Initial Orbit Research Articles

Optimization of orbit prediction strategies for GNSS satellites

The ability to provide precise orbit prediction of Global Navigation Satellite System (GNSS) satellites is essential in a wide range of applications in space geodesy and Earth sciences, including near real-time and real-time GNSS applications, forming broadcast ephemerides, or supporting Satellite Laser Ranging stations in tracking. In this study, we evaluate the impact of orbit modeling strategies on the accuracy of orbit predictions on short (one-day), and long (multi-day) time scales, focusing on the selection of the optimal approach for handling solar radiation pressure (SRP), the effects of including pseudo-stochastic parameters, and the impact of the arc length used for the initial orbit fit. The analysis includes 300 days of predictions in 2021 and the satellites belonging to the GPS, Galileo, GLONASS, BeiDou-3, (BDS-3), and QZSS constellations. Fitting an initial 2-day orbit arc is the optimal solution for all analyzed navigation satellite constellations. When official satellite construction metadata are available, e.g. for Galileo/QZSS, the hybrid strategy of combining both empirical and physical models, i.e. the extended Empirical CODE Orbit Model (ECOM2) with box-wing models, leads to the best results. Otherwise, using only the ECOM2 is a better choice. Finally, the results indicate that for all navigation satellites, the introduction of pseudo-stochastic parameters deteriorates the prediction quality. When using the optimal prediction strategy, the 95th percentiles of the position errors after the 1st/4th/9th day of prediction are equal to 0.09/0.93/4.52, 0.22/1.71/9.69, 0.20/2.19/11.30, 0.23/1.80/9.39, 0.23/2.28/7.78m for GPS-IIF, Galileo FOC, GLONASS-M, BDS-3 CAST, and QZSS, respectively.

Optimal delta-V-based strategies in orbital pursuit-evasion games

This research investigates the orbital pursuit-evasion games with impulsive maneuvers in long-distance interception scenarios. Specifically, this paper examines the influences of escape impulses, with different directions, applied by the evader on the intercept-correction delta-v (ΔVCorr) of the pursuer that is already on an interception orbit. After obtaining the evader’s strategies based on maximizing the ΔVCorr under different circumstances, it is found that, with the knowledge of the evader’s best strategy, the pursuer could make ΔVCorr smaller by adjusting its initial interception orbit. Then, a method to modify the initial orbit with energy constraints is designed so that the pursuer can match the evader’s escape maneuver with less delta-v to prepare. Finally, this paper summarizes the best strategies of both sides after considering the initial trajectory adjustment and discusses the impact of incomplete information on tactics in orbital pursuit-evasion games.

The Mass Fallback Rate of the Debris in Relativistic Stellar Tidal Disruption Events

Highly energetic stellar tidal disruption events (TDEs) provide a way to study black hole characteristics and their environment. We simulate TDEs with the Phantom code in a general relativistic and Newtonian description of a supermassive black hole’s gravity. Stars, which are placed in parabolic orbits with different β parameters, are constructed with the stellar evolution code MESA and therefore have realistic stellar density profiles. We study the mass fallback rate of the debris and its dependence on β, stellar mass, and age as well as the supermassive black hole’s spin and the choice of the gravity description. We calculate the peak value , time to peak t peak, duration of the super-Eddington phase t Edd, time during which , early rise-time τ rise, and late-time slope n ∞. We recover the trends of , t peak, τ rise, and n ∞ with β, stellar mass, and age which were obtained in previous studies. We find that t Edd, at a fixed β, scales primarily with the stellar mass, while scales with the compactness of stars. The effect of the SMBH’s rotation depends on the orientation of its rotational axis relative to the direction of the stellar motion in the initial orbit. Encounters in prograde orbits result in narrower curves with higher , while the opposite occurs for retrograde orbits. We find that disruptions, at the same pericenter distance, are stronger in a relativistic tidal field than in a Newtonian one. Therefore, relativistic curves have higher , and shorter t peak and t Edd.

Initial Orbit Determination from Only Heading Measurements

This work introduces the problem of initial orbit determination (IOD) from only heading measurements. Such a problem occurs in practice when estimating the orbit of a spacecraft using visual odometry measurements from an optical camera. After reviewing the problem geometry, a simple solution is developed in the form of an iterative scheme on the parameters describing the orbital hodograph. Numerical results are presented for an example spacecraft in low lunar orbit. The principal intent of this brief study is to communicate the existence of a new class of IOD problem to the community and to encourage the broader study of hodographs and heading-only IOD.

