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Tidal dissipation serves as the primary factor influencing the natural satellites’ orbital evolution and provides essential insights into planetary interior properties. The orbital evolution of the Neptune–Triton system due to tidal dissipation can be approximately determined from astrometrically observed positions of Triton over an extended period of time by using an accurate model of the orbital motion. The estimated accuracy of the Triton dynamical model we built and updated fit all the astrometric data. Based on the most complete weighting astrometric observations of Triton, a possible minimum value of the Neptunian tidal dissipation factor Q was estimated to be Q = (10.353 ± 2.517) × 103 for a conventional value k2 = 0.127 and a priori constraint of 10 × 103. When the a priori constraints have a smaller value, the Q-solution also has a smaller value but a weak fit to observations. Therefore, the Q estimated from the existing astrometric data is a plausible minimum value with the current accuracy of astronomical observations. Based on the plausible minimum value of Q and the Love number k2, it has been analyzed that Triton will reach Neptune’s Roche limit in approximately ~28 Gyr. This indicates a stable orbital evolution of Triton over a long period of time. [ABSTRACT FROM AUTHOR]

In the early stages of planetary system formation, young exoplanets gravitationally interact with their surrounding environments and leave observable signatures on protoplanetary disks. Among these structures, a pair of nearly symmetric spiral arms can be driven by a giant protoplanet. For the double-spiraled SAO 206462 protoplanetary disk, we obtained three epochs of observations spanning 7 yr using the Very Large Telescope's SPHERE instrument in near-infrared J-band polarized light. By jointly measuring the motion of the two spirals at three epochs, we obtained a rotation rate of − 0. ° 85 ± 0. ° 05 yr − 1 . This rate corresponds to a protoplanet at 66 ± 3 au on a circular orbit dynamically driving both spirals. The derived location agrees with the gap in ALMA dust-continuum observations, indicating that the spiral driver may also carve the observed gap. What is more, a dust filament at ∼63 au observed by ALMA coincides with the predicted orbit of the spiral-arm-driving protoplanet. This double-spiraled system is an ideal target for protoplanet imaging. [ABSTRACT FROM AUTHOR]

Subhalo dynamics in galaxy cluster host halos govern the observed distribution and properties of cluster member galaxies. We use the IllustrisTNG simulation to investigate the accretion and orbits of subhalos found in cluster-size halos. We find that the median change in the major axis direction of cluster-size host halos is approximately 80° between a ∼ 0.1 and the present day. We identify coherent regions in the angular distribution of subhalo accretion, and ∼68% of accreted subhalos enter their host halo through ∼38% of the surface area at the virial radius. The majority of galaxy clusters in the sample have ∼2 such coherent regions. We further measure angular orbits of subhalos with respect to the host major axis and use a clustering algorithm to identify distinct orbit modes with varying oscillation timescales. The orbit modes correlate with subhalo accretion conditions. Subhalos in orbit modes with shorter oscillations tend to have lower peak masses and accretion directions somewhat more aligned with the major axis. One orbit mode, exhibiting the least oscillatory behavior, largely consists of subhalos that accrete near the plane perpendicular to the host halo major axis. Our findings are consistent with expectations from inflow from major filament structures and internal dynamical friction: most subhalos accrete through coherent regions, and more massive subhalos experience fewer orbits after accretion. Our work offers a unique quantification of subhalo dynamics that can be connected to how the intracluster medium strips and quenches cluster galaxies. [ABSTRACT FROM AUTHOR]

A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation under Newtonian conditions and is a more accurate tool for astrodynamics than the traditional equation. Preliminary simulation results demonstrate the application potential of the modified vis-viva equation for more complex n-body systems. Spherical symmetry is assumed in this approach; however, this limitation could be removed in future research. This study is a pivotal step toward bridging classical and relativistic mechanics and thus makes an important contribution to the field of celestial dynamics. [ABSTRACT FROM AUTHOR]

In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained using the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion. [ABSTRACT FROM AUTHOR]

The regular quaternion equations of the orbital motion of a spacecraft (SC) proposed by us earlier in four-dimensional Kustaanheimo–Stiefel variables (KS variables) are considered. These equations use as a new independent variable a variable related to real time by a differential relation (Sundman time transformation) containing the distance to the center of gravity. Various new regular quaternion equations in these variables and equations in regular quaternion osculating elements (slowly changing variables) are also constructed, in which the half-generalized eccentric anomaly, widely used in celestial mechanics and space-flight mechanics, is used as a new independent variable. Keplerian energy and time are used as additional variables in these equations. These equations are used to construct quaternion equations and relations in variations of KS variables and their first derivatives and in variations of Keplerian energy and real time; the isochronous derivatives of the KS variables and of their first derivatives and the matrix of isochronous derivatives for the elliptical Keplerian motion of the spacecraft are found, which are necessary for solving the problems of predicting and correcting its orbital motion. The results of a comparative study of the accuracy of the numerical integration of the Newtonian equations of the spatial restricted three-body problem (the Earth, the Moon, and a spacecraft) in Cartesian coordinates and the regular quaternion equations of this problem in KS variables are presented, which show that the accuracy of the numerical integration of regular quaternion equations is much higher (by several orders) than the accuracy of numerical integration of the equations in Cartesian coordinates. This substantiates the expediency of using regular quaternion equations of the orbital motion of a spacecraft and the quaternion equations and relations in the variations constructed in the paper on their basis for the prediction and correction of the orbital motion of a spacecraft. [ABSTRACT FROM AUTHOR]

