High-precision Orbit Propagator Research Articles

Configuration Design Method of Mega Constellation for Low Earth Orbit Observation

The configuration optimization design of Low Earth Orbit observation mega constellation in complex space environment is a nonlinear problem that is difficult to solve analytically. In this paper, a constellation design method is proposed, considering satellite imaging width, formation flying of subgroup satellites, and global uniform coverage by payloads. Firstly, a configuration of satellites with the same subsatellite trajectory is proposed, and its orbital analytical expression under J2 perturbation is provided. Then, the relative motion feature points are extracted near the orbit of each satellite, and a group of uniform natural accompanying satellites are set to corresponding points. Afterwards, the orbit parameters of satellite and its companions are set as initial values, and the precise orbits under the High Precision Orbit Propagator model are solved in the neighborhood by using the Nondominated Sort Particle Swarm Optimization algorithm. Finally, the correctness of the configuration design method is verified by numerical simulation.

Effect of solar free oscillations on TianQin’s range acceleration noise

TianQin is a proposed space-based gravitational-wave detector mission to be deployed and operated in high Earth orbits. As a sequel to Zhang et al (2021 Phys. Rev. D 103 062001), we investigate a type of ‘orbital noise’ in TianQin’s range acceleration that is caused by gravitational perturbation associated with solar free oscillations. Frequencies of such oscillations are typically within TianQin’s measurement band of 0.1 mHz–1 Hz, and the disturbance level needs careful assessment. By using high-precision orbit propagation and adding the Sun’s time-variable oblateness J 2 to detailed gravity-field models, we examine the effect in the frequency domain and show that the solar free oscillation noise is expected to be two orders of magnitude lower than the noise requirement on single links and hence has little impact on the mission.

Effect of celestial body gravity on Taiji mission range and range acceleration noise

The Taiji project is a space gravitational-wave detection mission consisting of three satellites that form a giant equilateral triangle with a side length of approximately $3\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\mathrm{km}$ in the heliocentric orbit. The target of the mission is to detect gravitational-wave signals in the 0.1 mHz to 1 Hz band. However, its intersatellite distances are affected by celestial bodies in the solar system, introducing changes that may reach levels of 30,000 km in magnitude. Thus, it is important to investigate whether the gravitational fields of celestial bodies in the detection frequency band will have an impact on the realization of ultrahigh-sensitivity intersatellite ranging measurements. In this study, a high-precision orbit propagator with an accuracy of 0.03 pm on the 1 AU scale is developed. Based on this orbit propagator, the impact of the major large celestial bodies in the solar system on the detection sensitivity in the intersatellite measurements are analyzed. Detailed numerical studies show that the linear spectral density of the range and range acceleration are approximately $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ and $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}/\sqrt{\mathrm{Hz}}$, respectively, at 0.1 mHz, indicating that the gravitational disturbance generated by the major celestial bodies in the solar system will not affect the aim of the Taiji mission to detect gravitational waves in the frequency band 0.1 mHz to 1 Hz.

우주상황인식을 위한 인공우주물체 추락 예측 소프트웨어 개발

The high-level Space Situational Awareness (SSA) objective is to provide to the users dependable, accurate and timely information in order to support risk management on orbit and during re-entry and support safe and secure operation of space assets and related services. Therefore the risk assessment for the re-entry of space objects should be managed nationally. In this research, the Software for Re-Entry Prediction of space objects (SREP) was developed for national SSA system. In particular, the rate of change of the drag coefficient is estimated through a newly proposed Drag Scale Factor Estimation (DSFE), and is used for high-precision orbit propagator (HPOP) up to an altitude of 100 km to predict the re-entry time and position of the space object. The effectiveness of this re-entry prediction is shown through the re-entry time window and ground track of space objects falling in real events, Grace-1, Grace-2, Tiangong-1, and Chang Zheng-5B Rocket body. As a result, through analysis 12 hours before the final re-entry time, it is shown that the re-entry time window and crash time can be accurately predicted with an error of less than 20 minutes.

