Numerical Computation of Satellite Orbits Using Lie Series. Comparison with Other Methods
Lie series for numerical computation of satellite orbits
COMPUTATION↗
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Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets
Natural orbitals are often used to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual–virtual block of the state density matrix instead of the canonical Hartree–Fock orbitals results in smaller errors when the same fraction of virtual space is frozen. This strategy, termed frozen natural orbital (FNO) approach, is effective in reducing the cost of regular coupled-cluster (CC) calculations and some multistate methods, such as EOM-IP-CC (equation-of-motion CC for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip). In contrast to EOM-IP-CCSD, EOM-SF-CCSD relies on high-spin open-shell references. Using FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties due to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. Furthermore, by means of singular value decomposition (SVD) of the overlap matrix of the α and β orbitals, the OSFNO algorithm identifies the corresponding orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference, thus facilitating a safe truncation of the virtual space. The performance of OSFNO is benchmarked for selected diradicals and triradicals.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Spaceborne Gravity Gradiometers. Part 2: Role of gravity gradiometers in NASA's programs
Sources of information for present knowledge of Earth's gravitational field are discussed as well as the Goddard Earth models. Improvements to these models can be achieved by using additional data and reprocessing some earlier data. Plans for using satellite-to-satellite tracking and gravity gradiometers for the geopotential research mission are considered as well as the relative merits of each method. Present knowledge of solar system bodies and strategies for their exploration are also described. A core program for planetary exploration through the year 2000 is summarized as well as ten candidate subsequent missions. Of these, the lunar geoscience orbiter has the best justification for a gravity gradiometer since far side gravity data can be acquired without the requirement for a separate communications relay satellite. For rendezvous missions, the gradiometer can permit on-board automation of orbit computation and control thus reducing the time devoted to communication with an orbiter.
Source record↗
On the nature of the radial and cross track errors for artificial earth satellites
The analysis of the radial and cross track errors of artificial earth satellites is discussed in terms of the interference of two one-dimensional celestial mechanical wave trains. Resulting equations for these tracking errors describe the behavior of the uncertainties in the orbital parameters as oscillatory in nature, with a rapidly oscillating term, which is a function of the sum of the observed and computed orbital frequencies, modulated in amplitude by a slowly varying oscillation. This latter term is itself a function of either the difference between these orbital frequencies or between the values of the computed and observed right ascensions, depending upon whether it is the radial or cross track case under consideration. These results indicate that the cross track calculation describes the behavior of uncertainties in the right ascension of the ascending node and the inclination, while the radial calculation gives information on uncertainties in the semi-major axis, the eccentricity, and the argument of perigee. In addition, expressions for the radial and cross track oscillatory frequencies are obtained in terms of the orbital frequencies of the satellites. Data show that the time average of the radial and cross track errors in any case, will both approach zero.
Bonavito, N. L.↗
On the nature of the radial and cross track errors for artificial earth satellites
The paper discusses the analysis of the radial and cross track errors of artificial earth satellites in terms of the interference of two one-dimensional celestial mechanical wave trains. The resulting equations for these tracking errors describe the behavior of the uncertainties in the orbital parameters as oscillatory in nature, with a rapidly oscillating term, which is a function of the sum of the observed and computed orbital frequencies, modulated in amplitude by a slowly varying oscillation. This latter term is itself a function of either the difference between these orbital frequencies or between the values of the computed and observed right ascensions, depending upon whether it is the radial or cross track case under consideration. Results indicate that the cross track calculation describes the behavior of uncertainties in the right ascension of the ascending node and the inclination, while the radial calculation gives information on uncertainties in the semi-major axis, the eccentricity, and the argument of perigee.
Bonavito, N. L.↗
The computation of relative motion with increased precision
Encke's method as modified by Potter to increase the accuracy of orbit computations of gravitationally interacting bodies is applied to the problem of relative motion of non-interacting space vehicles. This technique is then combined with a simple transformation of the independent variable to arrive at a system of equations from which the relative motion may be determined with increased precision.
