Orbital Arc Research Articles

Modeling GPS satellite attitude variation for precise orbit determination

High precision geodetic applications of the Global Positioning System (GPS) require highly precise ephemerides of the GPS satellites. An accurate model for the non-gravitational forces on the GPS satellites is a key to high quality GPS orbit determination, especially in long arcs. In this paper the effect of the satellite solar panel orientation error is investigated. These effects are approximated by empirical functions to model the satellite attitude variation in long arc orbit fit. Experiments show that major part of the long arc GPS orbit errors can be accommodated by introducing a periodic variation of the satellite solar panel orientation with respect to the satellite-Sun direction, the desired direction for solar panel normal vector, with an amplitude of about 1 degree and with a frequency of once per orbit revolution.

Room temperature deposition of gold onto the diffuse and sharp diffraction spot [formula omitted] surfaces

Room temperature gold depositions onto Si(111)-( 3 × 3 ) R30° Au surfaces with diffuse and sharp diffraction spots [Surf. Sci. 242 (1991) 73] (diffuse and sharp 3 × 3 Au hereafter) under UHV conditions has been monitored using transmission electron diffraction (TED). Both systems display an increase in surface structure diffraction spot intensities up to the completion of 1.0 monolayer (ML) after which the surface beams display an exponential decrease in intensity with coverage. The exponential decay rate decreases after roughly 1.33 ML. These results can be attributed to gold initially diffusing to and filling 3 × 3 Au gold trimer sites in vacancy type surface domain walls [Surf. Sci. 342 (1995) 233], then filling one of three possible sites on the 3 × 3 Au structure with essentially no surface diffusion, disrupting nearby gold trimers. Gold deposition onto the diffuse type structure caused the formation and expansion of satellite arcs around the strongest 3 × 3 beams similar to those seen by others [Surf. Sci. 242 (1991) 73; Jpn. J. Appl. Phys. 16 (1977) 891; J. Vac. Sci. Technol. A 10 (1992) 3486] at elevated temperatures while the sharp structure displayed only a modest shoulder formation near the strongest 3 × 3 beams.

The Discovery and Orbit of 1993 (243)1 Dactyl

Dactyl was discovered in solid state imaging (SSI) data on February 17, 1994, during the long playback of approach images from the Galileo spacecraft's encounter with the asteroid 243 Ida. Forty-seven images of the Ida–Dactyl pair were obtained. A detailed search for other satellites was made. No confirmed detections were made, all other candidate features being consistent with radiation hits. We deduce a manifold of osculating two-body orbits that approximate Dactyl's motion over the observed orbital arc depending on the assumed mass of Ida. At the time of Galileo's encounter, Dactyl was found to be 85 km from the center of Ida, moving at ∼6 m·sec−1in the same rection as Ida's retrograde spin. The inclination of its orbit is ∼172° in Ida's equatorial system (IAU definition). It was not possible to obtain a definitive orbit or measure of Ida's mass from the observed motion even though supplemental techniques (search for Dactyl's shadow on Ida, changes in angular diameter and brightness, and attempts to determine the spin of Dactyl) were explored. The influence of Ida's irregular gravitational field and solar perturbations on two-body motion are evaluated and found to be undetectable in the observed orbital arc. These effects may, however, strongly influence the motion over orbital time scales. Limits to the value of Ida's gravitation parameter,GM, are derived. A robust lower limit,GM> 0.0023 km3·sec−2, is obtained by requiring Dactyl's orbit to be bound. Hubble Space Telescope observations, which show no evidence of Dactyl on a hyperbolic orbit, excludes values ofGMin the range 0.00216 <GM< 0.0023 km3·sec−2. An upper limit,GM< 0.0031 km3·sec−2, deduced by requiring that the orbital motion has a long lifetime in a realistic approximation to Ida's gravitational field, is illustrated with numerical calculations. Ida's mass is therefore constrained to the range 4.2 ± 0.6 × 1019g, which, together with a volume of 16,100 ± 1900 km3(Thomas P. C., M. J. S. Belton, B. Carcich, C. R. Chapman, M. E. Davies, R. Sullivan, and J. Veverka 1996.Icarus120, 20–32.) yields a bulk density of 2.6 ± 0.5 g·cm−3(Belton, M. J. S., C. R. Chapman, P. C. Thomas, M. E. Davies, R. Greenberg, K. Klaasen, D. Byrnes, L. D'Amario, S. Synnott, T. V. Johnson, A. McEwen, W. Merline, D. R. Davis, J-M. Petit, A. Storrs, J. Veverka, and B. Zellner 1995.Nature374, 785–788.).