We have demonstrated in the present report that dielectric microparticles exhibited orbital rotation in the light field of non-coaxially configured two counter-propagating laser beams both in numerical simulations and experiments. A series of computational simulations indicated that when irradiated with two non-coaxially counter-propagating parallel laser beams with the same intensity distributions in the absence of thermal (Brownian) motion, a microparticle did not exhibit orbital rotation due to the symmetry of the optical field. However, the computations predicted that a microparticle exhibited one directional orbital rotation in the presence of thermal motion because of the symmetry breaking of the optical force acting on the particle. This spontaneous orbital rotation was experimentally demonstrated for 1-µm dielectric particles in water at room temperature. [ABSTRACT FROM AUTHOR]

Intensity scintillations of radio pulsars are known to originate from interference between waves scattered by the electron density irregularities of interstellar plasma, often leading to parabolic arcs in the two-dimensional power spectrum of the recorded dynamic spectrum. The degree of arc curvature depends on the distance to the scattering plasma and its transverse velocity with respect to the line of sight. We report the observation of annual and orbital variations in the curvature of scintillation arcs over a period of 16 yr for the bright millisecond pulsar, PSR J0437-4715. These variations are the signature of the relative transverse motions of Earth, the pulsar, and the scattering medium, which we model to obtain precise measurements of parameters of the pulsar's binary orbit and the scattering medium itself. We observe two clear scintillation arcs in most of our >5000 observations, and we show that they originate from scattering by thin screens located at distances D 1 = 89.8 ± 0.4 pc and D 2 = 124 ± 3 pc from Earth. The best-fit scattering model we derive for the brightest arc yields the pulsar's orbital inclination angle, i = 137.°1 ± 0.°3, and longitude of ascending node, Ω = 206.°3 ± 0.°4. Using scintillation arcs for precise astrometry and orbital dynamics can be superior to modeling variations in the diffractive scintillation timescale, because the arc curvature is independent of variations in the level of turbulence of interstellar plasma. This technique can be used in combination with pulsar timing to determine the full three-dimensional orbital geometries of binary pulsars and provides parameters essential for testing theories of gravity and constraining neutron star masses.

Observations of the S stars, the cluster of young stars in the inner 0.1 pc of the Galactic center, have been crucial in providing conclusive evidence for a supermassive black hole at the center of our galaxy. Since some of the stars have orbits less than that of a typical human lifetime, it is possible to observe multiple orbits and test the weak-field regime of general relativity. Current calculations of orbits require relatively slow and expensive computations in order to perform numerical integrations for the position and momentum of each star at each observing time. In this paper, we present a computationally efficient, first-order post-Newtonian model for the astrometric and spectroscopic data gathered for the S stars. We find that future, 30 m class telescopes—and potentially even current large telescopes with very high spectroscopic resolution—may be able to detect the Shapiro effect for an S star in the next decade or so. [ABSTRACT FROM AUTHOR]

The paper considers the question of the possibility of using differential equations in Roy's elements for numerical simulation of the motion of artificial earth satellites. An original algorithm for reducing the integration step is proposed to preserve the accuracy of simulation when the satellite passes the Earth's shadow. Using a spacecraft of GLONASS as an example, it is shown that simulation in Roy's elements is as highly efficient as in regular Lagrange's elements. [ABSTRACT FROM AUTHOR]

Highlights: Study of LEO CubeSat dynamics using satellite position measurements. Refinement of ballistic coefficient using satellite position measurements of close-flying CubeSats. This paper addresses the possibility of reconstructing motion relative to the center of mass of a low Earth orbit (LEO) nanosatellite of the CubeSat 3U standard using satellite position measurements (Two-Line Element Set (TLE)). This kind of task needs to be performed in the case where it is not possible to establish radio communication with the nanosatellite after it is launched into orbit. Therefore, it is important for the nanosatellite developers to develop some understanding of what is going on with the nanosatellite in order to be able to analyze the current situation after deployment. The study was carried out on the example of the aerodynamically stabilized SamSat-218D nanosatellite developed by the professors and students of Samara National Research University. SamSat-218D was launched into a near-circular orbit with an average altitude of 486 km on April 2016 during the first launch campaign from the Vostochny cosmodrome. Knowledge of CubeSat aerodynamics allows estimating the nature of its possible motion relative to the CubeSat center of mass by ballistic coefficient changes, evaluated with the use of satellite position measurements. The analysis showed that SamSat-218D performed spatial rotation with an angular velocity of more than two degree per second and had not stabilized aerodynamically by 2 March 2022, when it entered the atmosphere and was destroyed. [ABSTRACT FROM AUTHOR]

