Orbital Plane Research Articles

GUIDANCE AND CONTROL OF A SPACE ROBOT DURING FLIGHTS IN A LOW-ORBIT CONSTELLATION OF EARTH SURVEY MINI-SATELLITES

Developed algorithms for guidance and motion control of a space robot when approaching with mini-satellites in adjacent orbital planes of low-orbit constellation for the earth survey and the results of computer verification demonstrating their effectiveness are presented.

General relativistic effects and the near-infrared and X-ray variability of Sgr A* I

The near-infrared (NIR) and X-ray emission of Sagittarius A* shows occasional bright flares that are assumed to originate from the innermost region of the accretion flow. We identified 25 4.5 μm and 24 X-ray flares in archival data obtained with the Spitzer and Chandra observatories. With the help of general relativistic ray-tracing code, we modeled trajectories of “hot spots” and studied the light curves of the flares for signs of the effects of general relativity. Despite their apparent diversity in shape, all flares share a common, exponential impulse response, a characteristic shape that is the building block of the variability. This shape is symmetric, that is, the rise and fall times are the same. Furthermore, the impulse responses in the NIR and X-ray are identical within uncertainties, with an exponential time constant τ ∼ 15 m. The observed characteristic flare shape is inconsistent with hot-spot orbits viewed edge-on. Individually modeling the light curves of the flares, we derived constraints on the inclination of the orbital plane of the hot spots with respect to the observer (i ∼ 30° , < 75°) and on the characteristic timescale of the intrinsic variability (a few tens of minutes).

Polar Circumtriple Planets and Disks Can Only Form Close to a Triple Star

Observations of protoplanetary disks around binary and triple star systems suggest that misalignments between the orbital plane of the stars and the disks are common. Motivated by recent observations of polar circumbinary disks, we explore the possibility of polar circumtriple disks and therefore polar circumtriple planets that could form in such a disk. With n-body simulations and analytic methods, we find that the inclusion of a third star, and the associated apsidal precession, significantly reduces the radial range of polar orbits so that circumtriple polar disks and planets can only be found close to the stellar system. Outside of a critical radius that is typically in the range of 3–10 times the outer binary separation, depending upon the binary parameters, the orbits behave the same as they do around a circular orbit binary. For some observed systems that have shorter-period inner binaries, the critical radius is considerably larger. If polar circumtriple planets can form, we suggest that it is likely that they form in a disk that was subject to breaking.

Laboratory Study of Microsatellite Control Algorithms Performance for Active Space Debris Removal Using UAV Mock-Ups on a Planar Air-Bearing Test Bed

In this paper, a planar air-bearing test bed with unmanned aerial vehicles (UAV) was used to test a microsatellite motion control system. The UAV mock-ups were controlled by four ventilator actuators that imitated the satellite thrusters and provided the required acceleration vector in the horizontal plane, and torque along the vertical direction. The mock-ups moved almost without friction along the planar air-bearing test bed due to the air cushion between the test bed surface and the flat mock-up base. The motion of the mock-ups motion imitated the motion of satellites in the orbital plane. The problem of space debris can be solved using special microsatellite missions able to dock to space debris objects and change their orbit. In this paper, two control algorithms based on the virtual potentials approach and the State Dependent Ricatti Equation (SDRE) controller, were proposed for docking to a non-cooperative space debris object. The algorithms were tested in a laboratory facility, and the results are presented and analyzed, including their main features demonstrated during the laboratory study. It was shown that the SDRE-based control was faster, although the virtual potential-based control required less characteristic velocity.