Electric Satellite Station Keeping, Attitude Control, and Momentum Management by MPC

We propose a model predictive control (MPC) policy for simultaneous station keeping, attitude control, and momentum management of a low-thrust nadir-pointing geostationary satellite equipped with reaction wheels and ON–OFF electric thrusters mounted on boom assemblies. Attitude control is performed using an inner loop SO(3)-based control law with the reaction wheels, while the outer loop MPC policy maintains the satellite within a narrow station-keeping window and performs momentum management using electric thrusters. For reducing propellant consumption, our MPC uses two different prediction horizons: a short horizon for the states associated with the orbit’s inclination and a longer horizon for all other states. Furthermore, to handle the ON–OFF nature of the thruster while retaining low computational burden, we develop a strategy for quantizing the continuous thrust command, which also allows for trading off the number thrust pulses and fuel consumption. We validate the controller in a closed-loop simulation with the high-precision orbit propagation provided by the Systems Tool Kit (STK) and assess the robustness to model uncertainty and measurement noise.

Long term and safe relative orbit design for heterogeneous spacecraft clusters

The problem of obtaining long term relative orbit configurations for spacecraft clusters with realistic operational considerations such as safety, station keeping and inter-spacecraft distances is addressed. Two different approaches are developed for station keeping and safety objectives. In the first approach, relative orbit configurations, or relative TLEs, are found minimizing deviations from reference mean orbit which would maximize the station-keeping objective. In second one, relative configurations are found from a reference initial condition by minimizing probability of collision, hence maximizing the safety objective, between the spacecraft in the cluster which are propagated numerically through a high precision orbit propagator. For the design optimization, a derivative free algorithm is proposed. Effectiveness of the approaches is demonstrated through simulations. Using this design framework, several configurations can be found by exploring the limits of the clusters in terms of spacecraft number, distance bounds and probabilities of collision for long time intervals.

Impact of solar activity on Low Earth Orbiting satellites

In the present paper, we investigate the impact of solar activity on Low Earth Orbiting (LEO) satellites. How the increase in the number of coronal mass ejections and solar flares raises the likelihood that sensitive instruments in space and will be damaged by energetic particles accelerated in these events. So, we study the effect of perturbation forces on the Keplerian orbital elements of two LEO satellites using atmosphere model NRLMSISE00. The equation of motion and the effect of all perturbation are solved by using a High-Precision Orbit Propagation (HPOP) model, with Runge-Kutta 7 method, this method was treated by Cowell’s technique. In this respect we deduce that solar activity influences the upper atmosphere; this influence is mediated through rapid geomagnetic disturbances.

Performance Analysis of Low-Gain Feedback for Saturated Differential Drag in a High-precision Orbit Propagator

Performance Analysis of Low-Gain Feedback for Saturated Differential Drag in a High-precision Orbit Propagator

Output Regulation Control for Satellite Formation Flying Using Differential Drag

This paper proposes a new approach of using differentials in aerodynamic drag in combination with thrusters to control satellite formation flying in low Earth orbits. Parameterized output regulation theory for formation-flying missions with combined control action is developed based on the Schweighart–Sedwick relative dynamics equations. The theory is implemented to precisely track the different trajectories of reference relative motion and eliminates the effects of the perturbations. The parametric Lyapunov algebraic equation is proposed to ensure the stability of the linear relative model subject to saturated inputs. The main goal of this study is to approve the viability of using the differentials in aerodynamic drag to precisely control different formation-flying missions. Numerical simulations using a high-fidelity relative dynamics model and a high-precision orbit propagator are implemented to validate and analyze the performance of the proposed control algorithm in comparison with the linear quadratic regulator algorithm based on actual satellite models.

Station keeping and momentum management of low-thrust satellites using MPC

This work proposes a Model Predictive Control (MPC) policy for simultaneous station keeping and momentum management of a low-thrust nadir-pointing satellite in geostationary orbit around the Earth. The satellite is equipped with six electrically powered thrusters and three axisymmetric reaction wheels, which must be coordinated to control the satellite's orbital position and, concurrently, unload the wheels' stored angular momentum. The MPC policy enforces constraints that maintain the satellite in a tight latitude and longitude window and in a tight nadir-pointing attitude configuration, while minimizing the delta-v provided by the thrusters. The MPC policy exploits a prediction model of the environmental disturbance forces in order to significantly reduce the delta-v required for station keeping, and enforces constraints determined by the thruster configuration to select control forces and torques that can be generated by the propulsion system. Numerical simulations of the control policy in closed-loop with the satellite nonlinear dynamics under high-precision orbit propagation provided by Systems Tool Kit (STK) that validate the performance of the proposed design in terms of thruster usage and constraint enforcement are presented.