The filtering effect of orbit correction on geopotential errors

The geophysical interpretation of satellite tracking residuals generally ignores the filtering effect of initial orbit correction on the true errors of the model. While the filtered information is usually regarded as lost, knowing the spectral characteristics of the filter is a great aid in the detailed interpretation of residuals, especially of global data sets. In this regard, we derive the filter characteristics (admittances) of orbit correction in the presence of geopotential-caused trajectory errors. We then apply the filter to determine the likely power of the lost radial information in crossover differences of sea heights determined from satellite altimetry or in the latitude lumped coefficients derived from them. For example, we find that resonant geopotential information with periods longer than the corrected orbit's arc length is largely lost in residual crossover data. Results are given for GEOSAT, ERS-1 and TOPEX/Poseidon in their Exact Repeat Missions, using calibrated variancecovariance matrices of the harmonic geopotential coefficients of several recent Earth gravity models. To prove that filtering is important, we first employed a simple cut of all perturbing terms with periods longer than the general tracking period (4 days for GEOSAT and ERS-1, and 10 days for TOPEX). But the cut is too crude a method from a theoretical viewpoint, and thus, we developed two new filters. A comparison of their admittances explains the differences (and sometimes anomalous behaviour) between them and the cut. Many numerical examples (single-satellite crossover errors and latitude lumped coefficient errors, as projected from the variance-covariance matrices) are presented. This paper has been presented during the Panel on Satellite Dynamics, at COSPAR 1994, in Hamburg, Germany.

Consideration of Practical Visibility of Geostationary Augmentation Satellites from Aircraft

The visibility of geostationary augmentation and GPS satellites from typical aircraft engaged in banked turning maneuvers is considered. First, the optical visibility from the GPS antenna location to the geostationary orbital arc is analyzed. It is shown that if two geostationary satellites at substantially different azimuths are available, they are blocked at different times during the aircraft turn, so that at no time during the maneuver is the aircraft without at least one geostationary's signal. Test flight data provided by Boeing for GPS satellites are then used to indicate that actual signal reception often continues well below the pessimistic optical mask. These considerations, as well as the operational fact that large banking angles do not occur in the final approach phase where integrity and continuity are most important, suggest that geostationary augmentation will remain effective at much higher latitudes than has been indicated in previous references.

Possibilities of using extreme observations to estimate cometary nucleus sizes

Not considering very rare ”in situ” measurements of cometary nuclei, observations of comets at large heliocentric distances are the only direct source of our knowledge on their sizes. Observations of a cometary nucleus in pure reflected sunlight, at the time when coma is absent, are the way in which the nucleus size can be estimated. Probabilities that extreme observations represent non—active stages of cometary nuclei and also reliability of derived cometary nucleus sizes are investigated. Statistical analysis is based on a sample of 2842 photometric observations of 67 long-period comets observed at large heliocentric distances. For any long-period comet, there is a probability of 2:3 that the sizes derived on the basis of observations at extreme distances are in good agreement with the real nucleus sizes. For new comets in Oort's sense the probability is 3:4 independent of investigated arcs of orbits. For old comets a chance to estimate correct sizes is 1:2 but on the pre-perihelion arc only 1:3. It is also demonstrated that a premature start of activity prior to perihelion or a longer fading after perihelion is more frequent than a short-time isolated activity at large heliocentric distances.

Radiative forces and LAGEOS' orbit

The orbit analysis of LAGEOS satellite has resulted into the discovery and/or reassessment of several very small sources of perturbation on satellite orbits. The analysis of orbital arcs of duration ranging from one month to several years has revealed that perturbative effects are present, having unpredicted long-term or secular components down to the 10 −12 m/s 2 acceleration level. It was soon realized that those perturbations have a non-gravitational origin. In recent years, we have devoted some effort to the physical modelling of radiative perturbations, caused by momentum exchanges with an appropriate radiative field, and have considered their potential role in the analysis of LAGEOS orbit residuals. These perturbations include: (i) direct solar radiation pressure; (ii) radiation pressure from the Earth's emitted/reflected/diffused radiation flux; (iii) the so-called thermal thrust force. The main results of this work are reviewed, discussing its relationships with models developed by other research groups. In particular, we present a list of the physical processes which still appear to need more detailed and realistic modelling to reach a better understanding of LAGEOS dynamics at the 10 −12 m/s 2 level.

