Elliptical Orbit Research Articles

Solution Space of Minimum-Time Low-Thrust Rephasing in Elliptical Orbit

Solution Space of Minimum-Time Low-Thrust Rephasing in Elliptical Orbit

Determination of the SO/PHI-HRT wavefront degradation using multiple defocused images

Context. The Polarimetric and Helioseismic Imager on board the Solar Orbiter mission (SO/PHI) offers refocusing capabilities to cope with the strongly varying thermal environment of the optical system along the spacecraft’s elliptical orbit. The series of images recorded during in-flight focus calibrations can be employed for phase diversity analyses. Aims. In this work we infer the wavefront degradation caused by the thermo-optical effects in the High Resolution Telescope (HRT) from images taken during the fine and coarse focus scans performed in the commissioning phase of the instrument. The difference between these two series of images are mainly related to the employed defocused step (smaller for the fine scans) and the signal-to-noise ratio (higher for the coarse scans). We use the retrieved wavefronts to reconstruct the original scene observed during the calibration of the instrument. Methods. We applied a generalized phase diversity algorithm that allowed us to use several images taken with different amounts of defocus to sense the wavefront degradation caused by the instrument. The algorithm also uses information from both the inferred wavefront and the series of images to restore the solar scene. Results. We find that most of the retrieved Zernike coefficients tend to converge to the same value when increasing the number of images employed for PD for both the fine and the coarse focusing scans. The restored scenes also show signs of convergence, and the merit function is minimized more as K increases. Apart from a defocus, the inferred wavefronts are consistent for the two datasets (λ/10 − λ/11). For the fine scan images, the quiet-sun contrast improves from 4.5% for the original focused image up to about 10%. For the coarse scan images, the contrast of the restored scene is as high as 11%.

Optimal Impulsive Rendezvous for Approaching Geostationary Earth Orbit Targets with Terminal Configuration Constraints

This paper explores multi-impulse trajectory design for approaching Geostationary Earth Orbit (GEO) targets, emphasizing the attainment of a 2:1 elliptical relative orbit for close inspection. The intricate optimization challenge includes dynamic and terminal constraints, as well as total mission duration limitations. Critical variables like transfer duration, impulse count, timing, and entry point are optimized using genetic algorithms to minimize velocity increment requirements. These optimal values are influenced by uncertain terminal states constrained by the 2:1 circling orbit. To address these complexities, the paper leverages a linear state transition matrix from relative orbital dynamics to formulate a multi-impulse optimization model. Additionally, a differential correction-based iterative approach mitigates nonlinear dynamics’ impact on terminal rendezvous errors. Through theoretical analysis and simulations, the study elucidates variations in optimization criteria, particularly in GEO missions with multiple impulses, and identifies optimal entry points for different impulse counts. The proposed models and methodologies offer theoretical insights for future GEO orbit approaching missions and potential applications in various space maneuver tasks.

On Bifurcations of Symmetric Elliptic Orbits

On Bifurcations of Symmetric Elliptic Orbits

Inserting a Maximum-Mass Spacecraft into a Target Orbit Using a Limited-Thrust Engine with Releasing the Separable Part of Its Launch Vehicle into the Earth’s Atmosphere

—Space debris is an urgent problem of our time. This paper considers the idea of reducing near-Earth space debris by releasing the spent additional fuel tank (AFT) and the booster’s central block (CB) into the Earth’s atmosphere. The spacecraft transfer from a reference circular orbit of an artificial Earth satellite to a target elliptical orbit is optimized. The transition maneuvers are carried out using a booster with a high limited-thrust engine and the AFT. The second zonal harmonic of the Earth’s gravitational field is taken into account. The optimal control problem is solved based on Pontryagin’s maximum principle. Bulky derivatives are calculated using a specially developed numerical-analytical differentiation technique. The Pontryagin extremals obtained below are the next step in implementing the problem hierarchy methodology.