Nacozy, P.↗
Formation of on-site normal points
We describe our methods of fitting a smoothing function to observational range differences from a predicted orbit, by deducing corrections to the orbit in the radial and along-track directions. The method has been used on observations of a variety of satellites, and using predicted orbits computed both by numerical integration using IRV's as starting values and analytically from orbital elements. The along-track corrections to the predicted orbit have been successfully used in the form of time biases to improve subsequent predictions, and a statistical test has been devised to ensure that the range residuals may be used to form unbiased quick look normal points.
Appleby, G. M.↗
Preliminary orbital parallax catalog
The study is undertaken to calibrate the more reliable parallaxes derived from a comparison of visual and spectroscopic orbits and to encourage observational studies of other promising binaries. The methodological techniques used in computing orbital parallaxes are analyzed. Tables summarizing orbital data and derived system properties are then given. Also given is a series of detailed discussions of the 71 individual systems included in the tables. Data are listed for 57 other systems which are considered promising candidates for eventual orbital parallax determination.
Halliwell, M.↗
THE SUN WAS NOT BORN IN M67
Using the most recent proper-motion determination of the old, solar-metallicity, Galactic open cluster M67 in orbital computations in a non-axisymmetric model of the Milky Way, including a bar and three-dimensional spiral arms, we explore the possibility that the Sun once belonged to this cluster. We have performed Monte Carlo numerical simulations to generate the present-day orbital conditions of the Sun and M67, and all the parameters in the Galactic model. We compute 3.5 Multiplication-Sign 10{sup 5} pairs of orbits Sun-M67 looking for close encounters in the past with a minimum distance approach within the tidal radius of M67. In these encounters we find that the relative velocity between the Sun and M67 is larger than 20 km s{sup -1}. If the Sun had been ejected from M67 with this high velocity by means of a three-body encounter, this interaction would have either destroyed an initial circumstellar disk around the Sun or dispersed its already formed planets. We also find a very low probability, much lower than 10{sup -7}, that the Sun was ejected from M67 by an encounter of this cluster with a giant molecular cloud. This study also excludes the possibility that the Sun and M67 were born in the same molecular cloud. Our dynamical results convincingly demonstrate that M67 could not have been the birth cluster of our solar system.
79 ASTRONOMY AND ASTROPHYSICS↗
Mission operations computing systems evolution
As part of its preparation for the operational Shuttle era, the Goddard Space Flight Center (GSFC) is currently replacing most of the mission operations computing complexes that have supported near-earth space missions since the late 1960's. Major associated systems include the Metric Data Facility (MDF) which preprocesses, stores, and forwards all near-earth satellite tracking data; the Orbit Computation System (OCS) which determines related production orbit and attitude information; the Flight Dynamics System (FDS) which formulates spacecraft attitude and orbit maneuvers; and the Command Management System (CMS) which handles mission planning, scheduling, and command generation and integration. Management issues and experiences for the resultant replacement process are driven by a wide range of possible future mission requirements, flight-critical system aspects, complex internal system interfaces, extensive existing applications software, and phasing to optimize systems evolution.
Kurzhals, P. R.↗
INFRARED SPECTROSCOPY OF SYMBIOTIC STARS. X. ORBITS FOR THREE S-TYPE SYSTEMS: V1044 CENTAURI, HEN 3-1213, AND SS 73-96
Employing new infrared radial velocities, we have computed orbits of the cool giants in three southern S-type symbiotic systems. The orbit for V1044 Cen, an M5.5 giant, has a period of 985 days and a modest eccentricity of 0.16. Hen 3-1213 is a K4 giant, yellow symbiotic with an orbital period of 533 days and a similar eccentricity of 0.18. For the M2 giant SS 73-96 the orbital period is 828 days, and this system has a somewhat larger eccentricity of 0.26. Measurement of the H i Paschen δ emission lines, which may at least partially reflect the motion of the secondary in SS 73-96, results in a mass ratio of 2.4 for the M giant relative to the presumed white dwarf. The estimated orbital inclinations of V1044 Cen and Hen 3-1213 are low, about 40°. However, for SS 73-96 the predicted inclination is 90°, and so an ephemeris for eclipses of the secondary or the hot nebula surrounding it is provided. A search of the orbital velocity residuals of V1044 Cen and SS 73-96 for pulsation periods produced no realistic or convincing period for either star.
