Satellite Orbit Analysis Research Articles

Large constellations for fast acquisition and delivery of information: Design and analysis by stereographic projection onto the equatorial plane

SummaryRecent space projects are designed by satellite constellations with a large number of spacecraft, a global character (i.e., from equatorial to high inclination orbits), and the possibility to transfer information to different satellites of the constellation (inter satellite link) in order to deliver the information to the ground as soon as possible. To cope with a large number of parameters, a fast tool for constellation design, performance evaluation and networking strategies is needed. The aim of this paper is to obtain the performance of any constellation in less than 1 s, even when the number of satellites in the constellation and the duration of the analysis is large (e.g., more than 200 satellites in a period of some days). The proposed algorithm is based on analytical formulae obtained by using the stereographic projection on the equatorial plane of the satellite orbits and the projection of the target and ground station orbits. It is believed that the two‐dimensional projection proposed here can offer some advantages with respect to the spatial analysis of satellite orbits and their ground tracks, such as the reduction in time required to calculate station/satellite and satellite/satellite encounter conditions, and the clear and simple representation of the motion of the satellite of the constellation and of the ground stations of interest.

Satellite Orbit Design and Analysis Based on STK

The design and analysis of satellite orbits has always been a hot topic in the aerospace field. Through the selection and optimization of orbital parameters, the satellite can meet the corresponding performance indicators and work requirements. However, there are often various constraints in actual scenes, so the orbital parameters cannot be set arbitrarily. Therefore, how to design the orbit under the constraints to make the satellite in optimum condition is very important. Based on STK, this paper proposes a satellite orbit design method, and realizes the optimization of the orbit through the simulated annealing algorithm. The simulation results show that this method can achieve satisfactory results and has certain practical value.

Long-Term Variations in the Parameters of the Middle and Upper Atmosphere and Ionosphere (Review)

The article reviews the main publications from the last eight years on long-term trends in the parameters of the middle atmosphere, thermosphere, and ionosphere. It is shown that the negative temperature trends in the middle atmosphere have been reliably established based on observations by various methods. An analysis of satellite orbits in the thermosphere showed negative density trends at heights of ~400 km. Unexpectedly high negative trends in ion temperature Ti above ~220 km obtained with the incoherent-scatter method. The same measurements high positive trends in Ti at the heights of the F1 layer. There are discrepancies in the estimates of the absolute value of the negative trends in the critical frequency and height of the F2 layer; however, these trends are high in the opinion of the authors.

Kinematic Post-processing of Ship Navigation Data Using Precise Point Positioning

Seafloor geodetic studies such as Global Positioning System (GPS)-Acoustic experiments often require the measurement platform on the sea surface to be positioned accurately to within a few centimetres. In this paper, we test the utility of Precise Point Positioning (PPP) for this application with two experiments. The first fixed platform experiment is a comparison between three independent processing software packages: Positioning and Navigation Data Analyst (PANDA), Global Navigation Satellite System-Inferred Positioning System and Orbit Analysis Simulation Software (GIPSY-OASIS), and the Canadian Spatial Reference System (CSRS)) and a more accurate solution based on conventional differential processing of a remote GPS station in the Aleutian Islands. The second moving platform experiment is a comparison among the three PPP software packages using 40 hours of ship navigation data collected during theRoger RevelleRR1605 cruise 170 nautical miles southwest of Palau in May 2016. We found the PPP solutions were repeatable to 5·49 cm in the horizontal components and 12·4 cm in the vertical component. This demonstrates not only that PPP is a useful tool for positioning marine platforms in remote locations, but also that modern ship navigation instruments such as the Kongsberg Seapath 330 + are suitable for seafloor geodetic application.