Can We Intercalibrate Satellite Measurements by Means of Data Assimilation? An Attempt on LEO Satellites

AbstractLow Earth Orbit satellites offer extensive data of the radiation belt region, but utilizing these observations is challenging due to potential contamination and difficulty of intercalibration with spacecraft measurements at Highly Elliptic Orbit that can observe all equatorial pitch‐angles. This study introduces a new intercalibration method for satellite measurements of energetic electrons in the radiation belts using a Data assimilation (DA) approach. We demonstrate our technique by intercalibrating the electron flux measurements of the National Oceanic and Atmospheric Administration (NOAA) Polar‐orbiting Operational Environmental Satellites (POES) NOAA‐15,‐16,‐17,‐18,‐19, and MetOp‐02 against Van Allen Probes observations from October 2012 to September 2013. We use a reanalysis of the radiation belts obtained by assimilating Van Allen Probes and Geostationary Operational Environmental Satellites observations into 3‐D Versatile Electron Radiation Belt (VERB‐3D) code simulations via a standard Kalman filter. We compare the reanalysis to the POES data set and estimate the flux ratios at each time, location, and energy. From these ratios, we derive energy and L* dependent recalibration coefficients. To validate our results, we analyze on‐orbit conjunctions between POES and Van Allen Probes. The conjunction recalibration coefficients and the data‐assimilative estimated coefficients show strong agreement, indicating that the differences between POES and Van Allen Probes observations remain within a factor of two. Additionally, the use of DA allows for improved statistics, as the possible comparisons are increased 10‐fold. Data‐assimilative intercalibration of satellite observations is an efficient approach that enables intercalibration of large data sets using short periods of data.

Imaging Algorithm for Sliding Spotlight SAR Operating in the Ascending and Descending Periods of Highly Elliptical Orbits

Imaging Algorithm for Sliding Spotlight SAR Operating in the Ascending and Descending Periods of Highly Elliptical Orbits

Creation of a simulation model of a solar battery

The article describes the process of creating a BS simulation model. The object of the study is the BS, which is part of the STAGE of a spacecraft placed in a highly elliptical orbit of an artificial Earth satellite. When creating a simulation model, the BS was formed by photovoltaic devices (PV) made of helium arsenide (AG), the efficiency of which is 27 %. When creating the simulation model, the following parameters were taken into account: the no- load voltage of the illuminated BS, at a steady temperature when the spacecraft leaves the Earth's shadow of the maximum duration with a deviation of the normal to the surface of the BS from the direction to the Sun, as well as a change in the output current. Also, when creating the model, the effects of external factors are taken into account, such as: a decrease in external atmospheric pressure, changes in the temperature of the BS during the passage of the spacecraft shadow sections of the orbit, ionizing radiation of the KP during interaction with magnetospheric plasma, shadowing by spacecraft structures, and others.

Taboo and dynamic framing in the media coverage of gang rape: the Ayia Napa case

The study examines the media coverage of the case of suspected gang rape in Aiya Napa, Cyprus in the summer of 2019. The research question examined how the media covered this event while giving expression to various representations through dynamic framing. The study analyzed some 30 reports in the main news edition on two Israeli television channels using an original model developed for this study: The Dynamic Media Coverage Spectrum around the Moral Nucleus (M.S.M) presenting the movement of media coverage around the moral nucleus: the social taboo against gang rape. Reporting was found to move in three elliptical orbits around the taboo: first, who is to blame, second, the law against the norm, and third, dynamic movement around positioning semantics. The study reveals different narratives chosen to frame the event, using gender, status, identity, and ethnic affiliation of participants and the geopolitics of the case. The findings show, a critical public discourse must be developed regarding the messages the media communicate regarding sexual offenses and advantages through the MSM model analysis.

Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

This work proposes a saturation control scheme for underactuated spacecraft formation reconfiguration in elliptic orbits without radial or along-track thrust. Firstly, the rank criterion method is applied to analyze the controllability and feasibility of formation reconfiguration by linearizing the linear time-varying dynamics to linear time-invariant ones. Based on the inherent coupling of the linear time-varying system, the underactuated error dynamics are presented for either underactuated case. Subsequently, the developed underactuated saturation controller can ensure that the time-varying system trajectory asymptotically converges to the specified configuration. The Lyapunov-based analysis presents the constraint conditions of controller parameters and the stable reconfiguration accuracy of the system states. Finally, numerical simulations for both underactuated scenarios are performed in the environment with J2 perturbation to verify the validity of the proposed underactuated control scheme.