In the present work, we define a new anomaly, Ψ$$ \Psi $$, termed semifocal anomaly. It is determined by the mean between the true anomaly, f$$ f $$, and the antifocal anomaly, f′$$ {f}^{\prime } $$; Fukushima defined f′$$ {f}^{\prime } $$ as the angle between the periapsis and the secondary around the empty focus. In this first part of the paper, we take an approach to the study of the semifocal anomaly in the hyperbolic motion and in the limit case corresponding to the parabolic movement. From here, we find a relation between the semifocal anomaly and the true anomaly that holds independently of the movement type. We focus on the study of the two‐body problem when this new anomaly is used as the temporal variable. In the second part, we show the use of this anomaly—combined with numerical integration methods—to improve integration errors in one revolution. Finally, we analyze the errors committed in the integration process—depending on several values of the eccentricity—for the elliptic, parabolic, and hyperbolic cases in the apsidal region. [ABSTRACT FROM AUTHOR]

The paper proposes an original nonlinear technique for stochastic simulation of the uncertainty in orbital parameters that arises in inverse problems of dynamical astronomy (orbit determination from observations) due to random observation errors. The technique is based on a vector differential equation describing transition lines from the dynamic state, obtained from observations, to virtual dynamic states of the uncertainty cloud in the space of orbital parameters at a given (initial) epoch. Using some numerical method for solving the differential equation, stochastic simulation for each virtual state is implemented as a sequence of piecewise state transitions. The new technique is tested in strongly nonlinear inverse problems of asteroid dynamics on the examples of one lost and two recently discovered objects. The results by the transition methods are compared with those obtained by the method of disturbed (noisy) observations, also known as the observational Monte Carlo method. A comparative analysis reveals a good agreement of the results, while the amount of calculations by the proposed technique is at least twice less. [ABSTRACT FROM AUTHOR]

A magnetic micro stirrer bar (MMSB) is used in the mixing operation of microfluidic devices. We have established a low-cost and easy method to make MMSBs using magnetic (neodymium magnets, magnet sheets) or non-magnetic powders (SUS304) as materials. We demonstrated three kinds of MMSB have respective advantages. To confirm the practical use of this MMSB, a cell suspension of the motile unicellular green alga Chlamydomonas reinhardtii was stirred in microwells. As a result, the number of rotating cells increased with only one of the two flagella mechanically removed by the shear force of the rotating bar, which facilitates the kinetic analysis of the flagellar motion of the cell. The rotational motion of the monoflagellate cell was modeled as translational (orbital) + spinning motion of a sphere in a viscous fluid and the driving force per flagellum was confirmed to be consistent with previous literature. Since the present method does not use genetic manipulations or chemicals to remove a flagellum, it is possible to obtain cells in a more naturally viable state quickly and easily than before. However, since the components eluted from the powder material harm the health of cells, it was suggested that MMSB coated with resin for long-term use would be suitable for more diverse applications. [ABSTRACT FROM AUTHOR]

Precise forecasting of renewable energy production is crucial for ensuring the reliable operation of the electricity grid. Developing more accurate predictive models and computational methodologies can enhance energy production and improve overall system stability. This paper introduces a novel computational approach utilizing quaternions to calculate expected solar irradiance on a given surface. The proposed method incorporates quaternion rotations and translation vectors to model the motion of astronomical objects, both independently and in relation to each other, a factor critical for accurate irradiance estimation. This approach has the potential to replace the commonly used equatorial coordinate system-based computations, offering significant improvements in adaptability, efficiency, and accuracy. The quaternion-based method provides a 9.9% improvement in average angle deviation and a 25.46% improvement in maximum angle deviation from the ground truth of the Sun's angle of incidence, compared to the equatorial coordinate system-based model. This improvement translates to a 6.5905 kWh/m 2 discrepancy in clear sky annual irradiation between the two models, which is highly significant for solar power plants. Additionally, the proposed quaternion-based calculation is adaptable for estimating irradiation on any surface following an orbital trajectory, as well as on other planets. Moreover, the model is easily extendable to include other motions, thanks to the composition property of quaternions. The article presents the calculation methodologies of both models, performs a comparative analysis of the computational results, and presents the differences in computational efficiency between the two approaches. • Correction Factors Not Required : No correction factors needed for each GPS coordinate. • Applicability to Various Orbital Trajectories : Works with any orbital path, unlike equatorial-based method. • Extensibility for Additional Motions : Extends to handle additional motions like obliquity, nutation, and precession. • Reduced Computational Complexity : Fewer trigonometric functions mean faster, more stable calculations. • Improved Accuracy : Provides more accurate solar irradiation estimates than equatorial-based method. [ABSTRACT FROM AUTHOR]