The Sensitivity of Eclipse Mapping to Planetary Rotation

Mapping exoplanets across phases and during secondary eclipse is a powerful technique for characterizing Hot Jupiters in emission. Since these planets are expected to rotate about axes normal to their orbital planes, with rotation periods synchronized with their orbital periods, mapping provides a direct correspondence between the orbital phase and planetary longitude. We develop a framework to understand the information content of planets where their rotation states are not well constrained, by constructing bases of light curves across different rotation rates and obliquities that are orthogonal in integrated flux across the secondary eclipse. These demonstrate that brightness variation during eclipse may arise from a variety of rotation rates, obliquities, and map structures, requiring priors to properly disentangle each of these components. By modeling eclipse observations of the Warm Jupiter HAT-P-18b we demonstrate that, at a signal-to-noise equivalent to ∼10 orbits with JWST, confusion about map structure is likely a concern only at the upper physical limits of possible rotation rates. Even without priors, one may nevertheless be able to put an order-of-magnitude constraint on rotation rate by determining at what rates the fitted map complexity is minimized, a prescription whose efficacy increases if out-of-eclipse data are available to isolate the effects of rotation. Finally, in the limit of maps with longitudinal symmetry, the projected obliquity in the plane of the sky determines the information available during eclipse, ranging from nondetections of structure to a basic constraint on hemispherical asymmetry and orientation depending on the obliquity angle.

Estimating the Potential Accuracy of Some Orbital Parameters from Angular Measurements: a 2D model

The problem of estimating some parameters of a cosmic body orbits from angular measurements is considered. Contrary to the existing opinion that angular measurements are unsuitable for obtaining accuracies that are of practical interest, it is shown that, if the orbit is such that the impact place is in the vicinity of the observer, then such parameters as the impact point and time can be determined with quite acceptable accuracy. A fairly simple means for evaluating the accuracy of the "motion-measurement" process by reducing it to an analysis in a plane is described. The analysis is based on several principles. A family of orbits unfavorable to the observer is singled out, and an analysis is performed on this family. These are orbits whose plane touches the observer's Earth parallel, with the touching point being the intersection point of the observer and cosmic body trajectories. The article substantiates a simple approximate plane model, in which the observer’s true motion is replaced without changing its velocity by motion in the orbit plane. Information about the impact point is contained in the observations when the height decreases, which makes it possible to consider the gravity acceleration of as a constant in the descending mode. The motion model is simplified compared with the Keplerian motion: a simple motion scheme is obtained in the polar coordinate system. As a result, it becomes unnecessary to solve the differential equation representing the change in acceleration. A measurement formula that takes into account the Earth curvature and the observer latitude is derived, and the parameters determining the analyzed scheme are added: the distance to the impact point, incidence angle and impact moment, and horizontal velocity. The model accuracy is analyzed using the Fisher matrix. As a result, an approximate problem on a plane with four parameters is obtained instead of a problem in 3D space with seven parameters. The difficulties with the accuracy of estimating the displacement and impact moment in the model remain, and they are analyzed. The accuracy is estimated using the concept of Fisher information and the multidimensional Rao-Kramer information inequality instead of analyzing the processing algorithm.

Ultraviolet spectropolarimetry: conservative and nonconservative mass transfer in OB interacting binaries

The current consensus is that at least half of the OB stars are formed in binary or multiple star systems. The evolution of OB stars is greatly influenced by whether the stars begin as close binaries, and the evolution of the binary systems depend on whether the mass transfer is conservative or nonconservative. FUV/NUV spectropolarimetry is poised to answer the latter question. This paper discusses how the Polstar spectropolarimetry mission can characterize the degree of nonconservative mass transfer that occurs at various stages of binary evolution, from the initial mass reversal to the late Algol phase, and quantify its amount. The proposed instrument combines spectroscopic and polarimetric capabilities, where the spectroscopy can resolve Doppler shifts in UV resonance lines with 10 km/s precision, and polarimetry can resolve linear polarization with \(10^{-3}\) precision or better. The spectroscopy will identify absorption by mass streams and other plasmas seen in projection against the stellar disk as a function of orbital phase, as well as scattering from extended splash structures, including jets. The polarimetry tracks the light coming from material not seen against the stellar disk, allowing the geometry of the scattering to be tracked, resolving ambiguities left by the spectroscopy and light-curve information. For example, nonconservative mass streams ejected in the polar direction will produce polarization of the opposite sign from conservative transfer accreting in the orbital plane. Time domain coverage over a range of phases of the binary orbit are well supported by the Polstar observing strategy. Special attention will be given to the epochs of enhanced systemic mass loss that have been identified from IUE observations (pre-mass reversal and tangential gas stream impact). We show how the history of systemic mass and angular momentum loss/gain episodes can be inferred via ensemble evolution through the r–q diagram. Combining the above elements will significantly improve our understanding of the mass transfer process and the amount of mass that can escape from the system, an important channel for changing the final mass and ultimate supernova of a large number of massive stars found in binaries at close enough separation to undergo interaction.

