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NASA NTRS1993

TOPEX/Poseidon precision orbit determination production and expert system

TOPEX/Poseidon (T/P) is a joint mission between NASA and the Centre National d'Etudes Spatiales (CNES), the French Space Agency. The TOPEX/Poseidon Precision Orbit Determination Production System (PODPS) was developed at Goddard Space Flight Center (NASA/GSFC) to produce the absolute orbital reference required to support the fundamental ocean science goals of this satellite altimeter mission within NASA. The orbital trajectory for T/P is required to have a RMS accuracy of 13 centimeters in its radial component. This requirement is based on the effective use of the satellite altimetry for the isolation of absolute long-wavelength ocean topography important for monitoring global changes in the ocean circulation system. This orbit modeling requirement is at an unprecedented accuracy level for this type of satellite. In order to routinely produce and evaluate these orbits, GSFC has developed a production and supporting expert system. The PODPS is a menu driven system allowing routine importation and processing of tracking data for orbit determination, and an evaluation of the quality of the orbit so produced through a progressive series of tests. Phase 1 of the expert system grades the orbit and displays test results. Later phases undergoing implementation, will prescribe corrective actions when unsatisfactory results are seen. This paper describes the design and implementation of this orbit determination production system and the basis for its orbit accuracy assessment within the expert system.

Putney, Barbara↗
NASA NTRS1994

High degree gravitational sensitivity from Mars orbiters for the GMM-1 gravity model

Orbital sensitivity of the gravity field for high degree terms (greater than 30) is analyzed on satellites employed in a Goddard Mars Model GMM-1, complete in spherical harmonics through degree and order 50. The model is obtained from S-band Doppler data on Mariner 9 (M9), Viking Orbiter 1 (VO1), and Viking Orbiter 2 (VO2) spacecraft, which were tracked by the NASA Deep Space Network on seven different highly eccentric orbits. The main sensitivity of the high degree terms is obtained from the VO1 and VO2 low orbits (300 km periapsis altitude), where significant spectral sensitivity is seen for all degrees out through degree 50. The velocity perturbations show a dominant effect at periapsis and significant effects out beyond the semi-latus rectum covering over 180 degrees of the orbital groundtrack for the low altitude orbits. Because of the wideband of periapsis motion covering nearly 180 degrees in w and +39 degrees in latitude coverage, the VO1 300 km periapsis altitude orbit with inclination of 39 degrees gave the dominant sensitivity in the GMM-1 solution for the high degree terms. Although the VO2 low periapsis orbit has a smaller band of periapsis mapping coverage, it strongly complements the VO1 orbit sensitivity for the GMM-1 solution with Doppler tracking coverage over a different inclination of 80 degrees.

Lerch, F. J.↗
NASA NTRS1994

Evaluation of semiempirical atmospheric density models for orbit determination applications

This paper presents the results of an investigation of the orbit determination performance of the Jacchia-Roberts (JR), mass spectrometer incoherent scatter 1986 (MSIS-86), and drag temperature model (DTM) atmospheric density models. Evaluation of the models was performed to assess the modeling of the total atmospheric density. This study was made generic by using six spacecraft and selecting time periods of study representative of all portions of the 11-year cycle. Performance of the models was measured for multiple spacecraft, representing a selection of orbit geometries from near-equatorial to polar inclinations and altitudes from 400 kilometers to 900 kilometers. The orbit geometries represent typical low earth-orbiting spacecraft supported by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The best available modeling and orbit determination techniques using the Goddard Trajectory Determination System (GTDS) were employed to minimize the effects of modeling errors. The latest geopotential model available during the analysis, the Goddard earth model-T3 (GEM-T3), was employed to minimize geopotential model error effects on the drag estimation. Improved-accuracy techniques identified for TOPEX/Poseidon orbit determination analysis were used to improve the Tracking and Data Relay Satellite System (TDRSS)-based orbit determination used for most of the spacecraft chosen for this analysis. This paper shows that during periods of relatively quiet solar flux and geomagnetic activity near the solar minimum, the choice of atmospheric density model used for orbit determination is relatively inconsequential. During typical solar flux conditions near the solar maximum, the differences between the JR, DTM, and MSIS-86 models begin to become apparent. Time periods of extreme solar activity, those in which the daily and 81-day mean solar flux are high and change rapidly, result in significant differences between the models. During periods of high geomagnetic activity, the standard JR model was outperformed by DTM. Modification of the JR model to use a geomagnetic heating delay of 3 hours, as used in DTM, instead of the 6.7-hour delay produced results comparable to or better than the DTM performance, reducing definitive orbit solution ephermeris overlap differences by 30 to 50 percent. The reduction in the overlap differences would be useful for mitigating the impact of geomagnetic storms on orbit prediction.