The controlled motion of a solar sail is considered, with the reflectivity being a control parameter. The equations of controlled orbital motion of the solar sail in the vicinity of a Sun–Earth collinear libration point are investigated. The model of the circular restricted three-body problem of the Sun–Earth system is used to describe the controlled orbital motion of the solar sail. The laws of change in reflectivity to keep the solar sail in the vicinity of the libration point by means of light pressure forces are constructed, and an estimate of the controllability region is given. The control laws constructed for a linearized model of the equations of orbital motion are extended to the nonlinear case. The proposed technique for constructing the control laws enhances the potential in solving the problems of motion stabilization in the vicinity of a collinear libration point, where the light pressure force can have a significant efficiency. Numerical simulations of controlled motion are presented. [ABSTRACT FROM AUTHOR]

Nanosatellite missions may contain payloads for high pointing accuracy such as laser communication systems for crosslinks or astronomical observations. Therefore, the satellite requires a precise orbital position and orientation determination in order to point the scientific instrument to the desired target. In this work, an elliptical rotation method based on quaternion representation is presented. The proposed method allows determining the future position of a satellite around its orbit. Furthermore, in Low Earth Orbits (LEO) with an eccentricity larger than zero, the distance between the satellite and the Earth is changing over the time, increasing the satellite velocity in the perigee region compared to the apogee, due to the gravity forces. The elliptical rotation method and the orbital current position are deduced, considering a variable sampling-time as a function of the eccentricity and the orbital current position. The proposed algorithm can increase the position accuracy four times compared to fixed sampling time along the satellite orbit.

This paper addresses the possibility of reconstructing motion relative to the center of mass of a low Earth orbit (LEO) nanosatellite of the CubeSat 3U standard using satellite position measurements (Two-Line Element Set (TLE)). This kind of task needs to be performed in the case where it is not possible to establish radio communication with the nanosatellite after it is launched into orbit. Therefore, it is important for the nanosatellite developers to develop some understanding of what is going on with the nanosatellite in order to be able to analyze the current situation after deployment. The study was carried out on the example of the aerodynamically stabilized SamSat-218D nanosatellite developed by the professors and students of Samara National Research University. SamSat-218D was launched into a near-circular orbit with an average altitude of 486 km on April 2016 during the first launch campaign from the Vostochny cosmodrome. Knowledge of CubeSat aerodynamics allows estimating the nature of its possible motion relative to the CubeSat center of mass by ballistic coefficient changes, evaluated with the use of satellite position measurements. The analysis showed that SamSat-218D performed spatial rotation with an angular velocity of more than two degree per second and had not stabilized aerodynamically by 2 March 2022, when it entered the atmosphere and was destroyed.

The paper investigates the efficiency of the new collocation integrator Lobbie, presented in (Avdyushev, 2020), in comparison with other integrators widely used in practice, namely, collocation Runge–Kutta, extrapolation Gragg–Bulirsch–Stoer, multistep Adams–Multon–Bashforth integrators, and also with the Everhart integrator, well known in celestial mechanics. The integrators are tested in orbital dynamics problems. In particular, a comparative analysis of efficiency shows that when simulating a complex orbital motion (strongly elliptical or with gravity assist maneuvers), Lobbie excels the other integrators (except Everhart) by several times in performance, and by several orders of magnitude in accuracy. A correct comparison of the efficiency of the Everhart integrator and Lobbie is not possible, since they have no common orders: the former has only odd orders on the Radau spacings, while the latter has only even orders on the Lobatto spacings. Nevertheless, if we compare the efficiency of integrators of adjacent orders, then in the strongly elliptic case the Everhart integrator (with a higher order) is one order of magnitude inferior to Lobbie in accuracy. Another advantage of Lobbie is that it allows solving mixed systems of differential equations of the second and first orders, which, for example, are used in celestial mechanics to study dynamic chaos, as well as to linearize, regularize, and stabilize the equations of motion. To use the Everhart integrator to solve such systems, all second-order equations must be reduced to first-order ones. However, as applied to systems of first-order equations, the efficiency of the Everhart integrator becomes noticeably worse. [ABSTRACT FROM AUTHOR]

A novel algorithm based on the Lindstedt–Poincaré method is proposed to construct an analytical solution of the lunar orbit. Based on the analytical solution, a numerical fitting algorithm is proposed to improve the coefficients of the analytical solution so that its accuracy can reach the level of a few kilometers within 20 yr. By fitting our solution to the long-term JPL ephemerides, we are able to recover the receding speed of the Moon from the Earth due to tidal effects. The proposed algorithm also provides a general way to treat the third-body perturbation in rectangular coordinates.