Radial orbit error reduction and mean sea surface computation from the Geosat altimeter data

Using the altimeter data from the Geosat Exact Repeat Mission, we have produced yearly averaged mean profiles and a global mean sea surface. The radial error of each 6‐day orbital arc computed with the GEM‐T2 geopotential was first estimated by calculating the amplitude and phase of the nine dominant frequencies of the difference between the altimetric profiles and the mean sea surface obtained when adding the permanent sea surface topography (computed from the Levitus' Climatological Atlas) to the GEM‐T2 geoid. We show that this operation is little affected by the choice of the geoid or by its formal error. The resulting correction has been subtracted from each individual arc. Yearly mean profiles were then obtained by averaging the corrected altimetric data of each repeat cycle on a yearly basis. Their noise level is 1 to 2 cm and their resolution is 20 km, but the differences of the altimetric heights at crossovers of ascending and descending tracks are still 30 cm nns. The latter can be reduced to 7 cm rms by a crossover analysis. In addition to the mean values, standard deviations were computed at each point of the repeat cycle. This “yearly along‐track variability” is of the order of 10 cm rms and is dominated by the ocean mesoscale variability. A global yearly mean sea surface has been derived by bilinear interpolation. Its resolution ranges approximately from 160 km to 80 km, depending on the latitude. It is shown to be much less noisy than those deduced from GEOS 3 and Seasat data.

低推力推進と重力捕捉による月周回軌道達成のための設計法

This paper discusses a trajectory synthesis for low thrust Lunar orbiter travelling between a low Earth circular orbit and a low Lunar one. The low thrust trajectory discussed here is made up of three phases which are the Earth spiral ascending phase, the Lunar capture phase and the Lunar spiral descending phase, each of which plays proper roles in the transfers to the Lunar orbit. The Lunar capture phase is the most important one in which the orbiter is guided from a parking orbit of around 150, 000km radius to an elliptical orbit with the eccentricity of about 0.3 by thrusting only in the one side of the orbital arc, attracted by the Lunar gravitational force and put into the Lunar sphere of influence on the conditions to achieve near circular but unstable Lunar orbit, and finally transferred to a stable circular orbit by using the low thrust with acceleration levels of the order of 10-5G. In this paper, the conditions to establish the Lunar capturing are considered and expressed as numerical relations of the entry radius and velocity into the Lunar sphere of influence. Such relations are derived from trajectory simulations. Also typical trajectories to the Moon are shown as samples to evaluate the time of flights, consumed propellant weights and the orbital control capabilities.

An improved gravity model for Mars: Goddard Mars model 1

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, Goddard Mars Model 1 (GMM‐1). This model employs nearly all available data, consisting of approximately 1100 days of S band tracking data collected by NASA's Deep Space Network from the Mariner 9 and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM‐1 is complete to spherical harmonic degree and order 50, which corresponds to a half‐wavelength spatial resolution of 200–300 km where the data permit. GMM‐1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM‐1 over previous models is a consequence of several factors: improved computational capabilities, the use of optimum weighting and least squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X band tracking data from the 379‐km altitude, near‐polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM‐1, particularly at high latitudes where current data poorly resolve the gravitational signature of the planet.

Spectral characteristics of time‐dependent orbit errors in altimeter height measurements