Cox, C. M.↗
NASA NTRS1994

Precision orbit determination of altimetric satellites

The ability to determine accurate global sea level variations is important to both detection and understanding of changes in climate patterns. Sea level variability occurs over a wide spectrum of temporal and spatial scales, and precise global measurements are only recently possible with the advent of spaceborne satellite radar altimetry missions. One of the inherent requirements for accurate determination of absolute sea surface topography is that the altimetric satellite orbits be computed with sub-decimeter accuracy within a well defined terrestrial reference frame. SLR tracking in support of precision orbit determination of altimetric satellites is significant. Recent examples are the use of SLR as the primary tracking systems for TOPEX/Poseidon and for ERS-1 precision orbit determination. The current radial orbit accuracy for TOPEX/Poseidon is estimated to be around 3-4 cm, with geographically correlated orbit errors around 2 cm. The significance of the SLR tracking system is its ability to allow altimetric satellites to obtain absolute sea level measurements and thereby provide a link to other altimetry measurement systems for long-term sea level studies. SLR tracking allows the production of precise orbits which are well centered in an accurate terrestrial reference frame. With proper calibration of the radar altimeter, these precise orbits, along with the altimeter measurements, provide long term absolute sea level measurements. The U.S. Navy's Geosat mission is equipped with only Doppler beacons and lacks laser retroreflectors. However, its orbits, and even the Geosat orbits computed using the available full 40-station Tranet tracking network, yield orbits with significant north-south shifts with respect to the IERS terrestrial reference frame. The resulting Geosat sea surface topography will be tilted accordingly, making interpretation of long-term sea level variability studies difficult.

Shum, C. K.↗
NASA NTRS1993

Orbit determination covariance analysis for the Deep Space Program Science Experiment mission

To define an appropriate orbit support procedure for the DSPSE mission, detailed permission orbit determination covariance analyses have been performed for the translunar and trans-Geographos mission phases. Preliminary analyses were also performed for the lunar mapping mission phase. These analyses are designed to assess the tracking patterns and the amount of tracking data needed to obtain orbit solutions of required accuracy for each mission phase and before and after each major orbit perturbation, such as orbit maneuvers and flybys of the Earth and Moon. In addition to operational orbit determination procedures, these analyses identify major error sources, estimate their contribution to orbital errors, and address possible strategies to reduce orbit determination error. For the lunar orbit phase, several lunar gravity error modeling approaches have been investigated. The covariance analysis results presented in this paper will serve as a guide for providing orbit determination support for the DSPSE mission.

Beckman, M.↗
NASA NTRS1958

Three-Dimensional Orbits of Earth Satellites, Including Effects of Earth Oblateness and Atmospheric Rotation