Orbital evolution of satellite galaxies in self-interacting dark matter models

Dark matter self-interactions can leave distinctive signatures on the properties of satellite galaxies around Milky Way--like hosts through their impact on tidal stripping, ram pressure, and gravothermal collapse. We delineate the regions of self-interacting dark matter parameter space---specified by interaction cross section and a velocity scale---where each of these effects dominates and show how the relative mass loss depends on the satellite's initial mass, density profile, and orbit. We obtain novel, conservative constraints in this parameter space using Milky Way satellite galaxies with notably high central densities and small pericenter distances. Our results for self-interacting dark matter models, in combination with constraints from clusters of galaxies, favor either velocity-dependent cross sections that lead to gravothermal core collapse in the densest satellites or small cross sections which more closely resemble cold and collisionless dark matter.

Models and Strategies for J 2 -Perturbed Orbital Pursuit–Evasion Games

This paper discusses the modeling and solving of orbital pursuit–evasion games (OPEGs) under J 2 perturbation. The optimal long-range maneuver method under J 2 perturbation is designed, and it is proved that the effect of eccentricity can be ignored when transfer times and the Δ V budgets are fixed. It is discovered that when the inclination between the initial and target orbit is equal and is between 10° and 25°, the whole maneuver process can be simplified to a fixed-inclination transfer. Subsequently, a long-term OPEG model is provided under the assumption of fixed inclination, zero eccentricity, and impulsive thrust. Winning conditions of OPEGs under J 2 perturbation are then carefully derived, with long-time OPEG ( J 2 dominated) and short-time OPEG (traditional) separated, and typical tactics of both sides formulated and verified. These studies are further extended to the “Arrival time matching game” for maintaining/avoiding resonant arrival time under J 2 perturbation, and the advantages and disadvantages of both sides are analyzed. The models and strategies obtained in this paper can be potentially used in practical applications of OPEGs, especially for evaders that have low thrust–weight ratios and are weak in traditional short-term OPEGs.

Autonomous Lunar L1 Halo Orbit Navigation Using Optical Measurements to a Lunar Landmark

<h3>Abstract</h3> Autonomous cislunar spacecraft navigation is critical to mission success as communication to ground stations and access to global positioning system (GPS) signals could be lost. However, if the satellite has a camera of sufficient quality, geometric line-of-sight (unit vector) measurements can be made to known lunar landmarks (e.g., Tycho Crater) to provide observations that enable autonomous estimation of the position and velocity of the spacecraft. In this study, an improved batch gaussian initial orbit determination (IOD) differential corrector (DC) algorithm, based on the approximated values of the two-body f and g series, is applied to initialize a (non-conic based) circular restricted three body problem (CR3BP) extended Kalman Filter (EKF) navigator. This navigator collects geometric line-of-sight unit vector (angle only) measurements to a known location on the Moon to sequentially estimate the position and velocity of an observer spacecraft flying on an approximate southern L1 Halo orbit. In this study, it was found that the best approach is to initialize the CR3BP EKF (navigator) using the solution from the batch DC filter with at least 10 measurements taken against the perceived centroid of Tycho Crater. Thereafter, it is best to continue the navigator with subsequent measurements taken against the same center coordinates of the Tycho Crater, where these coordinates are now expressed in the CR3BP rotating frame. For successful conic-based batch filter initialization and long-term CR3BP EKF convergence, it was found that the cadence for all optical measurements should be taken at 10 minutes for a simulated measurement noise of 0.1° one sigma uncertainty about the line-of-sight measurement unit vector.

Robust Initial Orbit Determination for Surveillance Doppler-Only Radars

An initial orbit determination algorithm for surveillance Doppler-only radars with embedded quantification capabilities is presented. The method is based on a combination of Gauss' and Lambert's solvers formulated in the differential algebra framework, which provides the Taylor expansion of the state estimate with respect to the measurement uncertainties. This feature makes the approach particularly suited for handling data association problems. The first part of the paper describes the mathematical formulation of the method, while an extensive analysis of its performance and a comparison with a reference algorithm are carried out in the second part, using both simulated and real data. The proposed approach is shown to be accurate and robust and particularly suited for short-arc observations.