고정밀 섭동모델을 이용한 실시간 On-board 궤도 결정 성능 향상

고정밀 섭동모델을 이용한 실시간 On-board 궤도 결정 성능 향상

Evaluation of the Modified Picard-Chebyshev Method for High-Precision Orbit Propagation

AbstractThe modified Picard-Chebyshev method, due to its formulation, has the potential for computationally efficient orbit propagation in a parallel computing environment. However, it has not found extensive use in commercial software applications, primarily due to its instability over long orbit propagation times. In this paper, the method was evaluated based on the propagation of several test orbits with a high-precision force model available through NASA’s Java Astrodynamics toolkit. The goal was to analyze the stability properties of the method, with emphasis on its dependence on the initial guess and the order of the approximating Chebyshev polynomial. Simulation results indicated a dependence of the method on the precision of the computation as well. Additionally, the performance of the method when implemented in parallel was evaluated by propagating the orbits on a multicore processing unit and comparing run times to well-known sequential numerical propagators. The preliminary results show that th...

Near-Earth object intercept trajectory design for planetary defense

Tracking the orbit of asteroids and planning for asteroid missions have ceased to be a simple exercise, and become more of a necessity, as the number of identified potentially hazardous near-Earth asteroids increases. Several software tools such as Mystic, MALTO, Copernicus, SNAP, OTIS, and GMAT have been developed by NASA for spacecraft trajectory optimization and mission design. However, this paper further expands upon the development and validation of an Asteroid Mission Design Software Tool (AMiDST), through the use of approach and post-encounter orbital variations and analytic keyhole theory. Combining these new capabilities with that of a high-precision orbit propagator, this paper describes fictional mission trajectory design examples of using AMiDST as applied to a fictitious asteroid 2013 PDC-E. During the 2013 IAA Planetary Defense Conference, the asteroid 2013 PDC-E was used for an exercise where participants simulated the decision-making process for developing deflection and civil defense responses to a hypothetical asteroid threat.

The Effects of the IERS Conventions (2010) on High Precision Orbit Propagation

The Earth is not perfectly spherical and its rotational axis is not fixed in space, and these geophysical and kinematic irregularities work as dominant perturbations in satellite orbit propagation. The International Earth Rotation Service (IERS) provides the Conventions as guidelines for using the Earth's model and the reference time and coordinate systems defined by the International Astronomical Union (IAU). These guidelines are directly applied to model orbital dynamics of Earth satellites. In the present work, the effects of the latest conventions released in 2010 on orbit propagation are investigated by comparison with cases of applying the previous guidelines, IERS Conventions (2003). All seven major updates are tested, i.e., for the models of the precession/nutation, the geopotential, the ocean tides, the ocean pole tides, the free core nutation, the polar motion, and the solar system ephemeris. The resultant position differences for one week of orbit propagation range from tens of meters for the geopotential model change from EGM96 to EGM2008 to a few mm for the precession/nutation model change from IAU2000 to IAU2006. The along-track differences vary secularly while the cross-track components show periodic variation. However, the radial-track position differences are very small compared with the other components in all cases. These phenomena reflect the variation of the ascending node and the argument of latitude. The reason is that the changed models tested in the current study can be regarded as small fluctuations of the geopotential model from the point of view of orbital dynamics. The ascending node and the argument of latitude are more sensitive to the geopotential than the other elements. This study contributes to understanding of the relation between the Earth's geophysical properties and orbital motion of satellites as well as satellite-based observations.