The neuronal and genetic bases of sleep, a phenomenon considered crucial for well-being of organisms, has been under investigation using the model organism Drosophila melanogaster. Although sleep is a state where sensory threshold for arousal is greater, it is known that certain kinds of repetitive sensory stimuli, such as rocking, can indeed promote sleep in humans. Here we report that orbital motion-aided mechanosensory stimulation promotes sleep of male and female Drosophila, independent of the circadian clock, but controlled by the homeostatic system. Mechanosensory receptor nanchung (Nan)-expressing neurons in the chordotonal organs mediate this sleep induction: flies in which these neurons are either silenced or ablated display significantly reduced sleep induction on mechanosensory stimulation. Transient activation of the Nan-expressing neurons also enhances sleep levels, confirming the role of these neurons in sleep induction. We also reveal that certain regions of the antennal mechanosensory and motor center in the brain are involved in conveying information from the mechanosensory structures to the sleep centers. Thus, we show, for the first time, that a circadian clock-independent pathway originating from peripherally distributed mechanosensors can promote daytime sleep of flies Drosophila melanogaster. [ABSTRACT FROM AUTHOR]

One of the major challenges in the Hayabusa2 sample-return mission was the second touchdown on the asteroid Ryugu, which was designed to collect subsurface materials near the artificial crater formed by a small carry-on impactor. Due to engineering and scientific requirements, a narrow area with a radius as small as 3.5 m was selected as the target landing site. To achieve pinpoint touchdown at the selected site, an artificial landmark called a target marker (TM) was used for optical navigation. The key to a successful touchdown was precise deployment of the TM in the microgravity environment of the asteroid. This study therefore investigates a viable trajectory for TM deployment, incorporating the uncertainty in the impact and rebound motions of the TM. Following the TM deployment operation, a detailed survey of the landing site around the TM settlement point is performed to assess the terrain conditions. To guarantee the observation quality and spacecraft safety, multi-impulse low-altitude trajectories are introduced in this paper, along with covariance analyses based on the high-fidelity polyhedral gravity model of Ryugu. Subsequently, a pinpoint touchdown trajectory that satisfies various engineering requirements, such as landing accuracy and velocity, is designed, taking advantage of optical TM tracking. The feasibility of the touchdown sequence is further validated by a Monte Carlo dispersion analysis. Consequently, Hayabusa2 successfully touched down within the target site on 11 July 2019. The current research also conducts a post-operation trajectory reconstruction based on the flight data to demonstrate the actual guidance performance in the TM deployment, landing site observations, and pinpoint touchdown. [ABSTRACT FROM AUTHOR]

Currently, ultra-small satellite aresubjectstostringentrequirementsintermsoftheaccuracyof determining the position of the satellite in orbit, while the satellite is the subject to restrictions on mass, size and power consumption. The aim of this work is to simulate of navigation receiver operation for the ultra-small satellite with restrictions on energy consumption and computational resources.The operating conditions are considered and the requirements to the onboard navigation receiver for the ultra-small satellite are determined. The navigation receiver operation at the initial stage, performance testing, error detection, analysis of the reliability of the solution of the navigation-time determination problem are described.The structure of the design ballistics problems for orbit prediction of ultra-small spacecraft and navigation satellites, radio visibility intervals for GLONASS and GPS systems, parameters of navigation signals have been developed.The motion relative to the satellite systems GPS and GLONASS for a preliminary orbit of СubeBel-1 have been simulated. The Doppler dynamics of the GPS satellite signals in the receiver without restrictions on the relative speed for one day has been calculated. Radio visibility intervals for GPS and GLONASS satellites were calculated and optimal conditions for the cold start of the navigation receiver with a relative speed limit (Vr < 500 m/s) for 1 hour of operation both in separate and in joint operation on both systems were determined.To test the verification methods of the experimental data of the СubeBel-1 satellite, the operation of the navigation receiver of the Nsight satellite was studied according to the received telemetry from the beginning of its flight until the moment it entered stable operation.It is shown that the telemetry data of the navigation receiver at the testing stage had a significant error. After software correction, the navigation receiver worked steadily throughout the week of observation, the error of longitude and latitude measurements did not exceed 0.2 degrees.

We have studied the influence of an evolving gravitational potential of the Milky Way Galaxy on the orbital motion of 152 globular clusters with proper motions from the Gaia EDR3 catalogue and mean distances from Baumgardt and Vasiliev (2021). To construct a semicosmological evolving model potential with changing masses and sizes of the Galactic components, we have used the algorithm described in Haghi et al. (2015). The adopted axisymmetric three-component model potential of the Galaxy includes a spherical bulge, a flat Miyamoto–Nagai disk, and a spherical Navarro–Frenk–White dark matter halo. The orbits are integrated backward in time. We compare the orbital parameters of globular clusters derived in static and evolving potentials when integrating the orbits for 5 and 12 Gyr backward. For the first time we have studied the influence of separately a change in the masses and a change in the sizes of the Galactic components. The changes in the masses and sizes of the components are shown to act on the orbital parameters in the opposite way. At small Galactocentric distances this influence is maximally compensated for. The orbits of distant globular clusters and those with a large apocenter distance undergo the biggest changes. We show that on time scales up to Gyr the orbits of globular clusters in the case of a potential with both changing masses and changing sizes of the components undergo, on average, minor changes compared to the case of a static potential. These changes fit into the limits of the statistical uncertainties caused by the errors in the data. So, on these time scales the Galactic potential may be deemed static. We provide tables with the orbital parameters of globular clusters derived in both static and evolving potentials. [ABSTRACT FROM AUTHOR]