79 ASTRONOMY AND ASTROPHYSICS↗
Computer simulation results of attitude estimation of earth orbiting satellites
Computer simulation results of attitude estimation of Earth-orbiting satellites (including Space Telescope) subjected to environmental disturbances and noises are presented. Decomposed linear recursive filter and Kalman filter were used as estimation tools. Six programs were developed for this simulation, and all were written in the basic language and were run on HP 9830A and HP 9866A computers. Simulation results show that a decomposed linear recursive filter is accurate in estimation and fast in response time. Furthermore, for higher order systems, this filter has computational advantages (i.e., less integration errors and roundoff errors) over a Kalman filter.
Kou, S. R.↗
Phase-space sensitivity (weight functions) of 3 MeV proton diagnostics
Abstract The weight function W ( X ) is a diagnostic sensitivity to phase-space variables X that relates the measured signal C to the distribution function F ( X ) through the equation C = ∫ W ( X ) F ( X ) d X . In the present work, an algorithm to calculate W for a diagnostic that measures 3 MeV protons produced in d(d,p)t fusion reactions between a fast ion and a thermal deuteron is developed. The emitted protons escape the tokamak on curved orbits and are detected. These curved orbits constitute effective diagnostic ‘sightlines’. The presented algorithm accounts for the complications associated with these curved sightlines. An initial calculation of time-reversed proton orbits computes effective solid angles and sightlines for the relevant range of incident proton velocity vectors. These precomputed orbits are then used within the framework of FIDASIM (2020 Plasma Phys. Cont. Fusion 62 105008) to calculate the reactivity averaged over the thermal distribution of the ‘target’ deuterons and the probability that a fast ion of specified energy and pitch has a gyroangle that is consistent with the kinematic equations along each of the sightlines. Comparisons with analytic formulas and with independent calculations for the Mega Amp Spherical Tokamak 3 MeV proton diagnostic verify the algorithm.
Physics↗
Analyses for precision reduced optical observations from the international satellite geodesy experiment (ISAGEX)
During the time period of December 1970 to September 1971 an International Satllite Geodesy Experiment (ISAGEX) was conducted. Over fifty optical and laser tracking stations participated in the data gathering portion of this experiment. Data from some of the stations had not been previously available for dynamical orbit computations. With the recent availability of new data from the Astrosoviet, East European and other optical stations, orbital analyses were conducted to insure compatibility with the previously available laser data. These data have also been analyzed using dynamical orbital techniques for the estimation of estimation of geocentric coordinates for six camera stations (for Astrosoviet, two East European). Thirteen arcs of GEOS-1 and 2 observations between two and four days in length were used. The uncertainty in these new station values is considered to be about 20 meters in each coordinate. Adjustments to the previously available values were generally a few hundred meters. With these geocentric coordinates these data will now be used to supplement earth physics investigations during the ISAGEX.