Integrable approximation of J 2-perturbed relative orbits

Most existing satellite relative motion theories utilize mean elements, and therefore cannot be used for calculating long-term bounded perturbed relative orbits. The goal of the current paper is to find an integrable approximation for the relative motion problem under the J2 perturbation, which is adequate for long-term prediction of bounded relative orbits with arbitrary inclinations. To that end, a radial intermediary Hamiltonian is utilized. The intermediary Hamiltonian retains the original structure of the full J2 Hamiltonian, excluding the latitude dependence. This formalism provides integrability via separation, a fact that is utilized for finding periodic relative orbits in a local-vertical local-horizontal frame and determine an initialization scheme that yields long-term boundedness of the relative distance. Numerical experiments show that the intermediary-based computation of orbits provides long-term bounded orbits in the full J2 problem for various inclinations. In addition, a test case is shown in which the radial intermediary-based initial conditions of the chief and deputy satellites yield bounded relative distance in a high-precision orbit propagator.

A Numerical Approach for Station Keeping of Geostationary Satellite Using Hybrid Propagator and Optimization Technique

In this paper, a method of station keeping strategy using relative orbital motion and numerical optimization technique is presented for geostationary satellite. Relative position vector with respect to an ideal geostationary orbit is generated using high precision orbit propagation, and compressed in terms of polynomial and trigonometric function. Then, this relative orbit model is combined with optimization scheme to propose a very efficient and flexible method of station keeping planning. Proper selection of objective and constraint functions for optimization can yield a variety of station keeping methods improved over the classical ones. Nonlinear simulation results have been shown to support such concept.

상대 운동과 최적화 기법을 이용한 정지궤도 위치유지에 관한 연구

In this paper, a method of station keeping strategy using relative orbital motion and numerical optimization technique is presented for geostationary spacecraft. Relative position vector with respect to an ideal geostationary orbit is generated using high precision orbit propagation, and compressed in terms of polynomial and trigonometric function. Then this relative orbit model is combined with optimization scheme to propose a very efficient and flexible method of station keeping planning. Proper selection of objective and constraint functions for optimization can yield a variety of station keeping methods improved over the classical ones. Results from the nonlinear simulation have been shown to support such concept.

Low-cost autonomous orbit control about Mars: Initial simulation results

Interest in studying the possibility of extraterrestrial life has led to the re-emergence of the Red Planet as a major target of planetary exploration. Currently proposed missions in the post-2000 period are routinely calling for rendezvous with ascent craft, long-term orbiting of, and sample-return from Mars. Such missions would benefit greatly from autonomous orbit control as a means to reduce operations costs and enable contact with Mars ground stations out of view of the Earth. This paper present results from initial simulations of autonomously controlled orbits around Mars, and points out possible uses of the technology and areas of routine Mars operations where such cost-conscious and robust autonomy could prove most effective. These simulations have validated the approach and control philosophies used in the development of this autonomous orbit controller. Future work will refine the controller, accounting for systematic and random errors in the navigation of the spacecraft from the sensor suite, and will produce prototype flight code for inclusion on future missions. A modified version of Microcosm's commercially available High Precision Orbit Propagator (HPOP) was used in the preparation of these results due to its high accuracy and speed of operation. Control laws were developed to allow an autonomously controlled spacecraft to continuously control to a pre-defined orbit about Mars with near-optimal propellant usage. The control laws were implemented as an adjunct to HPOP. The GSFC-produced 50 × 50 field model of the Martian gravitational potential was used in all simulations. The Martian atmospheric drag was modeled using an exponentially decaying atmosphere based on data from the Mars-GRAM NASA Ames model. It is hoped that the simple atmosphere model that was implemented can be significantly improved in the future so as to approach the fidelity of the Mars-GRAM model in its predictions of atmospheric density at orbital altitudes. Such additional work would take the form of solar flux (F10.7) and diurnal density dependencies. The autonomous controller is a-derivative of the proprietary and patented Microcosm Earth-orbiting control methodology which will be implemented on the upcoming Surrey Satellite Technology (SSTL) UoSAT-12 and the NASA EO-1 spacecraft missions. This work was funded by the NASA Jet Propulsion Laboratory under a Phase I SBIR (96.1 07.02 9444) and by internal Microcosm R&D funds as well as earlier supporting work done under a variety of USAF Research Laboratory-sponsored contracts [1, 2, 4, 12].