Spacecraft Rendezvous in Closed Keplerian Orbits Using Constant Radial Thrust Acceleration

An analytical solution for spacecraft rendezvous within closed Keplerian orbits is presented using continuous radial thrust. The two spacecraft are assumed to be initially placed within the same closed orbit with arbitrary phase angle separation. The target spacecraft is assumed to always remain in the same initial orbit. The chaser vehicle, however, uses a judiciously designed maneuver sequence comprising constant-acceleration radial thrust phases interspersed with coast phases. Importantly, the proposed maneuver design is analytically characterized by one or two (depending on whether the parking orbit is circular or elliptical, respectively) nonlinear algebraic equations that determine the time intervals for the different phases. The set of initial conditions from which rendezvous is feasible is also characterized. Additionally, orbit rotation (that is, changing the orbit argument of periapsis in plane) is also demonstrated for the elliptical parking orbit case. Finally, the remarkable emergence of the golden and silver ratios, as well as their connections to Kepler’s triangle, is demonstrated for a specific sequence of thrust and coast arcs.

Optimization of Multispacecraft Maneuvers for Mobile Target Tracking from Low Earth Orbit

This paper presents a method of planning spacecraft maneuvers for mobile target tracking. Agile, maneuverable spacecraft have been proposed as a means of modifying satellite orbits to observe discrete targets on the Earth on demand. This work adapts this concept to propose a method of using maneuverable spacecraft to observe a mobile target as it moves across the Earth. Previous work has shown the potential of such an approach to increase persistence of coverage of a moving target. This work applies a suitable optimizer to select possible maneuvers for a spacecraft, or a constellation of spacecraft, to repeatedly observe a moving target. A biased random key genetic algorithm is used, which adjusts the for each maneuver to minimize the total used and maximize target coverage over the full sequence of maneuvers. The developed method is applied to two case studies concerning monitoring of tropical storms. The results indicate that, using relatively small maneuvers, spacecraft orbits can be adjusted to improve the quantity and quality of views of a moving target. In the Typhoon Megi case study, a single spacecraft using less than is shown to double the access time and provide two additional observations of the storm eye compared with a nonmaneuvering spacecraft in an identical initial orbit. Opportunities for observations increase as the number of maneuverable spacecraft are increased, with a three-spacecraft constellation able to provide five complete observations of the storm eye for a total change in velocity of 12 m/s.

Analytical Nonlinear Observability Analysis for Spacecraft Autonomous Relative Navigation

Spacecraft autonomous relative navigation is widely required in the field of on-orbit services. In previous works, it has been shown that the monocular sequential images (MSIs) is a cost-effective autonomous relative navigation method. However, given the lack of size and initial orbit of noncooperative targets, the relative navigation system (RNS) with MSIs cannot ensure to estimate the entire relative motion states during the whole observation process. It is critical to perform an online observability analysis for RNS with MSIs to ensure autonomous relative motion estimation validity and accuracy. An analytical nonlinear observability analysis method is proposed in this article to improve the computational efficiency. We study the attributes of the relative orbit dynamics model and Lie algebra operations, and find that the observability matrix is only related to the limited states. The relationship among those states, rank, and the Frobenius norm of observability matrix is demonstrated, which simplify the observability criteria conditions and the degree measurements in analytical forms. In addition, based on the proposed method, we analyze the influence of the orbital manifolds on the observability degree of RNS with MSIs. Several suggestions are proposed for orbital manifolds detecting. The conclusion is a theoretical supplement to the past numerical research results. Finally, we implement the numerical simulations, and the current study’s findings verified the effectiveness of the proposed observability analysis method.

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.

Using radar beam-parks to characterize the Kosmos-1408 fragmentation event

We describe the use of radar beam-park experiments to characterize the space debris resulting from a recent fragmentation event, the deliberate demolition of the defunct Kosmos-1408 satellite. We identify the Kosmos-1408 fragments and present distribution of measurement parameters as well as proxy orbit parameters. We present and apply a novel technique to estimate the size of objects by matching the signal to noise ratio of the detection to the radiation pattern of the radar. With this method we estimate the size distribution of the debris cloud. We also demonstrate how a pair of beam-park observations can be used to perform a crude, yet seemingly reliable, initial orbit determination. Finally, we present followup observations ∼5 months after the fragmentation that show a still compact cloud of debris.