Degree-wise validation of satellite-only and combined Earth gravity models in the frame of an orbit propagation scheme applied to a short GOCE arc

The procedure of satellite orbit analysis apart from its significance in orbit dynamics can be also used as an independent assessment tool for the available Earth gravity models. The contribution of these models, which represent the main gravitational component in dynamic orbit computations, can be performed in a degree-wise cumulative sense, thus quantifying the band-limited performance of the individual models at satellite altitude. In order to demonstrate such a procedure, which can be applied as a closed assessment tool for any Low Earth Orbiter (LEO), we apply it in the frame of orbit propagation of the GOCE (Gravity Field and Steady-State Ocean Circulation) satellite. Differences of the obtained GOCE orbits are compared with the corresponding Rapid Science Orbit (RSO) data. For the contribution of the dynamic component we used the gravity models EGM2008, EIGEN-5C, GGM03S, ITG-Grace2010s and AIUB-CHAMP03S. The actual calculation of the orbit is based on the numerical integration of the equation of motion according to an 8th order Gauss-Jackson multi-step method using the predictor-corrector algorithm. The proposed scheme leads to a validation of the different gravity models, providing an insight to the effect of the gravitational counterpart to the geometry of the orbit by referring explicitly all computations to the three components of the orbital frame.

Spatial error correlation of GPS atmospheres as determined from simulations

We have made Monte Carlo simulations in order to quantify the influence of several error sources on the atmospheric delay derived in our regular “Precise Point Positioning” analysis of GPS data. Satellite position and clock errors were found to be the greatest sources of error. The RMS size of the atmospheric delay error due to these sources is suggested to be 4–8 mm, and the correlation of the delay error over 1000 km is 0.5-0.7. In our real-time analysis of the atmospheric delay satellite orbits and clock offsets are modelled in the Kalman filter. The modelled errors suggest an uncertainty in the atmospheric delay of 10–13 mm, and a decrease in the correlation coefficients to about 0.65 over a distance of 1000 km. For both the Precise Point Positioning and the real-time analysis the influence from antenna signal scatter will give additional error contributions.

Tiros satellite orbit determination and analysis

The NOAA-TIROS satellite AVHRR's (Advanced Very High Resolution Radiometer) image referencing is studied with respect to methods in use. New improvements, taking into account the very low value of their orbit excentricity are studied with an appropriate differential perturbation method. The discussion shows that the quality of image referencing remains strongly connected to the GCP (Ground Control Points) choices.

Tesseral harmonics of 13th order from the analysis of satellite orbits at resonance

Resonant satellite orbit analyses at 13th order are used to determine individual tesseral harmonic coefficients of order 13 in the geopotential. Four analyses are utilized in total, two of which are from recent analyses which yielded results of very high precision. The linear equations are solved by a modified least squares technique in order to determine ten C, S pairs of harmonic coefficients at odd degree and seven C, S pairs at even degree. The results are constrained to the JGM2 gravity field model.

Long-periodic and secular perturbations to the orbits of Explorer 19 and Lageos due to direct solar radiation pressure

A theory for the long-term variations in the orbit of a spherically symmetric satellite due to direct solar radiation pressure is tested using two satellite orbit analyses. The first of these analyses is in terms of mean elements for the balloon satellite Explorer 19. The results are compared with the expected theoretical variations with short-period terms omitted. The second analysis utilises satellite laser ranging observations of the geodetic satellite, Lageos. A novel long-term analysis technique is developed primarily for laser ranging studies. The technique is tested along with the solar radiation pressure perturbation theory by comparing the results from the theory and the analysis.

Tesseral harmonic coefficients of order 30 from 14 resonant satellite orbit analyses

The results from 14 satellite orbit analyses, two of which are new objects, are used to determine individual tesseral harmonic coefficients of 30th-order and even degree. Six C, S pairs are evaluated by solving the equations using a modified least-squares technique. The results are compared with comprehensive geopotential models. The recent models GRIM4-C1, GEM-T3 and JGM-2 emerge well from such tests and are generally closest to the resonance values. A tentative solution is found for four pairs of harmonic coefficients of 30th-order and odd degree.

Individual geopotential harmonic coefficients of order 15 from 30 resonant satellite orbit analyses

The results from 30 15th-order resonant satellite orbit analyses are used to determine individual tesseral harmonics of order 15 in the Earth 's geopotential. The equations are solved by a modified least-squares method to determine 11 C and nine S tesseral harmonic coefficients of odd degree and 11 C, S pairs of even degree. For degree 15 to 23 the average standard deviation is 9 x 10 -10 , corresponding to an error of 6 mm in geoid height. The resonance values thus provide a strict independent standard of comparison for comprehensive geopotential models. The models emerge well from such tests, and the most recent models, GRIM4-C1, GEM-T3 and JGM -1, are closest to the resonance values.