A mean reference surface and time‐dependent orbit errors are estimated simultaneously for each exact‐repeat ground track from the first two years of Geosat sea level estimates based on the Goddard Earth model (GEM)‐T2 orbits. Motivated by orbit theory and empirical analysis of Geosat data, the time‐dependent orbit errors are modeled as 1 cycle per revolution (cpr) sinusoids with slowly varying amplitude and phase. The method recovers the known “bow tie effect” introduced by the existence of force model errors within the precision orbit determination (POD) procedure used to generate the GEM‐T2 orbits. The bow tie pattern of 1‐cpr orbit errors is characterized by small amplitudes near the middle and larger amplitudes (up to 160 cm in the 2 years of data considered here) near the ends of each 5‐ to 6‐day orbit arc over which the POD force model is integrated. A detailed examination of these bow tie patterns reveals the existence of daily modulations of the amplitudes of the 1‐cpr sinusoid orbit errors with typical and maximum peak‐to‐peak ranges of about 14 cm and 30 cm, respectively. The method also identifies a daily variation in the mean orbit error with typical and maximum peak‐to‐peak ranges of about 6 cm and 30 cm, respectively, that is unrelated to the predominant 1‐cpr orbit error. It is suggested that the two daily signals arise from daily adjustments of the drag coefficient in the GEM‐T2 POD procedure. Application of the simultaneous solution method to the much less accurate Geosat height estimates based on the Naval Astronautics Group orbits concludes that the accuracy of POD is not important for collinear altimetric studies of time‐dependent mesoscale variability (wavelengths shorter than 1000 km), as long as the time‐dependent orbit errors are dominated by 1‐cpr variability and a long‐arc (several orbital periods) orbit error estimation scheme such as that presented here is used. The accuracy of POD becomes more important for studies of larger‐scale variability.

One Year of Daily Satellite Orbit and Polar Motion Estimation for Near Real Time Crustal Deformation Monitoring

The Permanent GPS Geodetic Array (PGGA) in southern California consists of five continuously operating stations established to monitor crustal deformation in near real time. The near real time requirement has been problematic since GPS satellite ephemerides and predicted earth orientation values (IERS Bulletins A and B) have been found to be neither sufficiently timely nor accurate to achieve horizontal position accuracies of several mm on regional scales. Therefore, we have been estimating precise GPS ephemerides and polar motion since August 1991. An examination of overlapping 24-hour satellite arcs indicates worst-case orbital errors of approximately 0.2 meters in the radial components, 1 meter in the cross-track components and 2–3 meters in the along-track components. A comparison with very long baseline interferometry indicates an accuracy of less than 1 mas in our determination of 24-hour values of pole position. These products are sufficiently timely and accurate to achieve several mm long-term horizontal precision in regional scale measurements of crustal deformation in near real time, as has been demonstrated during the 28 June, 1992 Landers and Big Bear earthquakes in southern California. The PGGA stations were able to detect seismically induced, sub-centimeter-level motions with respect to a terrestrial reference frame defined by the global tracking stations.

Geometric improvement of the spot satellite orbit using Doris Doppler residual data

After adjustment of a satellite orbit by classical dynamical methods, the residuals of tracking data from a Doppler satellite tracking network still contain information. They are used to further adjust geometrically the orbit, the station coordinates, and Doppler biases and drifts for each station. After extensive testing in simulation, the method is applied to 21 days of the DORIS data from the SPOT2 satellite. As this tracking network has an excellent coverage and a very low measurement noise, the orbit reproducibility in the tangential direction is reduced from 40–100 cm root‐mean‐squares (rms) with a classical dynamical orbit calculation to 7–32 cm rms for the geometrical orbit, based on the difference between 2‐day orbit arcs overlapping over 1 day. The reproducibility in the radial direction is slightly improved to 6–30 cm rms on the same arcs, with the most significant effect on the 1/revolution frequency. The formal error is also mostly reduced on this frequency. The Doppler residuals are reduced from 2–13 to 0.7–1.4 mm/s. This is only 3 times the measurement noise level and allows identification of ionospheric (magnetic storms), tropospheric (large atmospheric water vapor), and geometric effects (low elevation angles) in the data. Five‐day orbit arcs of this improved orbit are used to recalculate station positions: A reproducibility of 4–13 cm is achieved on short distances (50 km), which is better than what is obtained with 15‐day arcs of the initial dynamical orbit. Furthermore, for nine stations collocated with laser satellite tracking stations, the rms difference between their position calculated with 15 days of orbit and their independently estimated geodetic values is reduced from 56 cm rms with the dynamical orbit to 33 cm rms with the geometric orbit: This demonstrates that the improved reproducibility corresponds to an improved accuracy.

Length of arc as independent argument for highly eccentric orbits

For analytic step regulation in numerical integration of highly eccentric orbits it is proposed to use the orbital arc length of a moving particle as independent argument.

