system in the Poincaré–Delaunay elements. Linear stability is assessed through characteristic multipliers derived from the fundamental solution matrix of the linear varational system. Stability indices are computed for both the near-polar and planar near-circular periodic orbits across the range $j/k\in [9,50]$. Full article

Accurate orbit determination (OD) for spacecraft with impulsive maneuvers in a multi-body system is a challenging task, because the unknown magnitudes and epochs of the maneuvers make dynamic modeling difficult, disrupting the symmetry of state deviations before and after the maneuvers. This paper proposes an Adaptive State Noise Compensation (ASNC) algorithm for the OD of spacecraft with impulsive maneuvering in a three-body dynamics frame, which does not rely on maneuver parameters and can adaptively estimate state noise. Firstly, a decoupled matching factor is developed, which can be used to identify the maneuvering and non-maneuvering epochs of the target spacecraft. Next, based on the matching factor, a position state noise estimation method is presented. Moreover, a method for estimating velocity state noise through inverse mapping of the state transition matrix is formulated, and the compensated state noise is incorporated into the Kalman framework to achieve precise OD of maneuvering spacecraft. Finally, the proposed method is applied to solve the OD problem of a Near Rectilinear Halo Orbit (NRHO) near the Earth–Moon L2 point. Simulation results demonstrated that the proposed method improved accuracy by at least an order of magnitude compared to competitive methods, while effectively restoring the symmetry of the OD system. Full article

Physical properties of the Sun (orientation of rotation axis, oblateness coefficient $J_{2\odot }$, and change rate of the gravitational parameter ${\dot{\mu }}_{\odot }$) are determined using a dynamical model describing the motion of the Sun, planets, the Moon, asteroids, and Trans-Neptunian objects (TNOs). Among the many kinds of observations used to determine the orbits and physical properties of the bodies, the most important for our study are precise interplanetary ranging data: Earth–Mercury ranges from MESSENGER spacecraft and Earth–Mars ranges from Odyssey and MRO. The findings allow us to improve the model of the Sun in modern planetary ephemerides. First, the dynamically determined direction of the Sun’s pole is ≈2° off the visible axis of rotation of the Sun’s surface, which is corroborated by present knowledge of the Sun’s interior. Second, the change rate of the Sun’s gravitational parameter is found to be smaller (in absolute value) than the nominal value derived from the estimate of mass loss through radiation and solar wind. Possible interpretations are discussed. 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

In the near future, international space agencies have planned to achieve significant milestones in investigating the utilization of Global Navigation Satellite Systems (GNSS) within and beyond the current space service volume up to their application to lunar missions. These initiatives aim to demonstrate the feasibility of GNSS navigation at lunar altitudes. Based on the outcomes of such demonstrations, dozens of lunar missions will likely be equipped with a GNSS receiver to support autonomous navigation in the lunar proximity. Relying on non-invasive, consolidated differential techniques, GNSS will enable baseline estimation, thus supporting a number of potential applications to lunar orbiters such as collaborative navigation, formation flight, orbital manoeuvers, remote sensing, augmentation systems and beyond. Unfortunately, the large dynamics and the geometry of such differential GNSS scenarios set them apart from current terrestrial and low-earth orbit use cases. These characteristics result in an increased sensitivity to measurements time misalignment among orbiters. Hence, this paper offers a review of baseline estimation methods and characterizes the divergences and limitations w.r.t. to terrestrial applications. The study showcases the estimation of the baseline length between a lunar CubeSat mission, VMMO, and the communication relay Lunar Pathfinder mission. Notably, real GNSS measurements generated by an Engineering Model of the NaviMoon receiver in the European Space Agency (ESA/ESTEC) Radio Navigation Laboratory are utilized. A radio-frequency constellation simulator is used to generate the GNSS signals in these hardware-in-the-loop tests. The performed analyses showed the invalidity of common terrestrial differential GNSS ranging techniques for space scenarios due to the introduction of significant biases. Improved ranging algorithms were proposed and their potential to cancel ranging errors common to both receivers involved was confirmed. Full article

Lunar DRO pinpoint return is the final stage of manned deep space exploration via a lunar DRO station. A re-entry capsule suffers from complicated dynamic and thermal effects during an entire flight. The optimization of the lunar DRO return trajectory exhibits strong non-linearity. To obtain a global optimal return trajectory, an entire-flight lunar DRO pinpoint return model including a Moon–Earth transfer stage and an Earth atmosphere re-entry stage is constructed. A re-entry point on the atmosphere boundary is introduced to connect these two stages. Then, an entire-flight global optimization framework for lunar DRO pinpoint return is developed. The design of the entire-flight return trajectory is simplified as the optimization of the re-entry point. Moreover, to further improve the design efficiency, a rapid landing point prediction method for the Earth re-entry is developed based on a deep neural network. This predicting network maps the re-entry point in the atmosphere and the landing point on Earth with respect to optimal control re-entry trajectories. Numerical simulations validate the optimization accuracy and efficiency of the proposed methods. The entire-flight return trajectory achieves a high accuracy of the landing point and low fuel consumption. Full article