Searching masers from the Sagittarius stellar stream

AbstractLarge scale optical and infrared surveys have revealed numbers of accretion-derived stellar features within the halo of the Galaxy. These coherent tail-like features are produced by encounters with satellite dwarf galaxies. We conducted an SiO and H2O maser survey towards O-rich AGBs towards the orbital plane of the Sgr Stellar Stream from 2016. Up to now, maser emissions have been found from 60 sources, most of which are detected for the first time. However, their distances and kinematics suggest they are still disk stars.

Evolution equations of multi-planet systems with variable masses

In celestial mechanics and astrodynamics, the study  of the  dynamical evolution of exoplanetary systems is the   relevant topics.    For today more than 3,000 exoplanetary systems are known. In this paper, we study the dynamic evolution of extrasolar systems, when the leading factor of evolution  is the variability of the masses of gravitating bodies. The problem of spherically symmetric bodies with  variable masses is considered in a relative coordinate system, this bodies inter-gravitating according to Newton's law. The quasi-elliptical motions of planets whose orbits do not intersect during evolution are investigated. It is believed that the mass of bodies under consideration  varies isotropically by various known laws with different velocities. The mass of the parent star is considered to be the most massive than its planets and the origin of the relative coordinate system is in the center of the parent star.. Due to the variability of the masses, the differential equations of motion become non-autonomous and the task is difficult. The problem is investigated by methods of perturbation theory. The canonical perturbation theory based on a periodic motion over a quasi-canonical section is used.  Canonical equations of motion are obtained in analogues of the second Poincare system, which are effective in the case when the analogues of eccentricities and the analogues of the inclination of the orbital plane of planets are sufficiently small.  The secular perturbations of the planets, which determine the behavior of the orbital parameters over long time intervals, are studied. The evolutionary equations of many planetary systems with isotropically varying masses in analogues of the second system of Poincare variables are derived in an analytical form which are obtained using the Wolfram Mathematica computer algebra system. This takes into account the effects of the decreasing mass of the parent star and the growth of the masses of the planets due to the accretion of matter from the remnants of the protoplanetary disk. For the three-planetary problem of four bodies with variable masses, the evolutionary equations in dimensionless variables are obtained explicitly. In the future, these results will be used to study the dynamics of the three-planet system K2-3 in the non-stationary stage of its evolution.

The obliquity of Mercury: Models and interpretation

AbstractMercury is locked in an unusual 3:2 spin-orbit resonance and as such is expected to be in a state of equilibrium called Cassini state. In that state, the angle between the spin axis and orbit normal, called obliquity, remains almost constant while the spin axis remains almost in the plane, also called Cassini plane, defined by the normal to the Laplace plane and the normal to the orbital plane. The spin axis and the orbit normal precess together with a period of about 300 kyr. The orientation of the spin axis of Mercury has been estimated using different approaches: (i) Earth-based radar observations, (ii) Messenger images and altimeter data, and (iii) Messenger radio tracking data. The different estimates all tend to confirm that Mercury occupies the Cassini state. The observed obliquity is small and close to 2 arcmin. It indicates a normalized polar moment of inertia of about 0.34. This information, combined with the existence of a liquid iron core, as evidenced by the librations, allows to constrain the interior structure of Mercury. However, the different estimates of the orientation of the spin axis locate the spin axis somewhat behind or ahead of the Cassini plane, and it is difficult to reconcile and interpret them coherently in terms of detailed interior properties. We review recent models for the obliquity and spin orientation of Mercury, which include the effects of complex orbital dynamics, tidal deformations and associated dissipation, and internal couplings related to the presence of fluid and solid cores. We discuss some implications regarding the interpretations of the orientation estimates in term of interior properties.