Marsh, J. G.↗
Status of Precise Orbit Determination for Jason-2 Using GPS
The JASON-2 satellite, launched in June 2008, is the latest follow-on to the successful TOPEX/Poseidon (T/P) and JASON-I altimetry missions. JASON-2 is equipped with a TRSR Blackjack GPS dual-frequency receiver, a laser retroreflector array, and a DORIS receiver for precise orbit determination (POD). The most recent time series of orbits computed at NASA GSFC, based on SLR/DORIS data have been completed using both ITRF2005 and ITRF2008. These orbits have been shown to agree radially at 1 cm RMS for dynamic vs SLRlDORIS reduced-dynamic orbits and in comparison with orbits produced by other analysis centers (Lemoine et al., 2010; Zelensky et al., 2010; Cerri et al., 2010). We have recently upgraded the GEODYN software to implement model improvements for GPS processing. We describe the implementation of IGS standards to the Jason2 GEODYN GPS processing, and other dynamical and measurement model improvements. Our GPS-only JASON-2 orbit accuracy is assessed using a number of tests including analysis of independent SLR and altimeter crossover residuals, orbit overlap differences, and direct comparison to orbits generated at GSFC using SLR and DORIS tracking, and to orbits generated externally at other centers. Tests based on SLR and the altimeter crossover residuals provide the best performance indicator for independent validation of the NASAlGSFC GPS-only reduced dynamic orbits. For the ITRF2005 and ITRF2008 implementation of our GPS-only obits we are using the IGS05 and IGS08 standards. Reduced dynamic versus dynamic orbit differences are used to characterize the remaining force model error and TRF instability. We evaluate the GPS vs SLR & DORIS orbits produced using the GEODYN software and assess in particular their consistency radially and the stability of the altimeter satellite reference frame in the Z direction for both ITRF2005 and ITRF2008 as a proxy to assess the consistency of the reference frame for altimeter satellite POD.
Melachroinos, S.↗
Techniques for the analysis of geodynamic effects using laser data
New orbit computation techniques have been developed to realize the full precision of laser ranging measurements from a single tracking station used to accurately determine the orbital inclination of a satellite. In order to evaluate earth and ocean tidal effects on the satellite and polar motion effects on the station latitude, improved computational techniques are described for perturbations significantly influencing the satellite's inclination, such as solar radiation pressure and geopotential resonance. By using the time independent value of maximum latitude reached by the satellite as the experimental variable, orbit tracking errors caused by imprecise modelling of the gravity field and atmospheric drag have been largely overcome and made possible long term analysis of osculating elements. With these techniques, quarter day spans of laser data have been employed to monitor the inclination of the satellite to the order 0.01 arcseconds precision over a period of seventeen months.
Dunn, P. J.↗
Modeling radiation forces acting on TOPEX/Poseidon for precision orbit determination
Geodetic satellites such as GEOSAT, SPOT, ERS-1, and TOPEX/Poseidon require accurate orbital computations to support the scientific data they collect. Until recently, gravity field mismodeling was the major source of error in precise orbit definition. However, albedo and infrared re-radiation, and spacecraft thermal imbalances produce in combination no more than a 6-cm radial root-mean-square (RMS) error over a 10-day period. This requires the development of nonconservative force models that take the satellite's complex geometry, attitude, and surface properties into account. For TOPEX/Poseidon, a 'box-wing' satellite form was investigated that models the satellite as a combination of flat plates arranged in a box shape with a connected solar array. The nonconservative forces acting on each of the eight surfaces are computed independently, yielding vector accelerations which are summed to compute the total aggregate effect on the satellite center-of-mass. In order to test the validity of this concept, 'micro-models' based on finite element analysis of TOPEX/Poseidon were used to generate acceleration histories in a wide variety of orbit orientations. These profiles are then compared to the box-wing model. The results of these simulations and their implication on the ability to precisely model the TOPEX/Poseidon orbit are discussed.
Marshall, J. A.↗
In flight ground control of high drag satellites utilizing on-board accelerometer data and rapid orbit prediction techniques
High drag satellites frequently require precise verification of orbital maneuvers and the accurate prediction of perigee height. An in-flight ground support system designed to monitor and compute orbital state and maneuvers is described. The use of on-board three-axis accelerometer data in a flight support software system to perform on-line maneuver analysis and atmospheric model updating is discussed. In addition, automated analytic techniques to rapidly and accurately predict perigee height following a maneuver are described, as well as semianalytic averaging techniques designed to predict a decaying orbital state for mission control.
Fuchs, A. J.↗