To address the challenge of achieving both temporal consistency and spatial continuity in Earth observation data of polar regions, this paper proposes an innovative concept of Moon-based/Highly Elliptical Orbit (HEO) Spaceborne Bistatic Synthetic Aperture Radar (MH-BiSAR), with transmitters on the Moon and receivers on HEO satellites. By utilizing ephemeris data and an orbit propagator, this study explores MH-BiSAR’s geometric coverage capabilities in polar regions and conducts a preliminary analysis of its characteristics. The findings reveal that MH-BiSAR could provide continuous multi-day revisit observations of polar regions within each sidereal month, presenting a significant advantage for monitoring high-dynamic and large-scale scientific phenomena, such as polar sea ice observations. This innovative observational method offers a new perspective for polar monitoring and is expected to deepen our understanding of polar phenomena. Full article

This is a summary of the main results within the Scale-Invariant Vacuum (SIV) paradigm based on Weyl integrable geometry. We also review the mathematical framework and utilize alternative derivations of the key equations based on the reparametrization invariance as well. The main results discussed are related to the early universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. Some of the key SIV results for the early universe are a natural exit from inflation within the SIV in a later time $t_{\mathrm{exit}}$ with value related to the parameters of the inflationary potential along with the possibility for the density fluctuations to grow sufficiently fast within the SIV without the need for dark matter to seed the growth of structure in the universe. In the late-time universe, the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and dwarf spheroidals, where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth–Moon system. Full article

The launch azimuth of the Naro Space Center is limited toward the south of the Korean peninsula, at 170 ± 10 degrees, suitable for the polar orbit, sun-synchronous orbit, and safety range issues. In this circumstance, one option to send a satellite into GEO is to perform a dog-leg maneuver during ascent, thus forming a medium-inclination orbit under such a restrictive condition. However, this option requires an immense amount of energy for the dog-leg maneuver, as well as a plane change maneuver. The only remaining option is to raise the apogee to the Moon, utilizing lunar gravity to lower the inclination to near zero and then returning to the vicinity of the Earth at an altitude of 35,786 km without maneuver. In order to design lunar-assisted GEO transfer, all feasible paths are defined, but questions remain about how seasonal variations affect all these potential paths. Therefore, this study aims to design and analyze all available trajectories for the year 2031 using a high-fidelity dynamic model, root-finding algorithm, and well-arranged initial conditions, focusing on the impact of seasonal trends. The simulation results indicate that cislunar free-return trajectories generally require less $\mathit{\Delta }V$ compared to circumlunar free-return trajectories, and circumlunar trajectories are minimally affected by lunisolar effects due to their relatively short return time of flight. Conversely, cislunar trajectories show seasonal variations, so spring and fall seasons require up to 20 m/s less $\mathit{\Delta }V$ than summer and winter seasons due to the relatively long time of return duration. Full article

Planetary radar observations have provided invaluable information on the solar system through both ground-based and space-based observations. In this overview article, we summarize how radar observations have contributed in planetary science, how the radar technology as a remote-sensing method for planetary exploration and the methods to interpret the radar data have advanced in the eight decades of increasing use, where the field stands in the early 2020s, and what are the future prospects of the ground-based facilities conducting planetary radar observations and the planned spacecraft missions equipped with radar instruments. The focus of the paper is on radar as a remote-sensing technique using radar instruments in spacecraft orbiting planetary objects and in Earth-based radio telescopes, whereas ground-penetrating radar systems on landers are mentioned only briefly. The key scientific developments are focused on the search for water ice in the subsurface of the Moon, which could be an invaluable in situ resource for crewed missions, dynamical and physical characterization of near-Earth asteroids, which is also crucial for effective planetary defense, and a better understanding of planetary geology. Full article

Recently, a significant interest in space exploration has emerged, driven by the lack of resources and the quest for answers to issues like climate change. New technologies give us the possibility of exploring our solar system and its surroundings in greater detail. But current space communications operate with a lack of efficiency due to the vast distances between celestial bodies within our solar system. Also, factors such as bandwidth asymmetry contribute to disruptions in the satellite communication network. This paper proposes the definition of the infrastructure of an interplanetary communication network, built upon a communications protocol featuring dynamic routing. This infrastructure aims to optimize information transmission by adapting communications to surrounding conditions. The envisioned infrastructure involves strategically placing network nodes at key Lagrange points around each planet within the asteroid belt. The nodes will be aware of their position, integrating sensing capabilities and intelligent algorithms. Next to each planet, a node with more capabilities will collect information from nanosatellites orbiting a planet and relay the information back to Earth. This structure will allow decision-making processes based on exploration data of the most significant celestial bodies within the asteroid belt, providing valuable insights such as constant monitoring of the dark side of the moon and difficult-to-reach zones in the solar system. Full article

The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two possible configurations: A single planet orbiting the host star, and a two-planet system including the proposed inner planet close to the 4:1 mean motion rationalization. The emphasis is made on the secular changes of eccentricity and orbital inclination, which are important for the climate stability of the planet. It is demonstrated that the secular orbital dynamics of planet K2-18 b with an internal companion are accurately represented by the periodic eccentricity and inclination exchange on the time scales of a few Kyr. A single planet is not expected to experience fast orbital changes, with the much weaker tidal and rotation-driven perturbations mostly reflecting in a slow periastron and nodal precession. The tidal decay of the orbit is too insignificant on the time scale of the stellar age. However, the conditions for the habitability of a single K2-18 b planet are much improved if, like the Earth, it rotates faster than the mean motion and its rotation angle is tilted by a hypothetical moon. Milanković’s cycles of the habitable planet’s climate are discussed for both configurations. Full article