The Precession of Perihelion over Modification of Newton Gravity

In this paper the idea is revised how the metric in flat Minkowskian spacetime gets transformed from one coordinates system to another after successive Lorentz transformations. And likewise this idea is generalized to achieve the metric transformation from one curved spacetime to another. The introduction of mass perturbed the initial flat space time in to curved spacetime, here the corresponding perturbed metric assumed as point-to-point infinitesimal quasi Lorentz transformation of the Minkowski metric. For multiple sources the manifestation of perturbed metric is formulated performing the successive quasi-Lorentz transformations in non-Euclidean curved spacetime. This interactive model for multiple sources of nonlinear perturbation reveals a clear shift from Newtonian gravity. In case of gravity the synergy among the sources is obvious; interestingly this formula is checked in retrieving the unstable planetary elliptical orbit and the precession of perihelion for two body planetary systems that verifies the model.

Design of an Elliptical Orbit Constellation for High-Resolution Optical Observations over a Specific Area

Design of an Elliptical Orbit Constellation for High-Resolution Optical Observations over a Specific Area

Метод определения параметров движения космических аппаратов на основе радиоинтерферометрических измерений со сверхдлинной базой

The proposed method for measuring current navigational parameters of spacecrafts makes it possible to control them to a certain extent using a single ground-based automated station. With this the following specifics of a single-station control are taken into account: location of spacecraft spatial-time monitoring stations, geometrical interpretation of these measurements, difficulties in processing of the received information and proper selection of radio equipment required for performing such measurements. The proposed method for trajectory tracking is based on the ultra-long-baseline interferometry. Measuring base here is the distance between a ground-based radio complex and onboard radio complex of the reference spacecraft that is constantly visible by the ground-based monitoring station. Onboard radio complex can include an array of spacecrafts traveling either along elongated elliptical orbit with an apogee height of more than twenty thousand kilometers or along a 36000 km high geostationary orbit. Application of the proposed method will help extend capabilities of the space monitoring system in terms of prompt clarification of public and private catalogues of spacecrafts orbiting the Earth.

The Apparent Tidal Decay of WASP-4 b Can Be Explained by the Rømer Effect

Tidal orbital decay plays a vital role in the evolution of hot Jupiter systems. As of now, this has only been observationally confirmed for the WASP-12 system. There are a few other candidates, including WASP-4 b, but no conclusive result could be obtained for these systems as of yet. In this study, we present an analysis of new TESS data of WASP-4 b together with archival data, taking the light–time effect (LTE) induced by the second planetary companion into account as well. We make use of three different Markov chain Monte Carlo models: a circular orbit with a constant orbital period, a circular orbit with a decaying orbit, and an elliptical orbit with apsidal precession. This analysis is repeated for four cases. The first case features no LTE correction, with the remaining three cases featuring three different timing correction approaches because of the large uncertainties of the ephemeris of planet c. Comparison of these models yields no conclusive answer to the cause of WASP-4 b’s apparent transit timing variations. A broad range of values of the orbital decay and apsidal precession parameters are possible, depending on the LTE correction. However, the LTE caused by planet c can explain on its own—in full—the observed transit timing variations of planet b, with no orbital decay or apsidal precession being required at all. This work highlights the importance of continued photometric and spectroscopic monitoring of hot Jupiters.

Continuous-Thrust Reachable Set for Linear Relative Motion Near Elliptical Orbits

Continuous-Thrust Reachable Set for Linear Relative Motion Near Elliptical Orbits

Algebraic Geometry and Elliptic Integrals Approach for Calculation of the Propagation Time of a Signal Between GPS Satellites with Account of General Relativity Theory

