Repeating Ground Track Research Articles

Some Special Types of Orbits around Jupiter

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

Closed-form solution of repeat ground track orbit design and constellation deployment strategy

The present work proposes a closed-form solution for circular repeat ground track (RGT) orbit designs and constellations and its application strategy. The proposed solution is an equation of motion proving that the characteristic of a circular RGT orbit is similar to that of the parametric curve of Ptolemy's model and provides a low computational cost for the RGT orbit design and related numerical analysis. The application strategy is to coincide with the self-intersection point of an RGT orbit over a specific target of interest on Earth and make it the starting point of the first satellite orbit in the satellite group. The remaining satellites are designed to have the same RGT orbit as the first satellite; therefore, the entire group has twice the repeat cycle over a specific target. To this end, this study represents an algorithm to match the specific target and the intersection point through an iterative numerical analysis method centering on the RGT equation. A set of orbital elements for a satellite group is also derived herein. The satellite group with a repeat cycle that doubles for a specific target shows a significantly shorter revisit time compared with the conventional Walker constellation.

Sun-synchronous repeat ground tracks and other useful orbits for future space missions

ABSTRACTThe development of oceanography and meteorology has greatly benefited from satellite-based data of Earth’s atmosphere and ocean. Traditional Earth observation missions have utilised Sun-synchronous orbits with repeat ground tracks due to their advantages in visible and infrared wavelengths. However, diversification of observation wavelengths and massive deployment of miniaturised satellites are both enabling and necessitating new kinds of space missions. This paper proposes several unconventional satellite orbits intended for use in, but not limited to, Earth observation. This ‘toolbox’ of orbits and taxonomy thereof will thus support the definition of design requirements for the individual satellites in nano-satellite constellations developed by national space agencies, industries and academia.

General Perturbation Method for Satellite Constellation Reconfiguration Using Low-Thrust Maneuvers

A general perturbation solution to a restricted low-thrust Lambert rendezvous problem, considering circular-to-circular in-plane maneuvers using tangential thrust and including a coast arc, is developed. This provides a fully analytical solution to the satellite reconnaissance problem. The solution requires no iteration. Its speed and simplicity allow problems involving numerous spacecraft and maneuvers to be studied; this is demonstrated through two case studies. In the first, a range of maneuvers providing a rapid flyover of Los Angeles is generated, giving an insight to the trade space and allowing the maneuver that best fulfills the mission to be selected. A reduction in flyover time from 13.8 to 1.6 days is possible using a less than velocity change. A comparison with a numerical propagator including atmospheric friction and an 18th-order tesseral model shows 4 s of difference in the time of flyover. A second study considers a constellation of 24 satellites that can maneuver into repeating ground track orbits to provide persistent coverage of a region. A set of maneuvers for all satellites is generated for four sequential targets, allowing the most suitable maneuver strategy to be selected. Improvements in coverage of greater than 10 times are possible as compared to a static constellation using 35% of the propellant available across the constellation.

Multi-objective Heuristic Design Approach for SAR Mission for Monitoring Local Target Area

The Korea first synthetic aperture radar (SAR) satellite with a 1-m resolution—Korea Multi-purpose Satellite-5 (KOMPSAT-5)—was successfully launched in Korea in 2013, and its successors will be launched continuously to monitor specific target areas. The major requirements of the orbit design for KOMPSAT-5 are that the mean average revisit time (ART) over the Korean peninsula is no longer than 24 h and that the repeat ground track orbit is guaranteed. For this type of problem, an iterative and tedious process may be used to derive the appropriate mission orbit to satisfy the mission requirements. During the design process, sophisticated coverage analysis software should be employed to evaluate the mean ART over a specific local target area. Moccia et al. (Acta Astronaut 47(11):819–829, 2000) presented a feasibility study of a new space-based observation technique using a bistatic SAR and performed a numerical simulation to estimate the measurement accuracy for the bright point target position and velocity. Kim and Chang (Aerosp Sci Technol 40:17–32, 2015) developed an optimal scheduling method employing a genetic algorithm (GA) to reduce the system response time for an SAR satellite constellation. Wei and Chunsheng (Adv Sp Res 50:272–281, 2012) proposed a new design method for a distributed satellite-borne SAR system with an error-propagation model and used a monostatic design to determine the key parameters of a single SAR satellite. Apart from the SAR mission, the orbit design for Earth-observation missions over a specific area or target has been studied by others. Abdelkhlik et al. (J Guid Control Dyn 29(5):1231–1235, 2006) utilized the RGT concept to design natural orbits for visiting a target area without the use of propulsion systems. Kim et al. (J Spacecr Rocket 46(3):725–728, 2009) proposed a new strategy employing a GA to search the current mission orbit for a temporary target orbit to achieve a temporary reconnaissance mission over a particular target site using a low-Earth-orbit satellite during a specific period. We propose an effective approach for the design of the SAR mission for a local target area. Here, the ART and average transmitted power are key parameters for the mission requirements and the bus system, respectively. To our knowledge, no previous studies have considered this kind of problem. To satisfy the mission requirements for the ART over a local target area and simultaneously consider the average transmitted power, multi-objective heuristic algorithms including GEs, particle swarm optimization, and differential evolution are used, and their performances are compared. The computational approach of the design strategy proposed by the authors is based on the optimization algorithms in Matlab® and the powerful coverage analysis tool STK®. Therefore, the proposed strategy is adaptable for various types of SAR mission designs having complex requirements regarding both the orbit and the bus system, particularly for monitoring a specific local target area.