Application of Encke's method to long arc orbit determination solutions

Application of Encke's method to long arc orbit determination solutions

Optimum data weighting and error calibration for estimation of gravitational parameters

A new approach has been developed for determining consistent satellite-tracking data weights in solutions for the satellite-only gravitational models. The method employs subset least-squares solutions of the satellite data contained within the complete solution and requires that the differences of the parameters of subset solutions and the complete solution to be in agreement with their error estimates by adjusting the data weights. GEM-T2 model was recently computed and adjusted through a direct application of this method. The estimated data weights are markedly smaller than the weights implied by the formal uncertainties of the measurements. Orbital arc tests as well as surface gravity comparisons show significant improvements for solutions when more realistic data weighting is achieved.

First epoch geodetic measurements with the Global Positioning System across the Northern Caribbean Plate Boundary Zone

The first geodetic survey across the northern Caribbean plate boundary zone with the Global Positioning System (GPS) was conducted in June 1986. Baseline vectors defined by the six station regional GPS network ranged from 170 to 1260 km in length. Repeatability of independent daily baseline estimates was better than 8 mm plus 1.3 parts in 108 of baseline length for horizontal components. The wet tropospheric path delay during the experiment was both high, sometimes exceeding 30 cm at zenith, and variable, sometimes exceeding 5 cm variation over several hours. Successful carrier phase cycle ambiguity resolution (“bias fixing”) could not be achieved prior to construction of a regional troposphere model. Tropospheric calibration was achieved with water vapor radiometers at selected sites, and with stochastic troposphere models and estimation techniques at remaining sites. With optimum troposphere treatment and single‐day orbital arcs, we resolved most biases on baselines up to about 550 km in length. With multiday orbital arcs we resolved most biases in the network regardless of baseline length. Our results suggest that constraints on plate boundary zone deformation in the Greater Antilles, and on the North America‐Caribbean relative plate motion vector, can be obtained with a series of GPS experiments spanning less than 10 and 15 years, respectively.

On orbit determination accuracy of space-VLBI satellites

Abstract The usefulness of space-VLBI for astrometric and geodynamic applications depends strongly on the orbit determination accuracy of the satellites involved. The requirements are very strict. In this paper, the results are presented of some preliminary investigations on the achievable orbit accuracy of the Soviet Radioastron and the ESA QUASAT space-VLBI satellites. For this purpose, simulations have been performed for a total of 23 orbital arcs, in which satellite observations from Precise Range and Range-rate Equipment (PRARE) were considered, as well as VLBI-type tracking of the satellite signals. The assumed tracking network consisted of 2 to 3 VLBI and 3 to 18 PRARE stations. The computations were carried out at Delft University of Technology using a computer program for covariance analysis of orbit determination problems.

Variations in effective compensation depth across Aphrodite Terra, Venus

Aphrodite Terra is the largest elevated terrain on Venus and it serves as a focal point in current discussions of global tectonic style. Using the topography and gravity data acquired by the Pioneer Venus Orbiter (PVO) we have estimated an effective depth of Airy compensation for each of 75 orbital arcs that provide fairly uniform areal coverage of the entire province. The most pronounced pattern that emerges is a general increase in compensation depth to the east. The most rapid change occurs near 135°; the average west of there is 70 km, while the average to the east is 230 km. Superimposed on this larger trend are five distinctive regional patterns, four well defined peaks and one interval of widely scattered and poorly constrained depths. The maxima in compensation depth are well correlated with regional topographic highs. While these observations are easily reconciled with the general notion that Aphrodite is a region of crustal divergence, the great depth of compensation is difficult to accord with the more specific suggestion that Aphrodite is a terrestrial type divergent plate margin. The alternative suggestion that Aphrodite, and the other equatorial highlands on Venus, are surface manifestations of hot, upwelling mantle plumes is consistent both with the great depths of compensation and with the pattern of regional peaks and intervening troughs. The broader scale increase in effective depth of compensation from west to east is more enigmatic, but it might reflect an age progression of the plumes.

A satellite system synthesis model for orbital arc allotment optimization

A mixer-integer programming formulation is presented of a satellite system synthesis problem, or geostationary-orbital-planning synthesis problem, which is referred to as the arc allotment problem (AAP). Each satellite administration is to be allotted a weighted-length segment of the geostationary orbital arc within which its satellites may be positioned at any longitude. The objective function maximizes the length of the unweighted arc segment allotted to every administration, subject to single-entry cochannel interference restrictions and constraints imposed by the visible arc for each administration. Useful relationships between special cases of AAP and another satellite synthesis problem are established. Solutions to two example problems are presented. >