Orbital Plane Research Articles

Families of Planar Orbits in Polar Coordinates Compatible with Potentials

In light of the planar inverse problem of Newtonian Dynamics, we study the monoparametric family of regular orbits f(r,θ)=c in polar coordinates (where c is the parameter varying along the family of orbits), which are generated by planar potentials V=V(r,θ). The corresponding family of orbits can be uniquely represented by the “slope function” γ=fθfr. By using the basic partial differential equation of the planar inverse problem, which combines families of orbits and potentials, we apply a new methodology in order to find specific potentials, e.g., V=A(r)+B(θ) or V=H(γ) and one-dimensional potentials, e.g., V=A(r) or V=G(θ). In order to determine such potentials, differential conditions on the family of orbits f(r,θ) = c are imposed. If these conditions are fulfilled, then we can find a potential of the above form analytically. For the given families of curves, such as ellipses, parabolas, Bernoulli’s lemniscates, etc., we find potentials that produce them. We present suitable examples for all cases and refer to the case of straight lines.

TIC 435850195: The Second Triaxial Tidally Tilted Pulsator

The Transiting Exoplanet Survey Satellite (TESS) has enabled the discovery of numerous tidally tilted pulsators (TTPs), which are pulsating stars in close binaries where the presence of a tidal bulge has the effect of tilting the primary star’s pulsation axes into the orbital plane. Recently, the modeling framework developed to analyze TTPs has been applied to the emerging class of triaxial pulsators, which exhibit nonradial pulsations about three perpendicular axes. In this work, we report on the identification of the second-ever discovered triaxial pulsator, with 16 robustly detected pulsation multiplets, of which 14 are dipole doublets separated by 2ν orb. We jointly fit the spectral energy distribution and TESS light curve of the star, and find that the primary is slightly evolved off the zero-age main sequence, while the less massive secondary still lies on the zero-age main sequence. Of the 14 doublets, we associate eight with Y 10x modes and six with novel Y 10y modes. We exclude the existence of Y 11x modes in this star and show that the observed pulsation modes must be Y 10y . We also present a toy model for the triaxial pulsation framework in the context of this star. The techniques presented here can be utilized to rapidly analyze and confirm future triaxial pulsator candidates.

Estimating the Orbital Parameters of a Nanosatellite When Measuring the Total Electron Content in the Ionosphere Based on the Retransmission of GPS Navigation Signals

A method for estimating the orbital parameters of a nanosatellite-relay, implemented by measuring the total electron content in the ionosphere based on relaying GPS navigation signals at frequencies of 150/400 MHz, is substantiated. The method involves estimating the Cartesian coordinates of the nanosatellite-relay based on the results of measurements of the total ranges “navigation satellite – nanosatellite relay – ground receiving point”, obtaining estimates of the orbital plane inclination angle and the longitude of the ascending node using the least squares method, and estimating the remaining orbital parameters using the maximum likelihood method. Simulation results and accuracy characteristics of the proposed method are presented. It is shown that for a typical signal-to-noise ratio in the equipment of the receiving point and an observation time of the nanosatellite-relay of 600–800 s, the mean square errors in estimating the orbital parameters of the nanosatellite-relay are: for angular quantities – fractions of arc seconds, the semi-major axis of the ellipse – 4–5 m, eccentricity – 2–3 ppm.

Polar alignment of a dusty circumbinary disc–II. Application to 99 Herculis

ABSTRACT We investigate the formation of dust traffic jams in polar-aligning circumbinary discs. In our first paper, we found as the circumbinary disc evolves towards a polar configuration perpendicular to the binary orbital plane, the differential precession between the gas and dust components leads to multiple dust traffic jams. These dust traffic jams evolve to form a coherent dust ring. In part two, we use 3D smoothed particle hydrodynamical simulations of gas and dust to model an initially highly misaligned circumbinary disc around the 99 Herculis (99 Her) binary system. Our results reveal that the formation of these dust rings is observed across various disc parameters, including the disc aspect ratio, viscosity, surface density power-law index, and temperature power-law index. The dust traffic jams are long-lived and persist even when the disc is fully aligned polar. The midplane dust-to-gas ratio within the rings can surpass unity, which may be a favourable environment for planetesimal formation. Using 2D inviscid shearing box calculations with parameters from our 3D simulations, we find streaming instability modes with significant growth rates. The streaming instability growth time-scale is less than the tilt oscillation time-scale during the alignment process. Therefore, the dust ring will survive once the gas disc aligns polar, suggesting that the streaming instability may aid in forming polar planets around 99 Her.