A Multimodal Differential Evolution Algorithm in Initial Orbit Determination for a Space-Based Too Short Arc

Under the too short arc scenario, the evolutionary-based algorithm has more potential than traditional methods in initial orbit determination. However, the underlying multimodal phenomenon in initial orbit determination is ignored by current works. In this paper, we propose a new enhanced differential evolution (DE) algorithm with multimodal property to study the angle-only IOD problem. Specifically, a coarse-to-fine convergence detector is implemented, based on the Boltzmann Entropy, to determine the evolutionary phase of the population, which lays the basis of the balance between the exploration and exploitation ability. A two-layer niching technique clusters the individuals to form promising niches after each convergence detected. The candidate optima from resulting niches are saved as supporting individuals into an external archive for diversifying the population, and a local search within the archive is performed to refine the solutions. In terms of performance validation, the proposed multimodal differential evolution algorithm is evaluated on the CEC2013 multimodal benchmark problems, and it achieved competitive results compared to 11 state-of-the-art algorithms, which present its capability of multimodal optimization. Moreover, several IOD experiments and analyses are carried out on three simulated scenarios of space-based observation. The findings show that, compared to traditional IOD approaches and EA-based IOD algorithms, the proposed algorithm is more successful at finding plausible solutions while improving IOD accuracy.

Long-term deorbiting control for an electrodynamic tether system exploiting periodic solutions

This paper focuses on the nonlinear dynamics and control problem of deorbiting an electrodynamic tethered satellite system in an inclined elliptical orbit. Considering the perturbing Lorenz forces, a set of modified equinoctial elements is employed to describe the slow-varying orbital dynamics. In addition, the fast-varying attitude dynamics of the system is incorporated into dynamic modeling by adopting an assumption of a dumbbell model. To circumvent the difficulties in computation of a real-time optimal control law for a long-term deorbiting process, a compound control scheme is proposed. A time-scale separation method is adopted to facilitate the controller design. In the scheme, a nonlinear optimal control law accounting for system constraints and nonlinear dynamics is first proposed to find an initial nominal periodic orbit without considering the variations of orbital elements. Subsequently, a closed-loop feedback control law based on energy rate is presented to track the periodic solutions for several orbits by considering the overall dynamics. Notably, the periodic solution will be re-computed after each tracking procedure to account for the slow variation in orbital elements. Comparative studies are presented to demonstrate the advantages of the proposed control law in reducing computational costs.

The Rendezvous Mission of Two in-Orbit Sattelites Using Numerical Simulation

In this work, a rendezvous of two satellites is considered. The active satellite approaches the passive satellite for a remote partial recharge of the passive spacecraft’s dead battery. In the first case, the active and passive spacecraft are in geocentric circular orbits, having an altitude of 499.9 km and 500 km, respectively. It is assumed that the rendezvous is unperturbed and the rendezvous plane coincides with the plane of the passive satellite’s orbit. Close-range guidance starts as soon as the sensor on the active spacecraft recognizes the passive spacecraft. A method implementing the line of sight is used for the close-range guidance process. A mathematical model of the relative motion is formed and numerically solved to investigate the rendezvous parameters against time. For solving the model, different values of 499.9, 499.8, 499.7 km are considered as the initial orbit altitude of the active spacecraft, assuming that the angle between state vectors of the spacecraft has a small value of 0.01 degrees. The results show that the active spacecraft with an initial altitude of 499.7 km approaches the passive spacecraft to a distance of 80 meters in less than 50 seconds, where a final velocity impulse is needed to maintain this distance.

Transfer between the planar Lyapunov orbits around the Earth–Moon L2 point using low-thrust engine

We present a study of the low-thrust transfer problem near the secondary body in the Earth–Moon circular restricted three-body problem (CRTBP). Based on the Pontryagin maximum principle, the time-optimal, energy-optimal and fuel-optimal transfers between the planar Lyapunov orbits around the L2 point of the Earth–Moon system are constructed as a two-point boundary value problem (TPBVP). A criterion for identifying the best trajectory is also described. The Lyapunov orbit structure is used to deal with the potential difficulties of initial guess. As a result, the final transfer trajectory follows a multi-revolution structure, which takes a long time of flight. The homoclinic connection configuration is investigated by introducing the relevant invariant manifolds, allowing for faster transfer and less fuel consumption in the same case. It is designed a linear time-varying model predictive control (MPC) algorithm to perform trajectory tracking in the presence of initial orbit error and deviations in engine operation. Numerical simulations show the efficiency and practicability of the optimal transfer trajectory design strategy and trajectory tracking controller proposed in this paper for future lunar exploration missions.