The principal purpose of the present paper is to present sets of equations which may be used for calculating complete trajectories of earth satellites from outer space to the ground under the influence of air drag and gravity, including oblateness effects, and to apply these to several examples of entry trajectories starting from a circular orbit. Equations of motion, based on an "instantaneous ellipse" technique, with polar angle as independent variable, were found suitable for automatic computation of orbits in which the trajectory consists of a number of revolutions. This method is suitable as long as the trajectory does not become nearly vertical. In the terminal phase of the trajectories, which are nearly vertical, equations of motion in spherical polar coordinates with time as the independent variable were found to be more suitable. In the first illustrative example the effects of the oblateness component of the earth's gravitational field and of atmospheric rotation were studied for equatorial orbits. The satellites were launched into circular orbits at a height of 120 miles, an altitude sufficiently high that a number of revolutions could be studied. The importance of the oblateness component of the earth's gravitational field is shown by the fact that a satellite launched at circular orbital speed, neglecting oblateness, has a perigee some 67,000 feet lower when oblateness forces are included in the equations of motion than when they are not included. Also, the loss in altitude per revolution is double that of a satellite following an orbit not subject to oblateness. The effect of atmospheric rotation on the loss of altitude per revolution was small. As might be surmised, the regression of the line of nodes as predicted by celestial mechanics is unchanged when drag is included. It is clear that the inclination of the orbital plane to the equator will be relatively unaffected by drag for no atmospheric rotation since the drag lies in the orbital plane in this case. With the inclusion of atmospheric rotation it was found that the inclination of the plane changed about one-millionth of a radian per revolution. Thus the prediction of the position of the orbital plane of an earth satellite is not complicated by the introduction of drag. The line of apsides, which without drag but with oblateness moves slowly in space, tends to move with the satellite when drag is included in the calculations. As a results, the usual linearized solutions based on oblateness alone must be basically altered when drag is included to take into account the rapid movement of the line of apsides. In the second illustrative example the final revolution was calculated to impact for a number of trajectories in an orbital plane inclined at 650 to the equator. Of particular interest is the large effect the oblateness gravitational field and atmospheric rotation can have on the impact point. For a value of CDA/m of unity, and for an initial downward angle at 80 miles altitude of 0.01 radian, such as might be utilized for manned re-entry, oblateness had an influence of about 300 miles in the impact point, and atmospheric rotation had about a 150-mile influence.

Nielsen, Jack N.↗
NASA NTRS1999

A Comprehensive Orbit Reconstruction for the Galileo Prime Mission in the J2000 System

The Galileo spacecraft arrived at Jupiter in December of 1995 to begin an orbital tour of the Jovian system. The objective of the tour was up close study of the planet, its satellites, and its magnetosphere. The spacecraft completed its 11 orbit prime mission in November of 1997 having had 16 successful close encounters with the Galilean satellites (including two prior to Jupiter orbit insertion). Galileo continues to operate and will have made an additional 10 orbits of Jupiter by the date of this Conference. Earlier papers discuss the determination of the spacecraft orbit in support of mission operations from arrival at Jupiter through the first 9 orbits. In this paper we re-examine those earlier orbits and extend the analysis through orbit 12, the first orbit of the Galileo Europa Mission (GEM). The objective of our work is the reconstruction of the spacecraft trajectory together with the development of a consistent set of ephemerides for the Galilean satellites. As a necessary byproduct of the reconstruction we determine improved values for the Jovian system gravitational parameters and for the Jupiter pole orientation angles. Our preliminary analyses have already led to many of the results reported in the scientific literature. Unlike the Galileo Navigation Team which operates in the EME-1950 coordinate system, we elected to work in the (J2000) International Celestial Reference Frame (ICRF), the reference frame of the current JPL planetary and satellite ephemerides as well as the standard frame of the international astronomical and planetary science community. Use of this frame permits more precise modelling of the spacecraft and satellite observations. Moreover, it is the frame of choice for all other operational JPL missions and will probably be the frame for future missions for some time. Consequently, our adoption of the ICRF will facilitate the combination of our results with any obtained from future missions (e.g. the proposed Europa Orbiter mission). In addition, our results may be used by the science community, without need of a reference frame conversion.

Jacobson, Robert A.↗
NASA NTRS1994

Development of New Open-Shell Perturbation and Coupled-Cluster Theories Based on Symmetric Spin Orbitals

A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.

Lee, Timothy J.↗
NASA NTRS1996

Orbiter Aerodynamic Acceleration Flight Measurements in the Rarefied-Flow Transition Regime

Acceleration data taken from the Orbital Acceleration Research Experiment (OARE) during reentry on STS-62 have been analyzed using calibration factors taken on orbit. This is the first Orbiter mission which collected OARE data during the Orbiter reentry phase. The data examined include the flight regime from orbital altitudes down to about 90 km which covers the free-molecule-flow regime and the upper altitude fringes of the rarefied-flow transition into the hypersonic continuum. Ancillary flight data on Orbiter position, orientation, velocity, and rotation rates have been used in models to transform the measured accelerations to the Orbiter center-of-gravity, from which aerodynamic accelerations along the Orbiter body axes have been calculated. Residual offsets introduced in the measurements by unmodeled Orbiter forces are identified and discussed. Direct comparisons are made between the OARE flight data and an independent micro-gravity accelerometer experiment, the High Resolution Accelerometer Package (HiRAP), which also obtained flight data on reentry during the mission down to about 95 km. The resulting OARE aerodynamic acceleration measurements along the Orbiter's body axis, aid the normal to axial acceleration ratio in the free-molecule-flow and transition-flow regimes are presented and compared with numerical simulations from three direct simulation Monte Carlo codes.