The Spider Stellar Engine: a Fully Steerable Extraterrestrial Design?

A long-lived civilization will inevitably have to migrate towards a nearby star as its home star runs out of nuclear fuel. One way to achieve such a migration is by transforming its star into a stellar engine, and to control its motion in the galaxy. We first provide a brief overview of stellar engines and conclude that looking for technosignatures of stellar engines has taken two roads: on the observational side, hypervelocity stars have been the target of such searches, but without good candidates. On the theoretical side, stellar engine concepts have been proposed but are poorly linked to observable technosignatures. Since about half the stars in our galaxy are in binary systems where life might develop too, we introduce a model of a binary stellar engine. We propose mechanisms for acceleration, deceleration, steering in the orbital plane and outside of the orbital plane. We apply the model to candidate systems, spider pulsars, which are binary stars composed of one millisecond pulsar and a very low-mass companion star that is heavily irradiated by the pulsar wind. We discuss potential signatures of acceleration, deceleration, steering, as well as maneuvers such as gravitational assists or captures. Keywords: Pulsars: Spiders, Technosignatures, Stellar engine, Interstellar travel

Could very low-metallicity stars with rotation-dominated orbits have been driven by the bar?

The most metal-poor stars ( Fe/H are the ancient fossils from the early assembly epoch of our Galaxy. They very likely formed before the the thick disk. Recent studies have shown that a non-negligible fraction of them have prograde planar orbits, which means that their origin is a puzzle. It has been suggested that a later-formed rotating bar could have driven these old stars from the inner Galaxy outward and transformed their orbits so that they became more dominated by rotation. However, it is unclear whether this mechanism can explain these stars as observed in the solar neighborhood. We explore whether this scenario is feasible by tracing these stars backward in an axisymmetric Milky Way potential with a bar as perturber. We integrated their orbits backward for 6 Gyr under two bar models: one model with a constant pattern speed, and the other with a decelerating speed. Our experiments show that for the constantly rotating bar model, the stars of interest are little affected by the bar and cannot have been driven from a spheroidal inner Milky Way to their current orbits. In the extreme case of a decelerating bar, some of the very metal-poor stars on planar and prograde orbits can be brought from the inner Milky Way, but $ of them were nevertheless already dominated by rotation phi $ geq 1000 km s$^ $ kpc) 6 Gyr ago. The chance that these stars started with spheroid-like orbits with low rotation ($J_ phi $ lesssim 600 km s$^ $ kpc) is very low ($<$ 3$<!PCT!>$). We therefore conclude that within the solar neighborhood, the bar is unlikely to have shepherded a significant fraction of spheroid stars in the inner Galaxy to produce the overdensity of stars on prograde planar orbits that is observed today.

Research on Design and Staged Deployment of LEO Navigation Constellation for MEO Navigation Satellite Failure

Low Earth orbit (LEO) satellites have unique advantages in navigation because of their high signal intensity and rapid geometric changes in a short period. In order to solve the problem of constellation performance degradation after a potential failure pertaining one or more medium Earth orbit (MEO) navigation satellites, this paper designs the LEO navigation constellation and considers the task requirements of different stages of constellation deployment. Firstly, the LEO navigation constellation is designed by a non-dominated sorting genetic algorithm II (NSGA-II). The average position dilution of precision (PDOP) is 1.676, which is an improvement compared to the average PDOP offered by the four traditional GNSS. Secondly, the staged deployment of constellation takes into account the degradation of constellation performance caused by the failure of MEO navigation satellites, and the Monte Carlo method is used to analyze the case of three simultaneous satellite failures. The results show that a single satellite failure within each orbital plane and adjacent satellites with close phase separation has a great impact on the performance of the MEO navigation constellation. On this basis, a staged deployment strategy was adopted in order to balance cost, risk, and performance. The three phases deploy 66, 156, and 288 satellites, respectively; as a make-up constellation under contingencies, a navigation enhancement constellation, and an independent navigation constellation, the deployment of the staged sub-constellations meets the mission requirements. The constellation design and staged deployment method proposed in this paper can provide reference for the future study of LEO navigation constellations.