Low Earth orbit satellite constellation for regional positioning with prolonged coverage durations

Satellite navigation constellations orbit the Earth in medium and geosynchronous orbits. Their high altitude provides wide coverage, which may be redundant if only regional coverage is needed. In this paper, a design scheme for regional navigation satellite constellations in low-Earth orbit is proposed. The design yields long coverage durations, which are characterized by a minimized Geometric Dilution of Precision (GDOP), with respect to a predefined mid-latitude receiver. The proposed constellations are defined for various combinations of the following parameters: Repeat Ground-Track commensurability, receiver latitude, number of satellites, and internal satellite arrangement. Optimal constellations, with respect to the GDOP integral, are searched, design guidelines are set up, and a mathematical model is fitted. The proposed constellations provide GDOP-optimized coverage durations, recurring twice each day. The results include numerical solutions for prograde near-polar constellations in altitudes ranging between 550 and 870 km, with receivers positioned at latitudes from 30° to 60°, and number of satellites ranging from 13 to 36. The average coverage duration varies from 20 to 80 min, with a mean GDOP ranging from 2.5 to 3.

Improved Reference Orbits for the Repeat-Ground-Track Missions EnMAP and Tandem-L

The reference orbit implemented for the active TerraSAR-X mission works remarkably well for orbit control purposes, but an unexpected secular drift in the along-track separation between satellite and reference orbits has built up to a 60 s flight-time offset within 10 years of operation. The scope of this work is to understand the origin of the drift and to eliminate the effect for DLRs future repeat ground-track missions EnMAP and Tandem-L. The improved process of reference orbit generation is discussed and the underlying relations for the suggested inclination adjustment are derived. The improved process is successfully validated by means of 1-year numerical orbit control simulation. The presented process is generic and can be applied to any repeat-ground track mission.

Multi-asset System Design Methodology for Earth Observation

To better understand the Earth environment and climate change, to mitigate its effects and to provide emergency services, ensuring civil security, future European Earth observation (EO) infrastructures will heavily rely on operational satellite missions. To ensure continuous and timely provision of spaceborne Earth-observation data, these missions will be characterized by high temporal resolution, high availability, low latency and enhanced synergies between different observation products. These goals will likely be achieved by deploying multi-asset satellite systems, such as constellations. In order to design robustly the architecture of these EO systems, given a certain set of observational requirements, OHB System AG has developed a methodology and the associated tools, to optimize the multi-asset system, taking into account physical and technical constraints. In general, for a specific repeating ground track Sun-synchronous orbit and a given number of spacecraft, one (or more) optimal orbital configuration(s) (i.e. anomaly separation on the same orbit) exists that allows achieving full global coverage in a prescribed number of days and minimizes the required swath size. The objective of this paper is to define the optimization model associated to this problem: the swath size is a key design parameter, most of the time constrained by mission requirements and/or technology readiness. Both Non Linear Programming and Mixed Integer Linear Programming are proposed to solve the optimization problem and are investigated in the paper: the formulation is derived and advantages and drawbacks of each are detailed. Finally, the two formulations are tested with different software and on multiple study cases: the effectiveness of the developed methodology is supported by application and validation examples.