Blanchard, Robert C.↗
NASA NTRS2005

Mars Orbiter Sample Return Power Design

Mars has greatly intrigued scientists and the general public for many years because, of all the planets, its environment is most like Earth's. Many scientists believe that Mars once had running water, although surface water is gone today. The planet is very cold with a very thin atmosphere consisting mainly of CO2. Mariner 4, 6, and 7 explored the planet in flybys in the 1960s and by the orbiting Mariner 9 in 1971. NASA then mounted the ambitious Viking mission, which launched two orbiters and two landers to the planet in 1975. The landers found ambiguous evidence of life. Mars Pathfinder landed on the planet on July 4, 1997, delivering a mobile robot rover that demonstrated exploration of the local surface environment. Mars Global Surveyor is creating a highest-resolution map of the planet's surface. These prior and current missions to Mars have paved the way for a complex Mars Sample Return mission planned for 2003 and 2005. Returning surface samples from Mars will necessitate retrieval of material from Mars orbit. Sample mass and orbit are restricted to the launch capability of the Mars Ascent Vehicle. A small sample canister having a mass less than 4 kg and diameter of less than 16 cm will spend from three to seven years in a 600 km orbit waiting for retrieval by a second spacecraft consisting of an orbiter equipped with a sample canister retrieval system, and a Earth Entry Vehicle. To allow rapid detection of the on-orbit canister, rendezvous, and collection of the samples, the canister will have a tracking beacon powered by a surface mounted solar array. The canister must communicate using RF transmission with the recovery vehicle that will be coming in 2006 or 2009 to retrieve the canister. This paper considers the aspect and conclusion that went into the design of the power system that achieves the maximum power with the minimum risk. The power output for the spherical orbiting canister was modeled and plotted in various views of the orbit by the Satellite Orbit Analysis Program (SOAP).

Mardesich, N.↗
NASA NTRS2006

TRMM On-Orbit Performance Reassessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an H-I1 rocket on November 27, 1997, and transitioned in August, 2001, from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost, the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with 1/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees.

Bilanow, Stephen↗
NASA NTRS2006

The Disposal of Spacecraft and Launch Vehicle Stages in Low Earth Orbit

As a result of the increasing number of debris in low Earth orbit (LEO), numerous national and international orbital debris mitigation guidelines recommend the removal of spacecraft and launch vehicle stages from LEO within 25 years after mission termination. The primary purpose of this action is to enhance space safety by significantly limiting the potential of future accidental collisions resulting in the creation of large numbers of new orbital debris. Likewise, the passivation of these objects, i.e., the removal of residual stored energies, while they remain in orbit is important to prevent the generation of debris via self-induced explosions. Characteristics and trends in the growth of the derelict spacecraft and launch vehicle stage populations in LEO are examined. Depending upon the final operational altitude of the vehicle, achieving the goal of orbital lifetime reduction can influence the design and deployment philosophy of a new space system. Some spacecraft and launch vehicle stages have combined their end-of-mission passivation operations with maneuvers to vacate long-lived orbital regimes. Perhaps the most dramatic demonstration of this type occurred in 2006 when a U.S. Delta IV second stage executed an unprecedented controlled-reentry maneuver from a circular orbit at an altitude near 850 km. For space systems in orbital regimes near the upper regions of LEO (i.e., between 1400 km and 2000 km altitude), maneuvers to place the vehicle above LEO might be more attractive than attempting to ensure an atmospheric reentry within 25 years, and at least one space system operator has selected this option. In some cases, careful consideration of natural orbital perturbations can also lead to reduced orbital lifetimes, although new launch constraints might need to be imposed.