A mathematical model of a spacecraft (SC) with an arbitrary number of large flexible structural (appendages) elements (LFSEs) is developed, implemented, and verified. The SC model obtained based on the general equations of dynamics is written in generalized coordinates. It allows three types of articulation between the LFSEs and the SC's body: cantilever, and with the help of one-step and two-step hinges. Due to the procedure used in the derivation of the equations of motion, the proposed model allows us to change the number of LFSEs and types of articulation without rewriting the equations of motion in symbolic form, which makes it comfortable for software implementation. [ABSTRACT FROM AUTHOR]

Abstract In the past decades, space missions to small bodies (Galileo, OSIRIS‐REx, Hayabusa, Hayabusa2, Chang'e 2, Rosetta, etc.) have enriched us greatly with voluminous new knowledge on our solar system. In situ observations by these missions have revealed the extreme complexity and remarkable diversity of the spatial environment around their target asteroids. A study on the motion of objects in such complex environments is of great importance for understanding the evolution history of surface/subsurface materials on the asteroids. Establishing a reasonable dynamic model is obviously a crucial step. This paper proposes a method for tracking the motion of an object near the surface of an arbitrary asteroid. This method combines the irregular shape, an unlimited rotational state and asymmetric gravitational field, which are three key factors that dominate the complex movement of an object on and off the asteroid's surface. The gravitational attraction and potential are computed using the polyhedral method with corrections for the possible singularities. The asteroid's surface is then approximated using a continuous and differentiable surface, and the parametric representation forms of the body are derived based on polynomial series. An event‐driven scheme is designed, so that the orbital motion and surface motion are processed separately by checking the triggering events. The algorithm was implemented using C++. Benchmarking tests are organized on a local cluster, showing a satisfactory performance in both accuracy and efficiency. This method was further applied to improve the control accuracy of the landing spot of an asteroid surface lander.

A comprehensive research was conducted to establish the influence of solar pressure on the existence of artificial Earth satellites in their orbit. Six low-orbit satellites and one satellite with a high-elliptical orbit moving in orbit during 2001-2020 were selected for the study. We used the USSTRATCOM database of the satellites' orbital elements (http://www.space-track.org/), additional data were taken from CalSky (https://www.calsky.com) and TLEtools (https://tletools.readthedocs.io). Taking into account light pressure, we refined the calculation of the duration of a satellite's orbital motion, which we had performed earlier [M. M. Koval'chuk, Bull. Natl. Univ. Kyiv. Astron. 55, 39 (2017)], and clarified the moment of its destruction. Using the proposed method allowed us to reduce the difference between the calculated and the real lifetime of satellites: for low-orbit satellites, the difference between the calculated and the real time of their existence in orbit does not exceed ±1 day, for a satellite with a highly elliptical orbit it is ±2 days. Such accuracy is sufficient to produce proper forecasts. Thus, consideration of light pressure gives a small correction in the calculations in the case of loworbit satellites, but this correction can be significant for low-mass and large-surface objects moving in medium and high (geostationary) orbits [Ch. Lucking, C. Colombo, C. R. McInnes, Acta Astronaut. 77, 197 (2012)]. [ABSTRACT FROM AUTHOR]

A collision of an asteroid with the Earth in the future is always considered as a probabilistic event because the asteroid orbit determined from observations with random errors inevitably contains an uncertainty in its parameters. To establish the probability of collision, the parametric uncertainty as a probabilistic distribution of virtual objects is mapped by the orbital model into the physical space for the period of the asteroid rendezvous with the Earth, and then the probabilistic mass penetrating into the planet body is estimated. The asteroid impact on the Earth is a very significant phenomenon because it can have fatal consequences for mankind. Therefore, probabilistic estimation of collision with potentially hazardous asteroids must be carried out very carefully with allowance for various subtle aspects. In this work, nonlinearity in inverse problems of asteroid dynamics under different observation conditions for various types of determined orbits is studied. The main problem we set ourselves is to examine to what extent nonlinearity can affect the accuracy of a probabilistic estimation when the parametric uncertainty is simulated using classical linear stochastic methods. To study the total, parameter-effect, and intrinsic nonlinearities, we introduce original indices with justified threshold values determined from the maximum tolerable biases of probabilistic estimates due to nonlinearity. The general analysis of nonlinearity is carried out for potentially hazardous asteroids observed in one appearance before June 2020. In particular, it is shown that main factors of strong nonlinearity are the short observed orbital arc (less than one degree) and the small observation period (less than ten days). Moreover, the situation is aggravated if the asteroid moves during the observation along the ecliptic and near it on an arc with small curvature. It is also established that, due to strong nonlinearity in problems of probabilistic estimation, nonlinear stochastic methods are required to simulate the orbital uncertainty for almost half of the potentially hazardous asteroids (44%). [ABSTRACT FROM AUTHOR]