Multi-objective optimization of agile satellite orbit design

Satellite orbit design is a fundamental and important task during the mission analysis and the agile satellite design. In this paper we first investigate the design of a more realistic repeating ground track orbit in an accurate geopotential model of Earth. Furthermore, by considering the view field of the resource equipped on an agile satellite, we calculate the variation of the orbital altitude, the tilt angle, and the off-nadir resolution with the desired revisit time. Additionally, we analyze the distribution of all feasible solutions. In considering the spatial resolution and temporal resolution simultaneously, we propose a multi-objective optimization technique for optimal feasible orbits generation. Finally, through various case studies, the application of multi-objective optimization in orbit design of agile satellite is successfully demonstrated. Results also illustrate the validity and effectiveness of the proposed technique.

Multi-objective Optimization Method For Repeat Ground-track Orbit Design Considering the Orbit Injection Error

Considering the adverse effects of orbit injection error, a novel repeat ground-track orbit redesign approach is proposed to reduce the fuel consumption caused by the orbital maneuvering from the injection orbit to the nominal orbit. By introducing the performance indexes of revisiting accuracy and orbit injection maneuvering fuel consumption, the problem of repeat ground track orbit redesign considering the orbit injection error is transformed into a multi-objective optimization problem, which can be solved by multi-objective genetic algorithm. Finally, the numerical simulations show that the redesigned repeat ground-track orbits not only can meet the requirements of revisiting ground targets with high accuracy, but also can reduce the required fuel consumption significantly

Space-based Earth remote sensing: Part 1. Satellite orbit theory

The development of oceanography and meteorology has greatly benefited from remotely sensed satellite data of the atmosphere and ocean. For oceanographers, meteorologists, hydrologists and climatologists to obtain high-quality satellite data, orbits along which the satellites move must be designed carefully. For this reason, Sun-synchronous, repeat ground track orbits have traditionally been used for visible-wavelength and infrared Earth observations. As the needs for varied datasets are growing, however, new classes of Earth-observing missions are emerging such as interferometry and radiometry to name a few. On the other side, satellite platforms and onboard sensors are getting more compact and less expensive, allowing developing nations to launch their own satellites and under-researched parts of the Earth be studied. In light of these changes, this paper introduces new types of satellite orbits from celestial mechanics perspectives, whose applications will be detailed further in the follow-up work.

LEO constellation design methodology for observing multi-targets

This paper is based on the second problem of the 8th China Space Trajectory Design Competition (CTOC8). The background is LEO constellation design strategy for monitoring discrete multi-targets with small satellite under J2 model. The difficulty is that the small satellite is equipped with low-cost cameras with limited coverage ability and the targets are distributed separately in a key area, which result in long revisit time or large number of satellites based on traditional design method. In this paper, a specific LEO constellation design method is proposed to cope with the problems. First, grid search and numerical method are performed to construct a database consisting of repeating ground track orbits. Then several orbits are carefully selected by pruning method to visit each target. Finally, repeating ground track constellation is constructed to meet the maximum revisit time constraint. The present method provides a systematic constellation design methodology of remote sensing observation with limited coverage ability, and demonstrates the resulting constellation can obtain rapid revisit frequency over discrete multi-targets with the least number of satellites.

Ocean and Ice Shelf Tides from CryoSat-2 Altimetry

AbstractA new empirical model of ocean tides has been developed for the Weddell Sea, south of 66°S, between 90°W and 0°, using six years of radar altimeter data from the CryoSat-2 satellite mission. Because of its long ground-track repeat period (368 days) and its diverse measurement modes, low-rate mode (LRM) over the ocean and synthetic aperture radar interferometric mode (SARin) over ice surfaces and parts of the ocean, the CryoSat-2 data pose a number of challenges for tidal analysis. The space and time sampling properties of the exact repeat, near-repeat, and crossover ground tracks have been analyzed to discover which tides may be estimated using a combination of conventional harmonic analysis and local spatial regression. Using this information, the M2, S2, K2, N2, K1, O1, P1, and Q1 tides have been mapped for both the ocean and floating ice shelves in this domain. Validation against independent in situ data, along with comparison with existing tide models, finds that the CryoSat-2-derived tides are consistent with previous estimates and that they are more accurate than other models at the M2 and S2 frequencies. The high inclination of the CryoSat-2 orbit causes the orbit plane to precess relatively slowly, which leads to significantly less accurate estimates of the K2 tide. This purely empirical model ought to provide improved tidal corrections for studies of low-frequency variability and secular trends in ice shelf thickness, and it suggests that further increases in quantitative accuracy could be achieved by assimilation of CryoSat-2 data into dynamical tide models.