Spin-orbit alignment in very low mass tight binaries: results for the 2MASS J0746425+200032AB and 2MASS J1314203+132001AB systems using spectroscopic and optically derived rotational estimates

Context. Constraining the coplanarity status of very low mass (VLM) tight binary systems provides valuable information towards understanding the dominant mechanisms in star and planetary formation at the lower end of the initial mass function. Aims. We sought to constrain the v sin i degeneracies of two nearby tight VLM binary systems, 2MASS J0746+20AB and 2MASS J1314+13AB, by independently determining each companion’s rotational period and so characterize each system’s spin-orbit alignment. Methods. Long observational baseline high cadence I band photometry data were obtained for both systems using the Galway Ultra Fast Imager (GUFI) on the Mount Graham International Observatory’s Vatican Advanced Technology Telescope. Previously known rotational periods determined in other passbands were used as a basis for recovering additional periodic modulations in the time-series data. Results. Using the known rotational period of 3.32 hours for 2MASS J0746425+200032A, we recovered an underlying periodic modulation of 2.14 ± 0.11 hours, which we associate with 2MASS J0746425+200032B. Breaking each components’ v sin i corresponds to equatorial inclination angles of 32 ± 4 degrees and 37 ± 4 degrees for components A & B respectively. We recover a weaker 2.06 ± 0.05 hours modulation separate from the known 3.79 hour signature for J1314203+132001B, which we associate with J1314203+132001A. We place a lower limit on J1314203+132001A’s equatorial inclination angle to be in the range of 24.5−3+3.5 degrees, which deviates from the system’s orbital plane previously determined to be 49.34−0.23+0.28 degrees. Conclusions. We confirm long term, consistent periodic modulations from both binary systems and report the first definitive rotational period for J1314203+132001A of 2.06 ± 0.05 hours, in addition to coplanarity to within 10 degrees in the spin-orbit alignment of the 2MASS J0746425+200032AB system. The lack of separate v sin i values for the 2MASS J1314203+132001AB system limits a definitive assessment but best estimates suggest coplanarity to be unlikely.

On the Value of High Precision Radial Velocity Observations and Astrometric Orbits for Binary Stars Hosting Exoplanets

Observations have concluded that exoplanet hosting binary stars appear to have wider mean separations than a definitive sample of “field binaries” as well as an apparent deficit of very close pairs. Many exoplanets orbit near their host stars equatorial plane, especially for close-in, small planets. Precision radial velocities of exoplanets in close binary stars are sparse but badly needed in order to provide statistical samples revealing the host stars spin axis and determinations of the masses and orbital planes of their planets. Astrometric orbits of the stars can provide precise binary orbital elements. In the quest for occurrence rates, the detection of planets is biased against transit recognition of small planets in binary systems. Together the measurements of binary host stars and their planets are required to yield robust tests of planet formation, stability, and evolution mechanisms as well as provide correct small planet occurrence rates.

Studying geometry of the ultraluminous X-ray pulsar Swift J0243.6+6124 using X-ray and optical polarimetry