Johnson, Nicholas L.↗
NASA NTRS2007

Mission Design for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) will be the first mission under NASA's Vision for Space Exploration. LRO will fly in a low 50 km mean altitude lunar polar orbit. LRO will utilize a direct minimum energy lunar transfer and have a launch window of three days every two weeks. The launch window is defined by lunar orbit beta angle at times of extreme lighting conditions. This paper will define the LRO launch window and the science and engineering constraints that drive it. After lunar orbit insertion, LRO will be placed into a commissioning orbit for up to 60 days. This commissioning orbit will be a low altitude quasi-frozen orbit that minimizes stationkeeping costs during commissioning phase. LRO will use a repeating stationkeeping cycle with a pair of maneuvers every lunar sidereal period. The stationkeeping algorithm will bound LRO altitude, maintain ground station contact during maneuvers, and equally distribute periselene between northern and southern hemispheres. Orbit determination for LRO will be at the 50 m level with updated lunar gravity models. This paper will address the quasi-frozen orbit design, stationkeeping algorithms and low lunar orbit determination.

Beckman, Mark↗
NASA NTRS2007

GPS-Based Reduced Dynamic Orbit Determination Using Accelerometer Data

Currently two gravity field satellite missions, CHAMP and GRACE, are equipped with high sensitivity electrostatic accelerometers, measuring the non-conservative forces acting on the spacecraft in three orthogonal directions. During the gravity field recovery these measurements help to separate gravitational and non-gravitational contributions in the observed orbit perturbations. For precise orbit determination purposes all these missions have a dual-frequency GPS receiver on board. The reduced dynamic technique combines the dense and accurate GPS observations with physical models of the forces acting on the spacecraft, complemented by empirical accelerations, which are stochastic parameters adjusted in the orbit determination process. When the spacecraft carries an accelerometer, these measured accelerations can be used to replace the models of the non-conservative forces, such as air drag and solar radiation pressure. This approach is implemented in a batch least-squares estimator of the GPS High Precision Orbit Determination Software Tools (GHOST), developed at DLR/GSOC and DEOS. It is extensively tested with data of the CHAMP and GRACE satellites. As accelerometer observations typically can be affected by an unknown scale factor and bias in each measurement direction, they require calibration during processing. Therefore the estimated state vector is augmented with six parameters: a scale and bias factor for the three axes. In order to converge efficiently to a good solution, reasonable a priori values for the bias factor are necessary. These are calculated by combining the mean value of the accelerometer observations with the mean value of the non-conservative force models and empirical accelerations, estimated when using these models. When replacing the non-conservative force models with accelerometer observations and still estimating empirical accelerations, a good orbit precision is achieved. 100 days of GRACE B data processing results in a mean orbit fit of a few centimeters with respect to high-quality JPL reference orbits. This shows a slightly better consistency compared to the case when using force models. A purely dynamic orbit, without estimating empirical accelerations thus only adjusting six state parameters and the bias and scale factors, gives an orbit fit for the GRACE B test case below the decimeter level. The in orbit calibrated accelerometer observations can be used to validate the modelled accelerations and estimated empirical accelerations computed with the GHOST tools. In along track direction they show the best resemblance, with a mean correlation coefficient of 93% for the same period. In radial and normal direction the correlation is smaller. During days of high solar activity the benefit of using accelerometer observations is clearly visible. The observations during these days show fluctuations which the modelled and empirical accelerations can not follow.

VanHelleputte, Tom↗
NASA NTRS2002

Using GEO Optical Observations to Infer Orbit Populations

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit. When observing very dim objects with small field-of-view telescopes, though, the observations are generally too short to obtain accurate orbital elements. However, it is possible to use such observations to statistically characterize the small object environment. A telescope pointed at a particular spot could potentially see objects in a number of different orbits. Inevitably, when looking at one region for certain types of orbits, there are objects in other types of orbits that cannot be seen. Observation campaigns are designed with these limitations in mind and are set up to span a number of regions of the sky, making it possible to sample all potential orbits under consideration. Each orbit is not seen with the same probability, however, so there are observation biases intrinsic to any observation campaign. Fortunately, it is possible to remove such biases and reconstruct a meaningful estimate of the statistical orbit populations of small objects in GEO. This information, in turn, can be used to investigate the nature of debris sources and to characterize the risk to GEO spacecraft. This paper describes these statistical tools and presents estimates of small object GEO populations.