The Cross-Calibration of Spectral Radiances and Cross-Validation of CO2 Estimates from GOSAT and OCO-2

The Greenhouse gases Observing SATellite (GOSAT) launched in January 2009 has provided radiance spectra with a Fourier Transform Spectrometer for more than eight years. The Orbiting Carbon Observatory 2 (OCO-2) launched in July 2014, collects radiance spectra using an imaging grating spectrometer. Both sensors observe sunlight reflected from Earth’s surface and retrieve atmospheric carbon dioxide (CO2) concentrations, but use different spectrometer technologies, observing geometries, and ground track repeat cycles. To demonstrate the effectiveness of satellite remote sensing for CO2 monitoring, the GOSAT and OCO-2 teams have worked together pre- and post-launch to cross-calibrate the instruments and cross-validate their retrieval algorithms and products. In this work, we first compare observed radiance spectra within three narrow bands centered at 0.76, 1.60 and 2.06 µm, at temporally coincident and spatially collocated points from September 2014 to March 2017. We reconciled the differences in observation footprints size, viewing geometry and associated differences in surface bidirectional reflectance distribution function (BRDF). We conclude that the spectral radiances measured by the two instruments agree within 5% for all bands. Second, we estimated mean bias and standard deviation of column-averaged CO2 dry air mole fraction (XCO2) retrieved from GOSAT and OCO-2 from September 2014 to May 2016. GOSAT retrievals used Build 7.3 (V7.3) of the Atmospheric CO2 Observations from Space (ACOS) algorithm while OCO-2 retrievals used Version 7 of the OCO-2 retrieval algorithm. The mean biases and standard deviations are −0.57 ± 3.33 ppm over land with high gain, −0.17 ± 1.48 ppm over ocean with high gain and −0.19 ± 2.79 ppm over land with medium gain. Finally, our study is complemented with an analysis of error sources: retrieved surface pressure (Psurf), aerosol optical depth (AOD), BRDF and surface albedo inhomogeneity. We found no change in XCO2 bias or standard deviation with time, demonstrating that both instruments are well calibrated.

ANTARCTIC ICE SHEET SLOPE AND ASPECT BASED ON ICESAT’S REPEAT ORBIT MEASUREMENT

Abstract. Accurate information of ice sheet surface slope is essential for estimating elevation change by satellite altimetry measurement. A study is carried out to recover surface slope of Antarctic ice sheet from Ice, Cloud and land Elevation Satellite (ICESat) elevation measurements based on repeat orbits. ICESat provides repeat ground tracks within 200 meters in cross-track direction and 170 meters in along-track direction for most areas of Antarctic ice sheet. Both cross-track and along-track surface slopes could be obtained by adjacent repeat ground tracks. Combining those measurements yields a surface slope model with resolution of approximately 200 meters. An algorithm considering elevation change is developed to estimate the surface slope of Antarctic ice sheet. Three Antarctic Digital Elevation Models (DEMs) were used to calculate surface slopes. The surface slopes from DEMs are compared with estimates by using in situ GPS data in Dome A, the summit of Antarctic ice sheet. Our results reveal an average surface slope difference of 0.02 degree in Dome A. High resolution remote sensing images are also used in comparing the results derived from other DEMs and this paper. The comparison implies that our results have a slightly better coherence with GPS observation than results from DEMs, but our results provide more details and perform higher accuracy in coastal areas because of the higher resolution for ICESat measurements. Ice divides are estimated based on the aspect, and are weakly consistent with ice divides from other method in coastal regions.

A Novel Technique to Compute the Revisit Time of Satellites and Its Application in Remote Sensing Satellite Optimization Design

This paper proposes a novel technique to compute the revisit time of satellites within repeat ground tracks. Different from the repeat cycle which only depends on the orbit, the revisit time is relevant to the payload of the satellite as well, such as the tilt angle and swath width. The technique is discussed using the Bezout equation and takes the gravitational second zonal harmonic into consideration. The concept of subcycles is defined in a general way and the general concept of “small” offset is replaced by a multiple of the minimum interval on equator when analyzing the revisit time of remote sensing satellites. This technique requires simple calculations with high efficiency. At last, this technique is used to design remote sensing satellites with desired revisit time and minimum tilt angle. When the side-lap, the range of altitude, and desired revisit time are determined, a lot of orbit solutions which meet the mission requirements will be obtained fast. Among all solutions, designers can quickly find out the optimal orbits. Through various case studies, the calculation technique is successfully demonstrated.