Discovery of pulsations from a number of ultra-luminous X-ray (ULX) sources proved that accretion onto neutron stars can produce luminosities exceeding the Eddington limit by several orders of magnitude. The conditions necessary to achieve such high luminosities as well as the exact geometry of the accretion flow in the neutron star vicinity are, however, a matter of debate. The pulse phase-resolved polarization measurements that became possible with the launch of the Imaging X-ray Polarimetry Explorer (IXPE) can be used to determine the pulsar geometry and its orientation relative to the orbital plane. They provide an avenue to test different theoretical models of ULX pulsars. In this paper we present the results of three IXPE observations of the first Galactic ULX pulsar Swift J0243.6+6124 during its 2023 outburst. We find strong variations in the polarization characteristics with the pulsar phase. The average polarization degree increases from about 5<!PCT!> to 15<!PCT!> as the flux dropped by a factor of three in the course of the outburst. The polarization angle (PA) as a function of the pulsar phase shows two peaks in the first two observations, but changes to a characteristic sawtooth pattern in the remaining data set. This is not consistent with a simple rotating vector model. Assuming the existence of an additional constant polarized component, we were able to fit the three observations with a common rotating vector model and obtain constraints on the pulsar geometry. In particular, we find the pulsar angular momentum inclination with respect to the line of sight of $i_ p the magnetic obliquity of $ p and the pulsar spin position angle of $ p which significantly differs from the constant component PA of about 10 Combining these X-ray measurements with the optical PA, we find evidence for at least a 30 misalignment between the pulsar angular momentum and the binary orbital axis.

Analytical and Numerical Analysis of Circumbinary Disk Dynamics. I. Coplanar Systems

We present an analytical and numerical study of a system composed of a stellar binary pair and a massless, locally isothermal viscous accretion disk that is coplanar to the binary orbital plane. Analytically, we study the effect of the binary’s gravitational potential over short timescales through the stability of epicyclic orbits, and over long timescales by revisiting the concept of resonant torques. Numerically, we perform two-dimensional Newtonian simulations of the disk-binary system over a range of binary mass ratios. We find that the results of our simulations are consistent with those of previous numerical studies. We additionally show, by comparison of the analytical and numerical results, that the circumbinary gap is maintained on the orbital timescale through the driving of epicyclic instabilities, and does not depend on resonant torquing, contrary to the standard lore. While our results are applicable to any disk-binary system, we highlight the importance of this result in the search for electromagnetic and gravitational-wave signatures from supermassive black hole binaries.

Single track orbit determination analysis for low Earth orbit with approximated J2 dynamics

In the domain of Space Situational Awareness (SSA), the challenges related to orbit determination and catalog correlation are notably pronounced, exacerbated by data scarcity. This study introduces an initial orbit determination methodology that relies on data obtained from a single surveillance radar, with the need for fast algorithms within an operational context serving as the main design driver. The result is a linearized least-squares fitting procedure incorporating an analytically formulated approximation of the dynamics under the J2 perturbation, valid for short-term propagation. This algorithm utilizes all available observables, including range-rate, distinguishing it from other similar methods. A significant contribution of this paper is the enhancement of estimation quality by incorporating information about the object’s predicted orbital plane into the methodology, a method denoted as OPOD. The proposed methods are evaluated through a series of simulations against a classical range and angles fitting method (GTDS) to examine the effects of track length and measurement density on the quality of full state estimation, including the impact of using arcs that are too short. The OPOD methodology shows promising results throughout a wide range of scenarios.

Trajectory optimization of near-Earth asteroids exploration by using reusable probes from cislunar space

Implementing the flyby to Near-Earth Asteroids (NEAs) with the potential impact risks to the Earth allows for obtaining detailed physical parameters, thereby supporting the high-precision orbit prediction and planetary defense strategy. Different from those conducted asteroid flyby missions, in the 12th China Trajectory Optimization Competition (CTOC-12), a NEAs flyby trajectory design problem using reusable probes that depart from a Lunar Distant Retrograde Orbit (DRO) station in the cislunar space was released. The objective was flyby to as many NEAs as possible using up to 20 probes within a total of 10 years. The ∑ team proposed a solution that can explore 47 NEAs using 11 probes, ranking the first in the competition. In this paper, the methods and results from the winning team are introduced, including mission analysis and preliminary design, and low-energy transfer trajectory optimization. In particular, a round-trip trajectory is divided into three phases: deep space transfer, indirect transfer between the Earth to DRO, and DRO phasing and rendezvous. With the combination of global optimization and local optimization algorithms, the required velocity increments to change the orbital planes are effectively reduced, thus increasing the number of the explored NEAs. The final solution of our team is presented and the results are compared with those of the top three teams. The competition demonstrates that the regularization of flyby missions from the cislunar space to explore NEAs with the potential impact risks to the Earth is the feasible and promising.