The determination of the gas-surface interaction from satellite orbit analysis as applied to ANS-1 (1975-70A)

This paper considers the technique of orbital analysis as a means of determining the ill-defined gas-surface interaction between spacecraft and atmospheric molecules in Low Earth Orbit (LEO). The problem of representing the aerodynamics of complex vehicles in LEO is considered. The theory required to represent the relationship between the changes in the spacecraft trajectory and the gas-surface interaction is developed. This theory is then applied to the orbital data of ANS-1 (1975-70A) and the results of the analysis compared with those of previous investigators.

Ocean tides for satellite geodesy

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Precision orbit determination at the NASA Goddard Space Flight Center

The GEODYN Computer program has been developed by the Geodynamics Branch at the NASA Goddard Space Flight Center (GSFC) for accurate satellite orbit and tracking data analysis. The software is currently used for baseline solutions for the Crustal Dynamic Project (Smith et al. /1/), gravity field determination for the TOPEX/POSEIDON mission (Marsh et al. /2/), SEASAT and LAGEOS data analysis, Laser, Doppler and Altimetric data analysis, as well as prelaunch Mars Observer studies. A Bayesian least squares differential correction process is applied to the vehicle's trajectory, and a variety of force model, station, and measurement parameters can be simultaneously estimated.

Evaluation of 15th- and 30th-order geopotential harmonic coefficients from 26 resonant satellite orbits

The Earth's gravitational potential is usually expressed as an infinite series of harmonics, and the values of harmonic coefficients of order 15 and 30 can be determined most accurately by analysis of satellite orbits which experience 15th-order resonance. The results from two recent resonance analyses, for 1965-09A and 1968-70A, have here been added to those previously available, to produce an improved evaluation of 44 coefficients of order 15 and degree 15–36, and 12 coefficients of order 30 and even-degree 30, 32, …, 40. Compared with previous results, the new evaluation shows a great improvement in the standard deviations of many of the 15th-order coefficients of even-degree, thanks largely to the contribution of 1965-09A at inclination 31.8°: for the coefficients of degree 24, 26, 28 and 30, the standard deviation has been reduced by a factor of 3.1 on average; and for degree 32, 34 and 36 by a factor of 1.4 on average. For the other coefficients—those of 30th-order, and odd-degree 15th-order—the changes are relatively small. In the new 15th-order solution, all the 30 coefficients of degree 15–29 have standard deviations ⩽ 2.0 × 10 −9, and the average standard deviation of these 30 values is equivalent to an error in geoid height of 0.7 cm. Comparison of our values with those in comprehensive geoid models, which usually have larger standard deviation, lead us to conclude that, for order 15 and 30, the nominal standard deviations of the comprehensive models are quite realistic.

Explicit forms of some functions arising in the analysis of resonant satellite orbits

The analysis of resonant satellite orbits has been pursued for 18 years, and has led to the most accurate values available for lumped geopotential harmonics of the relevant orders. The basic theory for the resonance effects was developed in the 1960s, but the detailed application of the technique calls for a systematic notation and for the evaluation of two subsidiary functions, namely F̄ , a function of the orbital inclination, and G , a function of the eccentricity. The present paper sets out explicitly the variations in inclination and eccentricity produced by relevant harmonics at the most common resonances (15:1, 14:1, 16:1, 29:2 and 31:2), using the notation that has become standardized in recent years. The paper also gives appropriate expressions for calculating F̄ and G , and lists a Fortran program GQUAD for evaluating G .

Geopotential harmonics of orders 15 and 30

The Earth's gravitational potential is usually expressed as a double infinite series of spherical harmonics. In recent models1–3, derived from photographic, radio and laser observations of satellites, gravimetry and satellite altimetry, the harmonics have been evaluated up to a degree and an order of 36 or more, so that there are 1,296 or more coefficients to be evaluated. The geoid surfaces derived from such models have errors of approximately 1 m, but much better accuracy is required to take advantage of satellite altimeter measurements accurate to 10 cm or better. So there is a continuing demand to improve the models. The accuracy of the individual coefficients is questionable, and difficult to estimate4. The most precise technique for determining coefficients of a particular order is by analysis of satellite orbits which experience resonance with the Earth's gravitational field. We have recently5 re-evaluated individual harmonic coefficients of orders 15 and 30 from analyses of 24 orbits having a wide range of inclinations to the Equator. These coefficients have standard deviations equivalent to an accuracy in geoid height of 1 cm, for degree up to 23, and are valuable as a standard against which the comprehensive gravity field models can be tested.