Integrated design of solar thermal propulsion system for microsatellite with liquid ammonia as propellant

This paper presents a design of solar thermal propulsion (STP) system for microsatellite with liquid ammonia as propellant. The system was equipped with two concentrators, which were respectively placed in the tank and thrust chamber for propellant supply and heating. A platelet heat exchanger was adopted to heat the propellant in the chamber, and the fluid–solid coupling effect between the wall and the gas was considered. Meanwhile, the effects of satellite mass, initial orbit, nozzle size and target temperature on the performance of STP system were analyzed. The results show that for microsatellites with a total mass of 100 kg, the STP system can fully heat the propellant to more than 2050 K, generate an intermittent thrust of about 26 N, and enable the satellite to obtain a velocity increment of more than 1470 m/s within 19 days, consuming only 42 kg of propellant, which can directly meet the transfer mission from the geostationary transfer orbit (GTO) to the geostationary orbit (GEO). The maximum velocity increment could reach more than 1950 m/s when the propellant was completely consumed; Changing the mass and initial orbit of the satellite will not affect the thrust and specific impulse. Satellites with smaller mass will spend less time and propellant during orbit transfer. The lower is the perigee height of the initial orbit, the greater is the propellant consumption, while the shorter is the time of orbit transfer; The reduction of nozzle throat size and target temperature will lead to the increase of specific impulse and the decrease of orbital transfer time, but the reduction of thrust.

Implications of Jupiter Inward Gas-driven Migration for the Inner Solar System

The migration history of Jupiter in the Sun’s natal disk remains poorly constrained. Here we consider how Jupiter’s migration affects small-body reservoirs and how this constrains its original orbital distance from the Sun. We study the implications of large-scale and inward radial migration of Jupiter for the inner solar system while considering the effects of collisional evolution of planetesimals. We use analytical prescriptions to simulate the growth and migration of Jupiter in the gas disk. We assume the existence of a planetesimal disk inside Jupiter’s initial orbit. This planetesimal disk received an initial total mass and size–frequency distribution (SFD). Planetesimals feel the effects of aerodynamic gas drag and collide with one another, mostly while shepherded by the migrating Jupiter. Our main goal is to measure the amount of mass in planetesimals implanted into the main asteroid belt (MAB) and the SFD of the implanted population. We also monitor the amount of dust produced during planetesimal collisions. We find that the SFD of the planetesimal population implanted into the MAB tends to resemble that of the original planetesimal population interior to Jupiter. We also find that unless very little or no mass existed between 5 au and Jupiter’s original orbit, it would be difficult to reconcile the current low mass of the MAB with the possibility that Jupiter migrated from distances beyond 15 au. This is because the fraction of the original disk mass that gets implanted into the MAB is very large. Finally, we discuss the implications of our results in terms of dust production to the so-called NC–CC isotopic dichotomy.

An orbit determination approach to associating optical tracklets of space objects

The advances in the optical space surveillance technology and the possibly more deployments of space-based optical sensors enable more and more space objects detectable and make the catalog expansion more realistic. The cataloging of an optically detected new object requires finding three or more tracklets over a few days from the object. In this process, the tracklet-to-tracklet association is a critical step, but associating short-arc optical tracklets remains a difficult task. This paper develops a novel orbit determination approach to the optical tracklet association. The main idea is to determine accurate orbit elements from two tracklets of the same object by exclusively using the Gooding angles-only initial orbit determination (IOD) method. Before applying the Gooding IOD method to two tracklets apart by a few days, the dominant secular effects on the angular observations have to be considered. The significant short-periodic effects may also need consideration if tracklet-to-tracklet IOD is to achieve high accuracy. In this paper, the secular effects from the J2 and lunisolar gravitational perturbations, as well as the short-periodic effects due to J2 and J2,2, are accounted for in the tracklet-to-tracklet IOD. Extensive tests using tracklets from low Earth orbit (LEO), high elliptical orbit (HEO), medium Earth orbit (MEO), geosynchronous Earth orbit (GEO), and Molniya orbit are performed to assess the performance of the developed method. It is shown that the true positive (TP) rate for associating two tracklets from the same object within 48 h is 98.3% for LEO objects and higher than 89.8% for HEO and Molniya objects. The TP rate is remarkably high at around 99.0% for MEO and GEO objects. The analytic approach is also computationally very efficient. The results demonstrate the strong applicability of the developed method to associate optical tracklets of uncatalogued objects of all orbit types.