Discrete search-based determination of a local orbital frame in unknown environments

A local orbital frame is an important and often applied coordinate frame in attitude and orbit control. Usually, a navigation filter estimates the position and velocity vector, which are used to build up this reference frame. It is beneficial for many space applications, such as communication or Earth observation missions, or for conducting orbit control maneuvers to change the orbit plane. Furthermore, satellite formation flying can require an orbital frame to describe relative motion. This work investigates the feasibility of determining the local-vertical local horizontal (LVLH) frame without full knowledge of the orbit. This scenario often applies to non-characterized small bodies like asteroids or comets. A discrete search method is used to determine the complete LVLH frame in real-time, assuming that one axis, a line-of-sight vector to the body’s center of mass, is known. By minimizing an objective function, the remaining axes can be determined. The estimated parameters are the inclination and the right ascension of the ascending node of the osculating orbit plane. This study investigates the feasibility of this concept and then applies it to perturbed orbits and sensor noise. The proposed method demonstrates that a discrete search can determine the LVLH frame. The approach can be seen as a step toward increasing the autonomy of a spacecraft near small bodies with unknown environments.

Novel Insights on the Dust Distribution in the Zodiacal Dust Cloud from PSP/WISPR Observations at Large Elongations

The Wide-Field Imager for Solar Probe (WISPR) on the Parker Solar Probe (PSP) mission maps the brightness produced by the zodiacal dust cloud (ZDC) from an historically unprecedented viewpoint. The brightness results from the scattering of photospheric light by dust particles in the ZDC, and is called zodiacal light (ZL). We exploit the PSP nominal science encounters in orbits 10 through 16 for an in-depth study of the location and brightness evolution of the symmetry axis of the ZL in images taken with the WISPR outer telescope (WISPR-O). During these 11 day encounters, PSP covered heliocentric distances between 0.25 and 0.0617 au (∼53.78−13.28 R ☉) and ∼255° in helioecliptic longitude from within the orbital plane of Venus. The unique WISPR-O viewpoint, which comprises line-of-sight elongations of 80° ± 27°, has led to further insights about the ZDC. Namely, we find that the gravitational pull of the planets warps the ZDC symmetry plane and shifts the ZDC towards the solar system barycenter, creating an east–west asymmetry in the ZL brightness. Additionally, our analysis provides the first consistent observational evidence of a circumsolar dust enhancement resulting from the sublimation of dust grains at ∼25 R ☉. Overall, the WISPR observations from the PSP platform are opening a new window in the remote sensing of the ZDC.

Less fuel strategies for space debris removal in Low Earth Orbit

This paper proposes less fuel strategies for space debris removal. To mitigate the risk of space debris cost-efficiently, multi-rendezvous missions are under development. On the other hand, multi-rendezvous missions often require changing orbital planes of removal satellites, which requires a huge amount of ΔV. Therefore, this study focuses on exploiting the J2 perturbation force as an auxiliary force and aims to establish maneuver rules that minimize ΔV consumption while maximizing the benefit of the J2 perturbation. The J2 perturbation equation is explored analytically, which clarifies whether the change in the semi-major axis or the inclination dominates the efficiency of the exploitation. A straightforward criterion is extracted which determines the efficient maneuver based on the initial inclination of the satellite.