The Earth's shape and gravity field: a report of progress from 1958 to 1982

Summary. A major step forward in geophysics during the last 25 years has been the progress in the determination of the Earth’s shape and gravity field, from the halting steps of the first satellite orbit analyses to the global solutions expanded in spherical harmonics up to degree 36, and from painstaking gravity surveys on land to the detailed regional geoids derived from altimeter observations. No other geophysical quantity pertaining to lateral variations in the structure of the crust and mantle is now known with a comparable accuracy and spatial resolution. An increasingly acute problem has been to find ways to validate the global results since differences between individual solutions remain substantial. Absolute tests are not available but statistical comparisons produce some useful insight into the status of the recent gravity field models. A number of recent models are evaluated in this paper. A primary conclusion is that the gravity or geoid anomalies are frequently not as well determined as stated by the autbors. We estimate, for example, that the root mean square errors of the geoid heights deduced from models by Lerch et al. and Gaposchkin are about 3m and that maximum errors may exceed 10m in some places. A considerable part of this comes from uncertainties in the low degree harmonics, in particular the degree and order 3 coefficients and more generally the odd degree coefficients, for while the signal-to-noise ratio of these coefficients is high the power in the spectrum is also high. Most tests developed for evaluating the gravity fields are insensitive to the long wavelength components in the spatial spectrum. Future projects call particular attention to improving the high degree part of the geopotential spectrum but thought should also be given to these low degree harmonics. Considerable progress in determining the gravity field can still be made by using data already available.

Upper-atmosphere zonal winds from satellite orbit analysis

In this paper we review and interpret the values of upper-atmosphere rotation rate (zonal winds) obtained by analysing satellite orbits determined from observations. The history of the method is briefly reviewed, the basic principles are explained, objections to the method are answered, and three examples are given. Existing analyses of the atmospheric rotation rate A are critically reviewed, and, after rejecting some and revising others, we are left with 85 values. These are divided according to local time and season, to give the variation of A with height in nine situations—namely morning, evening and average local time, for summer, winter and average season. These observational results indicate that the value of Λ (in rev/day), averaged over both local time and season, increases from 1.0 at 125 km to 1.22 at 325 km and then decreases to 1.0 at 430 km and 0.82 at 600 km. The value of Λ is higher in the evening (18–24 h), with a maximum value (near 1.4) corresponding to a West-to-East wind of 150 m s −1 at heights near 300 km. The value of Λ is lower in the morning (06–12 h), with East-to-West winds of order 50 m s −1 at heights of 200–400 km. There is also a consistent seasonal variation, the values of Λ being on average 0.15 higher in winter and 0.1 lower in summer than the average seasonal value. No significant variation with solar activity is found, but there is a slight tendency for a greater rotation rate at lower latitudes for heights above 300 km. Unexpectedly, the values for the 1960s are found to be significantly higher than those for the 1970s. Finally, these observational values are compared with the theoretical global model of Fuller-Rowell and Rees: there is complete agreement on the trends, though there are some differences in the mean values.

The inverse problem of constructing a gravimetric geoid

Computation of a single geoidal height from gravity acceleration data formally requires that the latter be known everywhere on the earth. We present a computational procedure based on linear inverse theory for estimating geoidal heights from incomplete sets of data. The same scheme can be used to estimate gravity accelerations from altimetry‐derived geoids. The systematic error owing to lack of data and the choice of a particular inverse operator is described by using resolution functions and their spherical harmonic expansions. An rms value of this error is also estimated by assuming a spectrum for the unknown geoid. The influence of the size of the data region, the spacing between data, the filtering applied to the data, and the model weighting function chosen are all quantified in a spherical geometry. The examples presented show that when low degree spherical harmonic coefficients are available—from satellite orbit analysis—a band‐passed version of the geoid can be constructed from local gravity data, even with a relatively restricted data set.