Jovian encounter manifolds

AbstractRecent numerical studies have shown that the entire solar system is permeated with arch-like structures originating from all planets. Particles placed on such arches experience planetary close encounters after only one or few orbital revolutions. In this work, we are interested how thece arches, which we associate to encounter manifolds of Jupiter, appear in three dimensions for higher inclinations.Our results show that about 0.5% of the observed domain [a, e, i] = [2 AU, 11.5 AU] × [0, 0.7] × [0°, 90°] is covered by the manifolds. For inclinations up to ∼5°, the arch-like structures are almost unchanged compared to those initially observed in the orbital plane of Jupiter. At higher inclinations, the number of encounter orbits rapidly decreases to narrow domains where the manifolds stretch up to inclinations of 90° (and above) in a very steep manner.

On one Approach to the Solution of the Lambert Problem using the Decompositional Method of Modal Control

A new approach to the solution of the Lambert’s problem in spaceflight mechanics is proposed for elliptical orbits. The system of four transcendental algebraic equations is solved using the method of modal synthesis which is based on multilevel decomposition of discrete dynamic system and applied to solve the problem of identification of parameters of discrete system by a state observer. The solution algorithm is as follows: conditional and identification discrete models (systems) are built for the specified system of equations; initial values of estimates are given; initial conditions in the equations of residuals are formed. Using the method of modal synthesis, the problem of search for control of the auxiliary system is solved, as a result of which the matrix of state observer feedback coefficients is calculated. This matrix is used to predict the state vector and to obtain refined estimates --- parameters of the planar orbit. A numerical example of the Lambert’s problem solution using the proposed algorithm is given. In essence, an approach to the solution of nonlinear algebraic systems of the fourth order, which can be extended to systems of any observable order, is proposed. The peculiarity of the proposed algorithm is that the convergence of the iterative process of finding a solution can have a different "adjustable" speed using the control law

An island of linearly stable non-hierarchical unequal mass periodic three-body orbits — A harbinger of circumbinary exoplanets?

We analyze all publicly available planar periodic three-body orbits in Newtonian gravity with zero angular momentum, which pass through a symmetrical collinear configuration. We find correlations between scale-invariant parameters, such as the ratio m3/m of the central and equal mass, the topological quantifier Lf of an orbit, the scale-invariant period T|E|3/2 , and the distribution of marginally linearly stable orbits. The elliptical (S) and marginal (M) linearly stable orbits are contained in a compact, non-zero measure domain with an apparently continuous boundary in the space spanned by the topological index Lf and the mass ratio m3/m. The distribution of S and M orbits predicts a sharp increase of both numbers of S and M orbits in this region as m3 is lowered below m/2. This indicates an island of stability of non-hierarchical three-body systems consisting of a light object (planet) orbiting two heavier ones (binary stars). We also find one-dimensional (sub)manifolds in the phase space of initial conditions that contain many of these linearly stable orbits. Orbits with increasingly longer periods populate/converge to these manifolds which suggests these manifolds are attractors.