In the past decades, space missions to small bodies (Galileo, OSIRIS‐REx, Hayabusa, Hayabusa2, Chang'e 2, Rosetta, etc.) have enriched us greatly with voluminous new knowledge on our solar system. In situ observations by these missions have revealed the extreme complexity and remarkable diversity of the spatial environment around their target asteroids. A study on the motion of objects in such complex environments is of great importance for understanding the evolution history of surface/subsurface materials on the asteroids. Establishing a reasonable dynamic model is obviously a crucial step. This paper proposes a method for tracking the motion of an object near the surface of an arbitrary asteroid. This method combines the irregular shape, an unlimited rotational state and asymmetric gravitational field, which are three key factors that dominate the complex movement of an object on and off the asteroid's surface. The gravitational attraction and potential are computed using the polyhedral method with corrections for the possible singularities. The asteroid's surface is then approximated using a continuous and differentiable surface, and the parametric representation forms of the body are derived based on polynomial series. An event‐driven scheme is designed, so that the orbital motion and surface motion are processed separately by checking the triggering events. The algorithm was implemented using C++. Benchmarking tests are organized on a local cluster, showing a satisfactory performance in both accuracy and efficiency. This method was further applied to improve the control accuracy of the landing spot of an asteroid surface lander. Key Points: A new numerical method is proposed for modeling the surface of asteroids using smooth parameter mappingIn this paper, we present a method to model the migration of an individual object around asteroid's surfaceWe simulate the deployments of the lander on asteroid Ryugu [ABSTRACT FROM AUTHOR]

The paper describes the features and capabilities of the software to simulate the dynamics of near-Earth satellites. The software package allows the passive and controlled angular and orbital motion simulation of both single satellites and formations. The software also allows using the mathematical models of varying precision and complexity while performing the computations. The user-friendly GUI is designed in a way to prevent or minimize the possibility of inappropriate data entry. The package was created in C++ using Qt Framework, which ensures cross-platform functionality and compatibility. [ABSTRACT FROM AUTHOR]

The motion of a spacecraft with a solar sail is considered within the restricted three-body problem of the Sun–Earth system. The equations of controlled orbital motion of the solar sail in the vicinity of the Sun–Earth collinear libration point are investigated. Modified equations of the circular restricted three-body problem of the Sun–Earth system are used to describe the controlled orbital motion of the spacecraft and to develop the control laws. Our main result is the proposed control law in the form of a feedback that provides spacecraft keeping in the vicinity of the libration point using the light pressure forces. [ABSTRACT FROM AUTHOR]

Einstein stated two dictums, so that more experimental facts can replace the previously adopted hypotheses and General Relativity (GR) can evolve to "grand aim" or perfection. In the absence of appropriate experimental facts during pre-CEREPAC (Century-long Experience of Relativity-related Experiments on Physics, Astronomy and Celestial-mechanics) era, Einstein found no "escape" from the consequence of non-Euclidean geometry, while keeping all frames permissible based on contemporary knowledge. Bergmann also stated in 1968 that the "principle of general covariance" has brought about serious complication in GR. During CEREPAC, relativists and mathematical-astronomers invariably identified the appropriate "nature's preferred-frame," which was later found essential for operation of conservation laws. Based on CEREPAC, replacing the experimentally unverifiable hypotheses with experimentally proven principles, and improving upon the GR-astronomers model (developed by JPL, USA, as an evolved-version of GR-conventional model) in two successive stages, GR was remodeled to what became evident as Evolved GR (EGR), after it enabled the elimination of all earlier-adopted ad-hoc methods or approaches, and of the problems, paradoxes and anomalies, associated with the applications of GR, during CEREPAC, and after it unraveled the "General-relativistic nature of speed-of-light (c)" which links the variable cr with Fr, the local Gravitational Red-Shift Factor (as stated by Einstein between 1911-1921). As a consequence of the space-age developments in numerical simulation and in the availability of precision observational data, it got proven that nature itself operates the conservation laws of energy, and of linear and angular momentums (both magnitudes and directions), with respect to the appropriate "nature's preferred frame"; this provided sufficient reason for giving up the "relativity of all frames," bringing back Euclidean geometry in EGR. Euclidean space in EGR enabled development of a Prototype of future Ephemerides, leading to five orders-of-magnitude improvement in accuracy of computation of precession of celestial orbits, using three independent methods; this methodology of Prototype Ephemeris and "three-methods-match" can also be applied while remaining exclusively within the precincts of GR, by using one alternative mode of running the EGR program for planetary and Lunar orbits, by opting for GRTOPT=Y; this mode utilizes exclusively the GR equations instead of EGR equations; in fact, this mode is the GR-astronomers (modified) model that was really an intermediate stage of evolution (as mentioned above) between the GR-astronomers model and the EGR model. This model incorporates: (1) All good (and, experimentally proven) features from the three generations of GR models (Einstein's original, Bergmann's and Misner-Thorne-Wheeler or MTW), and (2) The "Nature-adopted" real orbital model (as proven from comparison of the computed precession values at Micro-arcsecond {μas} level using the "three-methods-match") for its Methodology for Conservation of Linear and Orbital Angular Momentums, in a polar coordinate system (r, θ, Φ). This model computes: (1) Precession of celestial orbits at nearly the same accuracy as that done using the EGR model, and (2) About three digit more accurate (than reported by Folkner in 2014, from fitting lunar laser ranging data with an updated lunar gravity field from the GRAIL mission, etc.) orbits of inner planets and the Moon. [ABSTRACT FROM AUTHOR]