The approach for calculating the propagation time of a signal between GPS satellites will be summarized, based on the proposed new theoretical approach in several previous publications, as well as the perspectives for future development of the theory. Topics include: 1. Basic notions of inter-satellite communications. 2. Shapiro delay formulae in General Relativity Theory - basic formalism and the necessity to extend the formalism by taking into account the satellite motion on a plane elliptic or space-distributed elliptic orbit. 3. Basic facts about the disturbed motion in celestial mechanics and the necessity to incorporate it in the theory of inter-satellite communications, accounting for General Relativity Effects. 4. Propagation time of a signal, emitted by a satellite on a plane and also space-distributed elliptical orbit in terms of zero-order elliptic integrals and respectively of higher order integrals. Proof of the real-valuedness of the propagation time for all cases as one of the criteria for the correctness of the theoretical approach. 5. New analytical algorithms for calculation of zero-order elliptic integrals in the Legendre form. Relation to two representations in the Weierstrass form. 6. The new formalism of intersecting four-dimensional null cones and the resulting physical notions of the (intersecting)) space-time interval (with the property of being positive, negative or equal to zero) and the (intersecting) geodesic distance (being only positive, because is related to the distance, travelled by light or radio signals). Proof of these properties in the general case and in some partial cases. New numerical estimate E lim > 45.002510943228 [deg], above which the space-time interval is positive and thus inter-satellite communications between satellites on one plane elliptical orbit are possible. The angular distance of 45[ deg] is typical for the disposition of 8 satellites on one orbit in the Russian satellite constellation GLON ASS, so it might be claimed that such a configuration is favourable from the point of view of inter-satellite communications (with account of GRT effects).

Numerical Simulation of Liulin-MO Instrument for Measuring Cosmic Radiation Onboard ExoMars Trace Gas Orbiter

We present the results from numerical simulation of Liulin-MO instrument for measurement of the space radiation on board Trace Gas Orbiter (TGO) satellite of ExoMars-2016 mission during its transit to Mars in April-September 2016 [Semkova J., T. Dachev, St. Maltchev, B. Tomov, Yu. Matviichuk} et al. (2015) Radiation environment investigations during ExoMars mission to Mars – objectives, experiments and instrumentation, C. R. Acad. Bulg. Sci., 68 (4), 485–496] [Semkova J., R. Koleva, V. Benghin, T. Dachev, Yu. Matviichuk et al. (2018) Charged particles radiation measurements with Liulin-MO dosimeter of FREND instrument aboard ExoMars Trace Gas Orbiter during the transit and in high elliptic Mars orbit, Icarus, 303, 53–66], using the Geant4 package. The methodology for calculating galactic cosmic rays (GCR) linear energy transfer (LET) is described. A methodology for screening false signals in the deposited energy spectra in the Liulin-MO detectors and correspondingly LET spectra is proposed. The contribution of the individual components of the spectrum of GCR in the LET spectrum is estimated. The calculated average radiation quality factor of GCR using the cleaned from false signals LET spectrum is compared with the experimental results obtained during the transit to Mars and a reasonable agreement is observed.

M5 — Mars Magnetospheric Multipoint Measurement Mission: A multi-spacecraft plasma physics mission to Mars

Mars, lacking an intrinsic dynamo, is an ideal laboratory to comparatively study induced magnetospheres, which can be found in other terrestrial bodies as well as comets. Additionally, Mars is of particular interest to further exploration due to its loss of habitability by atmospheric escape and possible future human exploration. In this context, we propose the Mars Magnetospheric Multipoint Measurement Mission (M5), a multi-spacecraft mission to study the dynamics and energy transport of the Martian induced magnetosphere comprehensively. Particular focus is dedicated to the largely unexplored magnetotail region, where signatures of magnetic reconnection have been found. Furthermore, a reliable knowledge of the upstream solar wind conditions is needed to study the dynamics of the Martian magnetosphere, especially the different dayside boundary regions but also for energy transport phenomena like the current system and plasma waves. This will aid the study of atmospheric escape processes of planets with induced magnetospheres. In order to resolve the three-dimensional structures varying both in time and space, multi-point measurements are required. Thus, M5 is a five spacecraft mission, with one solar wind monitor orbiting Mars in a circular orbit at 5 Martian radii, and four smaller spacecraft in a tetrahedral configuration orbiting Mars in an elliptical orbit, spanning the far magnetotail up to 6 Mars radii with a periapsis just outside the Martian magnetosphere of 1.8 Mars radii. We not only present a detailed assessment of the scientific need for such a mission but also show the resulting mission and spacecraft design taking into account all aspects of the mission requirements and constraints such as mass, power, and link budgets. Additionally, different aspects of the mission programmatics like a possible mission timeline, cost estimates, or public outreach are shown. The common requirements for acceptance for an ESA mission are considered. The mission outlined in this paper was developed during the Alpbach Summer School 2022 on the topic of “Comparative Plasma Physics in the Universe”.