低推力推進による回帰軌道遷移のためのグラフを用いた多目的軌道最適化手法に関する研究

低推力推進による回帰軌道遷移のためのグラフを用いた多目的軌道最適化手法に関する研究

Circular revisit orbits design for responsive mission over a single target

The responsive orbits play a key role in addressing the mission of Operationally Responsive Space (ORS) because of their capabilities. These capabilities are usually focused on supporting specific targets as opposed to providing global coverage. One subtype of responsive orbits is repeat coverage orbit which is nearly circular in most remote sensing applications. This paper deals with a special kind of repeating ground track orbit, referred to as circular revisit orbit. Different from traditional repeat coverage orbits, a satellite on circular revisit orbit can visit a target site at both the ascending and descending stages in one revisit cycle. This typology of trajectory allows a halving of the traditional revisit time and does a favor to get useful information for responsive applications. However the previous reported numerical methods in some references often cost lots of computation or fail to obtain such orbits. To overcome this difficulty, an analytical method to determine the existence conditions of the solutions to revisit orbits is presented in this paper. To this end, the mathematical model of circular revisit orbit is established under the central gravity model and the J2 perturbation. A constraint function of the circular revisit orbit is introduced, and the monotonicity of that function has been studied. The existent conditions and the number of such orbits are naturally worked out. Taking the launch cost into consideration, optimal design model of circular revisit orbit is established to achieve a best orbit which visits a target twice a day in the morning and in the afternoon respectively for several days. The result shows that it is effective to apply circular revisit orbits in responsive application such as reconnoiter of natural disaster.

Multi-Decadal Monitoring of Lake Level Changes in the Qinghai-Tibet Plateau by the TOPEX/Poseidon-Family Altimeters: Climate Implication

Lake levels in the Qinghai-Tibet Plateau (QTP) provide valuable records for climate change studies. We use two decades of measurements (January 1993–December 2014) from the TOPEX/Poseidon (T/P)-family satellite altimeters (T/P, Jason-1 and -2) to detect lake level variations at 23 lakes along their repeat ground tracks every 10 days. We employ an optimal processing technique to obtain quality measurements, including outlier detection, averaging and filtering. The lake level accuracies are improved by subwaveform retracking. Jason-1 delivers few measurements after waveform retracking and a cluster classification at most lakes. From January 1993 to December 2014, most lake levels in eastern Tibet rose, while those in western Tibet declined. In Qinghai, lake levels dropped before 2005 and then rose afterwards, coinciding with the measure in 2005 that protects the Qinghai ecosystem (e.g., grassland conservation). The overall pattern of lake level change in the QTP is largely affected by monsoons and lake locations. Most lake levels show clear annual and inter-annual oscillations. Certain lakes show alternating level highs and lows in the same seasons and varying amplitudes of annual oscillations due to lake level changes. We detect a sudden rise of lake level by 7 m caused by floods, varying lake level trends associated with the 1997‒98 El Niño and other factors, and persistently rising and declining lake levels associated with the long-term precipitation trends in the QTP. The T/P-family satellites will continue to monitor lake levels here as long as the sea level monitoring program lasts, collecting a long-term climate record at highlands echoing sea level change.

An analytical approach to retrieve the effects of a non-coplanar disturbing body

The determination of analytical expressions which, including the main perturbative effects, allow the retrieval of the orbit elements of a probe represents an important requirement in designing science trajectories. One of these perturbations is given by the third body attraction. The case in which the perturbing body moves on a plane coincident with the equatorial plane of the primary body has been investigated in previous studies and equations able to provide the temporal evolution of the orbit elements have been determined and applied to the main moons of the Solar System. In this paper an extension of this topic has been carried out and equations which allow the determination of the orbit evolution have been analytically retrieved in the general case in which one or more perturbing bodies describe elliptical and inclined orbits with respect to the equatorial plane of the primary. Then, introducing these equations into the periodicity condition for the probe ground track, and considering the \(J_{2}\) and \(J_{4}\) effects coming from the primary body, an equation able to provide repeating ground track orbits has been determined.