In this study flow around a freely vibrating circular cylinder in two-degrees-of-freedom is investigated using two-dimensional numerical approach. The equations of motion, the continuity and the pressure Poisson equations are solved for incompressible constant property Newtonian fluid using the finite difference method. Systematic computations are carried out to investigate the effect of the natural frequency f N of the cylinder on the oscillation amplitudes and aerodynamic force coefficients. The mass ratio and the structural damping coefficient values are fixed at m* =10 and ζ = 0 , respectively. In addition to the typical distorted figure-eight motion, a raindrop-shaped path is also found whose range widens with increasing f N. Within this range the streamwise oscillation amplitude reaches higher values compared to figure-eight motions and the curves shift upwards with increasing f N. Different vortex structures belong to each cylinder path: 2S or C(2S) modes are observed for distorted figure-eight and P+S mode is found for raindrop-shaped trajectories. The time-mean values of lift jump abruptly between two solutions. Pre-and post-jump analysis reveals that these solutions are mirror images of each other. The root-mean-square (rms) values of lift plotted against U* St shift upwards in the raindrop-shaped motion range and downwards in the figure-eight motion range, while the rms of drag shifts to higher values in both regimes with increasing f N. Chaotic cylinder paths are observed when increasing the natural frequency over a critical value. • A freely vibrating cylinder is investigated at different natural frequencies. • Orbital and distorted-figure-eight cylinder paths are found. • The streamwise oscillation amplitude increases steeply for orbital paths. • For orbital motion asymmetric wake is found and time-mean of lift is non-zero. • A hysteretic boundary separates the two cylinder motion ranges. [ABSTRACT FROM AUTHOR]

Abstract The effect of orbital motion of drill pipe on the transport of non-Newtonian fluid and cuttings is simulated by means of the two-fluid model in combination with the kinetic theory of granular flow in the horizontal wellbore annulus. The drill pipe self-rotates around its own axis while pursuing a circular orbit around the axis of the wellbore annulus, in which the orbital radius is the eccentric distance of the drill pipe from the axis of the wellbore. The embedded sliding mesh method is adopted to achieve the effect of the orbital movement of the drill pipe wall on the liquid-solid mixture. The cuttings transport ratio (CTR) which is defined as the ratio of the concentration of injected cuttings to the concentration of cuttings retained in the annulus is chosen as the measurement to evaluate hole cleaning. Cuttings transport behaviors in the annuli with the four motion states of drill pipe are investigated respectively. Simulations indicate that if the drill pipe is not concentric, there must be the fluid force that causes the lateral movement of drill pipe when it rotates. The orbital motion of drill pipe improves cuttings transport ratio in the annulus due to the periodical stirring and entrainment effect on cutting particles. The tangential flow within the annulus is dominated by the orbital motion of drill pipe rather than the self-rotation. The secondary flow appears especially when the self-rotation and orbital motion of drill pipe are in the opposite direction. With the increase of the orbital radius, the cuttings transport ratio is improved and the pressure drop is reduced because of the agitation of the drill string against the flow field. Increasing the rotating speed of the drill pipe contributes to a better wellbore cleaning, while an excessive rotating speed causes a higher pressure drop. Although the orbital motion of the drill pipe improves the hole cleaning, it also greatly increases the resistance and resultant moment exerted by the liquid-solid mixture, especially at high rotation speeds and eccentricity ratios. Graphical abstract Image 1 Highlights • Cuttings transport in annuli with four motion states of drill pipe were studied. • The orbital motion of drill pipe improves cuttings transport in drilling annulus. • Effects of rotation speeds and eccentricity ratios of orbiting pipe were studied. • Orbital motion of drill pipe plays the dominant role in tangential flow in annulus. • Orbital motion significantly increases the resultant moment on the drill pipe. [ABSTRACT FROM AUTHOR]