Symmetric and asymmetric dynamics of a tethered satellite in nontypical planes

The dynamics of tethered satellite systems operating in typical planes (e.g., the orbital plane and the planes perpendicular to the orbital plane) has been well analyzed. However, studying the orbital system in nontypical planes might be more practical. Hence, this paper concentrates on the dynamic behaviors of a tethered system with two satellites in any plane, along with active out-of-plane suppressions. First, noninertial and inertial reference frames are introduced to build a billiard and a bead model for the original system. The low-dimensional model is applicable to efficient evaluation, while the high-dimensional model is more suitable for depicting the configuration changes of a flexible tether. Then, the in-plane motion stability in a transformed reference frame is examined via the Poincaré map. A numerical dynamic zone that depends on the system parameters and initial states is utilized to sketch the system spins, pendulum-like motions, and irregular oscillations. The simulation results demonstrate that the parameter zone is periodic. The symmetry and asymmetry of the dynamic forms are also presented. Finally, a corresponding relationship between model selection and dynamic behaviors is proposed.

Fundamental photon orbits in the double Schwarzschild space-time

We consider photon orbits in the space-time consisting of two identical Schwarzschild black holes in static equilibrium. In particular, we focus on fundamental photon orbits – bound photon orbits that do not fall into either black hole or go to infinity. It is known that there could exist up to two circular photon orbits lying in the plane of symmetry between the black holes. In this paper, we present more examples of fundamental photon orbits in this space-time. This includes non-circular orbits lying in the plane of symmetry, circular orbits that lie off the plane of symmetry, polar orbits, and non-planar orbits that orbit around one or both of the black holes. These orbits are all unstable. Finally, in an appendix, we present a class of circular time-like orbits that lie off the plane of symmetry.

The phase space structure of retrograde mean motion resonances with Neptune: the 4/5, 7/9, 5/8 and 8/13 cases

We compute planar and three-dimensional retrograde periodic orbits in the vicinity of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and we concentrate on the dynamics of higher-order exterior mean motion resonances with Neptune. By using the circular planar model as the basic model, families of retrograde symmetric periodic orbits are computed at the 4/5, 7/9, 5/8 and 8/13 resonances. We determine the bifurcation points from the planar circular to the planar elliptic problem and we find all the corresponding families. In order to obtain a global view of the families of periodic orbits, the eccentricity of the primaries takes values in the whole interval 0<e'<1. Then, we find all the possible vertical critical orbits (v.c.o) of the planar circular problem and we proceed to the three-dimensional circular restricted 3-body problem. In this model, retrograde periodic orbits are generated mainly from the retrograde v.c.o. Also, if we continue families of direct orbits for i>90^circ , then we can obtain families of 3D symmetric retrograde periodic orbits. The linear stability is examined too. Stable periodic orbits are associated with phase space domains of resonant motion where TNOs can be captured. In order to study the phase space structure of the above resonances, we construct dynamical stability maps for the whole inclination interval (0<i<180^circ ) by using the well-known “MEGNO Chaos Indicator”. Finally, we discuss about TNOs which are currently located at these resonances.

Analysis of Initial Deployment Strategy for Low-Orbit Large-Scale Constellations

With the development of commercial space technology, low-orbit large-scale satellite constellation has shown great development potential in communication services and military applications due to its advantages of low delay, strong signal, high coverage rate, fast communication rate, and low cost of mass production. It has become an urgent problem in the field of satellite constellations to study the perturbation evolution law of low-orbit large-scale constellation initialization and orbit maintenance, and how to maintain and control the deployment and initialization of low-orbit satellite constellations efficiently, economically, and stably. In this paper, the satellite motion law, constellation configuration evolution characteristics, and constellation initialization control strategy are analyzed considering the perturbation of earth’s nonspherical gravity and atmospheric drag under the orbit deviation of satellite orbit elements. Firstly, MonteCarlo simulation was used to simulate the deviation of satellite initial orbit elements, and the evolution law of ascending ascension point and phase angle of different constellations was analyzed and, secondly, establish the initialization phase constellation deployment and the ascending node right ascension deployment of mathematical equations, using Starlink constellation (V1.0-L3, 8) satellite TLE data; initialization of Leo constellation orbit plane is analyzed, by considering the orbit bias satellite simulation data; the same orbital plane satellite initialization phase deployment method is analyzed; finally, this paper provides some suggestions for the future deployment and maintenance control strategy of low-orbit constellation.