Ellipsoidal estimation of parameters of rotational and translational motion of a non-cooperative space vehicle from visual information


 The use of near-Earth space is currently complicated by the presence of space debris objects in Earthʼs orbit, which include spent stages of launch vehicles, inoperative spacecraft, and other large and small objects associated with human activity in space. One of the elements of solving the problem of space debris is the docking and capture of an uncontrolled non-cooperative space object or spacecraft by a so-called on-orbit servicing spacecraft to carry out further actions to repair it, refuel or change its orbit. The situation is complicated by the fact that, under the influence of various factors, uncontrolled space objects are in a state of rotation. The parameters of the orbital motion of such objects are known quite accurately from measurements from the Earth. To carry out safe approach and docking, knowledge of the parameters of rotational motion, as well as the parameters of relative motion, is also required. The most general case of motion of a non-cooperative tumbling spacecraft located in an elliptical orbit is considered. It is assumed that the three-dimensional graphic model of such spacecraft is known. The servicing spacecraft (SSC) is equipped with a mono camera that takes pictures of the non-cooperative spacecraft (NSC). Based on a comparison of the characteristic features of photographs and images obtained using the graphical model, the computer vision system (CVS) determines the distance vector to the so-called graphical coordinate system, rigidly fixed on the NSC and the quaternion of its relative attitude. The specific type of CVS is not considered. It is assumed that the SSC carries out some maneuvers near the satellite. All parameters of the SSC angular motion are assumed to be known. This work considers the most general case of the relative motion of SSC and NSC. Using quaternion calculus, all basic kinematic and dynamic equations are obtained. The measured parameters are not enough to ensure safe rendezvous and docking with the NSC. The stochastic characteristics of errors of the CVS measurement are not assumed to be known and, accordingly, are not used. Only their maximum values are specified for them. We consider the use of new dynamic set-membership filter using ellipsoids to solve the problem of determining the parameters of the relative motion of the NSC which is in free uncontrolled motion. The filter can be implemented under conditions of the limited computational capability available on onboard processors. The relative motion parameters include the distance vector between the centers of mass (c.m.) of the NSC and the SSC, the relative velocity vector, the quaternion of the orientation of the main axes of inertia of the satellite relative to the inertial coordinate system, the ratio of the moments of inertia of the satellite, the vector of the position of the NSC c.m. in the graphical coordinate system. The properties of the proposed algorithm are demonstrated using numerical simulation. The results obtained are expected to be used in the development, creation and testing of a navigation system for the rendezvous and docking of the SSC, developed by a group of Ukrainian space industry enterprises under the leadership of the LLC «Kurs-orbital» (https://kursorbital.com/).

Modelling the light curves of transiting exomoons: a zero-order photodynamic agent added to the Transit and Light Curve Modeller

ABSTRACT Despite the ever-growing number of exoplanets discovered and the extensive analyses carried out to find their potential satellites, only two exomoon candidates, Kepler-1625b-i and Kepler-1708 b-i, have been discovered to date. A considerable amount of effort has been invested in the development of algorithms for modelling, searching, and detecting exomoons in exoplanetary light curves. In this work, we incorporate moon handling capabilities into the state of the art and publicly available code, the Transit and Light Curve Modeller (tlcm). The code is designed for the analysis of transiting exoplanet systems with the inclusion of a wavelet-based noise handling algorithm. Here, we present an updated version of tlcm that is capable of modelling a coplanar planet–moon system on an elliptical orbit around its host, accounting for mutual eclipses between the two bodies (and neglecting perturbative effects) – a so-called photodynamic model. The key benefit of this framework is the ability for a joint analysis of multiple planet–moon transits. We demonstrate the necessity of this software on a case study of Kepler-1625b. Similarly to prior works, we conclude that there is no firm evidence of an exomoon in that system, by showing that temporally correlated noise can mimic apparent lunar transits.