Matney, Mark↗
NASA NTRS2011

Solar Radiation Pressure Binning for the Geosynchronous Orbit

Orbital maintenance parameters for individual satellites or groups of satellites have traditionally been set by examining orbital parameters alone, such as through apogee and perigee height binning; this approach ignored the other factors that governed an individual satellite's susceptibility to non-conservative forces. In the atmospheric drag regime, this problem has been addressed by the introduction of the "energy dissipation rate," a quantity that represents the amount of energy being removed from the orbit; such an approach is able to consider both atmospheric density and satellite frontal area characteristics and thus serve as a mechanism for binning satellites of similar behavior. The geo-synchronous orbit (of broader definition than the geostationary orbit -- here taken to be from 1300 to 1800 minutes in orbital period) is not affected by drag; rather, its principal non-conservative force is that of solar radiation pressure -- the momentum imparted to the satellite by solar radiometric energy. While this perturbation is solved for as part of the orbit determination update, no binning or division scheme, analogous to the drag regime, has been developed for the geo-synchronous orbit. The present analysis has begun such an effort by examining the behavior of geosynchronous rocket bodies and non-stabilized payloads as a function of solar radiation pressure susceptibility. A preliminary examination of binning techniques used in the drag regime gives initial guidance regarding the criteria for useful bin divisions. Applying these criteria to the object type, solar radiation pressure, and resultant state vector accuracy for the analyzed dataset, a single division of "large" satellites into two bins for the purposes of setting related sensor tasking and orbit determination (OD) controls is suggested. When an accompanying analysis of high area-to-mass objects is complete, a full set of binning recommendations for the geosynchronous orbit will be available.

Hejduk, M. D.↗
NASA NTRS2011

Constraining the Absolute Orientation of eta Carinae's Binary Orbit: A 3-D Dynamical Model for the Broad [Fe III] Emission

We present a three-dimensional (3-D) dynamical model for the broad [Fe III] emission observed in Eta Carinae using the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS). This model is based on full 3-D Smoothed Particle Hydrodynamics (SPH) simulations of Eta Car's binary colliding winds. Radiative transfer codes are used to generate synthetic spectro-images of [Fe III] emission line structures at various observed orbital phases and STIS slit position angles (PAs). Through a parameter study that varies the orbital inclination i, the PA(theta) that the orbital plane projection of the line-of-sight makes with the apastron side of the semi-major axis, and the PA on the sky of the orbital axis, we are able, for the first time, to tightly constrain the absolute 3-D orientation of the binary orbit. To simultaneously reproduce the blue-shifted emission arcs observed at orbital phase 0.976, STIS slit PA = +38deg, and the temporal variations in emission seen at negative slit PAs, the binary needs to have an i approx. = 130deg to 145deg, Theta approx. = -15deg to +30deg, and an orbital axis projected on the sky at a P A approx. = 302deg to 327deg east of north. This represents a system with an orbital axis that is closely aligned with the inferred polar axis of the Homunculus nebula, in 3-D. The companion star, Eta(sub B), thus orbits clockwise on the sky and is on the observer's side of the system at apastron. This orientation has important implications for theories for the formation of the Homunculus and helps lay the groundwork for orbital modeling to determine the stellar masses.

Madura, T. I.↗
NASA NTRS2012

The Effect of Geocenter Motion on Jason-2 and Jason-1 Orbits and the Mean Sea Level

We have investigated the impact of geocenter motion on Jason-2 orbits. This was accomplished by computing a series of Jason-1, Jason-2 GPS-based and SLR/DORIS-based orbits using ITRF2008 and the IGS repro1 framework based on the most recent GSFC standards. From these orbits, we extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. The fitted annual and seasonal terms of these time-series are compared to two different geocenter motion models. Subsequently, we included the geocenter motion corrections in the POD process as a degree-1 loading displacement correction to the tracking network. The analysis suggested that the GSFC's Jason-2 std0905 GPS-based orbits are closely tied to the center of mass (CM) of the Earth whereas the SLR/DORIS std0905 orbits are tied to the center of figure (CF) of the ITRF2005 (Melachroinos et al., 2012). In this study we extend the investigation to the centering of the GPS constellation and the way those are tied in the Jason-1 and Jason-2 POD process. With a new set of standards, we quantify the GPS and SLR/DORIS-based orbit centering during the Jason-1 and Jason-2 inter-calibration period and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the full term of the geocenter motion correction.

Melachroinos, Stavros A.↗