Radiation from axion star-neutron star binaries with a tilted rotation axis in the presence of plasma

We investigate the form of the radiation emitted by an axion star-neutron star binary using a f(r) = sech(r/R) profile for the axion star. Our analysis takes into account the co-rotating plasma of the neutron star. We find that there is significant enhancement to the radiated power if the neutron star’s spin is tilted towards the plane of the axion star-neutron star orbit, compared to the case where it is perpendicular. We also examine whether the neutron star’s co-rotating plasma can play a role in the emitted power and we find that even though dilute axion stars can in principle radiate more efficiently than dense axion stars, they will be pulled apart by the tidal forces of the neutron star.

Attitude Stability Analysis and Configuration Design of Pyramid Drag Sail for Deorbit Missions

Deorbit disposal of constellation satellites at the end of their operational lifetime is considered a necessary task to maintain the safety and sustainability of low Earth orbit (LEO). In LEO region, especially below 800 km, the drag sail device emerges as one of the most promising techniques to accelerate the deorbit process by the advantages of atmospheric drag. In this paper, an attitude-orbit coupled dynamics model is established for satellites equipped with pyramid drag sail devices. The number and length of support booms, the flare angle, and the initial orbital height are not limited, so that the obtained model could describe a number of drag sail systems. Then, by simplifying the attitude dynamics model in the orbital plane and considering circular orbit motions, a key parameter is proposed to evaluate the stability of the drag sail system. With this parameter, the influence of geometries on the attitude stability is analyzed for pyramid drag sails, and further conclusions about the optimal configurations are obtained from the analysis results. Finally, numerical simulations with the attitude-orbit coupled dynamics model are conducted to verify the conclusions drawn from the key parameter, and optimal configurations under three different conditions are obtained as well as simulated with deorbit missions to show the optimality. The results from this work would offer theoretical guidance to the configuration design of drag sail systems in application.

Observable tests for the light-sail scenario of interstellar objects

Context.Enigmatic dynamical and spectral properties of the first interstellar object (ISO), 1I/2017 U1 (Oumuamua), led to many hypotheses, including a suggestion that it may be an “artificial” spacecraft with a thin radiation-pressure-driven light sail. Since similar discoveries by forthcoming instruments, such as theVera C. Rubintelescope and the Chinese Space Station Telescope (CSST), are anticipated, a critical identification of key observable tests is warranted for the quantitative distinctions between various scenarios.Aims.We scrutinize the light-sail scenario by making comparisons between physical models and observational constraints. These analyses can be generalized for future surveys of ‘Oumuamua-like objects.Methods.The light sail goes through a drift in interstellar space due to the magnetic field and gas atoms, which poses challenges to the navigation system. When the light sail enters the inner Solar System, the sideways radiation pressure leads to a considerable non-radial displacement. The immensely high dimensional ratio and the tumbling motion could cause a light curve with an extremely large amplitude and could even make the light sail invisible from time to time. These observational features allow us to examine the light-sail scenario of interstellar objects.Results.The drift of the freely rotating light sail in the interstellar medium is ~100 au even if the travel distance is only 1 pc. The probability of the expected brightness modulation of the light sail matching with ‘Oumuamua’s observed variation amplitude (~2.5–3) is &lt;1.5%. In addition, the probability of the tumbling light sail being visible (brighter thanV= 27) in all 55 observations spread over two months after discovery is 0.4%. Radiation pressure could cause a larger displacement normal to the orbital plane for a light sail than that for ‘Oumuamua. Also, the ratio of antisolar to sideways acceleration of ‘Oumuamua deviates from that of the light sail by ~1.5σ.Conclusions.We suggest that ‘Oumuamua is unlikely to be a light sail. The dynamics of an intruding light sail, if it exists, has distinct observational signatures, which can be quantitatively identified and analyzed with our methods in future surveys.