Characterization of the δ Scuti eclipsing binary KIC 4851217 and its tertiary companion as well as detection of tidally tilted pulsations

Abstract Stellar theory enables us to understand the properties of stars at different stages of their evolution, and contributes to other fields of astrophysics such as galactic and exoplanet studies. Assessing the accuracy of stellar theories necessitates high precision, model-independent measurements of the properties of real stars, such as those obtainable for the components of double lined eclipsing binaries (DLEBs), while asteroseismology offers probing power of the stellar interior if one or both components pulsate. KIC 4851217 is a DLEB containing two late A-type stars and exhibits pulsations of the δ Scuti type. By analysing high resolution HERMES and moderate resolution ISIS spectra, jointly with Kepler and TESS light curves, we measured the masses, radii and effective temperatures of the components to precisions of ∼0.5, ∼1.1 and ∼1 per cent, respectively. We additionally report the discovery and characterisation of a tertiary M-dwarf companion. Models of the system’s spectral energy distribution agree with an age of 0.82 Gyr, with the more massive and larger secondary component near the end of the main sequence lifetime. An examination of the pulsating component’s pulsation frequencies reveals 39 pulsation multiplets that are split by the orbital frequency. For most of these, it is evident that the pulsation axes have been tilted into the orbital plane. This makes KIC 4851217 a tidally tilted pulsator (TTP). This precisely characterized δ Scuti DLEB is an ideal candidate for advancing intermediate-mass stellar theory, contributing to our understanding of hierarchichal systems as well as to the topic of TTPs.

Binary craters on Ceres and Vesta and implications for binary asteroids

Context. Airless planetary objects have their surfaces covered by craters, and these can be used to study the characteristics of asteroid populations. Planetary surfaces present binary craters that are associated with the synchronous impact of binary asteroids. Aims. We identify binary craters on asteroids (1) Ceres and (4) Vesta, and aim to characterize the properties (size ratio and orbital plane) of the binary asteroids that might have formed them. Methods. We used global crater databases developed in previous studies and mosaics of images from the NASA DAWN mission high-altitude and low-altitude mapping orbits. We established selection criteria to identify craters that were most likely a product of the impact of a binary asteroid. We performed numerical simulations to predict the orientation of the binary craters assuming the population of impactors has mutual orbits coplanar with heliocentric orbits, as the current census of binary asteroids suggests. We compared our simulations with our survey of binary craters on Ceres and Vesta through a Kolmogorov-Smirnov test. Results. We find geomorphological evidence of 39 and 18 synchronous impacts on the surfaces of Ceres and Vesta, respectively. The associated binary asteroids are widely separated and similar in diameter. The distributions of the orientation of these binary craters on both bodies are statistically different from numerical impact simulations that assume binary asteroids with coplanar mutual and heliocentric orbits. Conclusions. Although the identification of binary craters on both bodies and the sample size are limited, these findings are consistent with a population of well-separated and similarly sized binary asteroids with nonzero obliquity that remains to be observed, in agreement with the population of binary craters identified on Mars.

The dynamics around the collinear points of the elliptic three-body problem: A normal form approach

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating–pulsating barycentric frame, taking the true anomaly as independent variable. We consider the Hamiltonian modeling this problem in the extended phase space and we implement a normal form to make a center manifold reduction. The normal form provides an approximate solution for the Cartesian coordinates, which allows us to construct several kinds of orbits, most notably planar and vertical Lyapunov orbits, and halo orbits. We compare the analytical results with a numerical simulation, which requires special care in the selection of the initial conditions.

Extended Lambert-Based Approach for Ground-Track Adjustment with Specified Overflight Altitude

This paper presents an extended Lambert-based approach for ground-track adjustment under J2 perturbation, aiming to achieve a satellite flyby over a designated ground location at a predetermined altitude. Extended equations are developed in the orbital plane based on Lagrange’s form for the unperturbed Lambert’s problem to address the J2-perturbed two-body motion. By combining them with the out-of-plane flight time equation constraint regarding the ground-track adjustment, a nonlinear system of equations with two unknowns and two equations is established and split into different modes. To solve these modes, a modified Newton–Raphson method is used, and a necessary condition is established to determine the maximum allowable number of revolutions. To enhance computational efficiency, a radius restriction method is proposed to narrow down the allowable range of the number of revolutions. The proposed algorithm is applicable to various scenarios, including single- or multiple-day flights, ascending or descending overflights, coplanar or non-coplanar transfers, and initial or reverse-initial directional transfers. The simulation results demonstrate that the proposed algorithm is effective and accurate for the perturbed adjustment problem.