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Calculating Trajectories And Orbits

Double-Precision Trajectory Analysis Program, DPTRAJ, and Orbit Determination Program, ODP, developed and improved over years to provide highly reliable and accurate navigation capability for deep-space missions like Voyager. Each collection of programs working together to provide desired computational results. DPTRAJ, ODP, and supporting utility programs capable of handling massive amounts of data and performing various numerical calculations required for solving navigation problems associated with planetary fly-by and lander missions. Used extensively in support of NASA's Voyager project. DPTRAJ-ODP available in two machine versions. UNIVAC version, NPO-15586, written in FORTRAN V, SFTRAN, and ASSEMBLER. VAX/VMS version, NPO-17201, written in FORTRAN V, SFTRAN, PL/1 and ASSEMBLER.

Alderson, Daniel J.↗

Precise Tracking of the Magellan and Pioneer Venus Orbiters by Same-Beam Interferometry. Part 2: Orbit Determination Analysis

A new radio metric positioning technique has demonstrated improved orbit determination accuracy for the Magellan and Pioneer Venus Orbiter orbiters. The new technique, known as Same-Beam Interferometry (SBI), is applicable to the positioning of multiple planetary rovers, landers, and orbiters which may simultaneously be observed in the same beamwidth of Earth-based radio antennas. Measurements of carrier phase are differenced between spacecraft and between receiving stations to determine the plane-of-sky components of the separation vector(s) between the spacecraft. The SBI measurements complement the information contained in line-of-sight Doppler measurements, leading to improved orbit determination accuracy. Orbit determination solutions have been obtained for a number of 48-hour data arcs using combinations of Doppler, differenced-Doppler, and SBI data acquired in the spring of 1991. Orbit determination accuracy is assessed by comparing orbit solutions from adjacent data arcs. The orbit solution differences are shown to agree with expected orbit determination uncertainties. The results from this demonstration show that the orbit determination accuracy for Magellan obtained by using Doppler plus SBI data is better than the accuracy achieved using Doppler plus differenced-Doppler by a factor of four and better than the accuracy achieved using only Doppler by a factor of eighteen. The orbit determination accuracy for Pioneer Venus Orbiter using Doppler plus SBI data is better than the accuracy using only Doppler data by 30 percent.

Folkner, W. M.↗

GFO-1 Geophysical Data Record and Orbit Verifications for Global Change Studies

This final report summarizes the research work conducted under NASA's Physical Oceanography Program, entitled, GFO-1 Geophysical Data Record And Orbit Verifications For Global Change Studies, for the investigation time period from December 1, 1997 through November 30, 2000. The primary objectives of the investigation include providing verification and improvement for the precise orbit, media, geophysical, and instrument corrections to accurately reduce U.S. Navy's Geosat-Followon-1 (GFO-1) mission radar altimeter data to sea level measurements. The status of the GFO satellite (instrument and spacecraft operations, orbital tracking and altimeter) is summarized. GFO spacecraft has been accepted by the Navy from Ball Aerospace and has been declared operational since November, 2000. We have participated in four official GFO calibration/validation periods (Cal/Val I-IV), spanning from June 1999 through October 2000. Results of verification of the GFO orbit and geophysical data record measurements both from NOAA (IGDR) and from the Navy (NGDR) are reported. Our preliminary results indicate that: (1) the precise orbit (GSFC and OSU) can be determined to approx. 5 - 6 cm rms radially using SLR and altimeter crossovers; (2) estimated GFO MOE (GSFC or NRL) radial orbit accuracy is approx. 7 - 30 cm and Operational Doppler orbit accuracy is approx. 60 - 350 cm. After bias and tilt adjustment (1000 km arc), estimated Doppler orbit accuracy is approx. 1.2 - 6.5 cm rms and the MOE accuracy is approx. 1.0 - 2.3 cm; (3) the geophysical and media corrections have been validated versus in situ measurements and measurements from other operating altimeters (T/P and ERS-2). Altimeter time bias is insignificant with 0-2 ms. Sea state bias is about approx. 3 - 4.5% of SWH. Wet troposphere correction has approx. 1 cm bias and approx. 3 cm rms when compared with ERS-2 data. Use of GIM and IRI95 provide ionosphere correction accurate to 2-3 cm rms during medium to high solar activities; (4) the noise of the GFO altimeter data (uncorrected SSH) is about 15 mm, compared to 19 min for ERS-2, and 12 min for TOPEX. It is anticipated that the operational GFO-1 altimeter data will contribute to a number of researches in physical oceanography. A list of relevant presentations and publications is attached.

Shum, C. K.↗

Improved Orbit Determination of the Cygnss Satellites and its Application to Gnss-R Ocean Altimetry

The accuracy of spaceborne ocean surface altimetry depends on precise knowledge of the altimeter satellite orbit. Previous studies of the potential utility of CYGNSS GNSS Reflectometry (GNSS-R) measurements for ocean altimetry have identified its orbit error as a limiting factor. To address this, a recent firmware upgrade to the CYGNSS satellites have enabled the downlink of additional GPS raw measurements from its navigation receiver and increased numerical precision in open-loop GNSS-R tracking information. In this paper, we present improvements to the accuracy of both the orbit determination and the ocean surface height retrievals as a result of these recent upgrades. JPL’s GipsyX software is used to process 120 days of GPS navigation measurements for one of the 8 CYGNSS satellites. Incorporating high fidelity dynamic models and antenna group delay correction, daily orbit overlaps throughout the period show mean RMS differences of 3 cm in height, 7 cm in cross-track, and 10 cm in along-track. Applying these new orbits reduced the standard deviation of retrieved surface height anomalies. When spatially averaged, the sea surface height anomalies were reduced from 1.0 m to 0.8 m. Further improvements are expected using new ionospheric corrections and re-tracking methods currently in development.

Conrad, Alex↗

Nozomi Cis-Lunar Phase Orbit Determination

Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998. Scientific objectives of the mission are to study the structure and dynamics of the Martian upper atmosphere and its interaction with the solar wind. Nozomi is a cooperative mission between ISAS and the National Aeronautics and Space Administration (NASA). The NASA contribution includes navigation and tracking services provided by the Jet Propulsion Laboratory (JPL). The spacecraft also serves as an engineering demonstration of basic technology for planetary exploration. One of the new technologies was a unique trajectory, developed by ISAS, which used solar gravitational perturbations at the weak stability boundary as an aid to achieve an Earth-Mars transfer orbit. This trajectory saves approximately 120 m/s of Delta V compared to direct hyperbolic insertion and is considered an enabling technology for the mission. Nozomi was the first spacecraft to employ this trajectory and provided on-orbit validation of the technique. The trajectory was achieved by initially placing the spacecraft in a highly elliptical cis-lunar phasing orbit. Six maneuvers were performed during this period to correct injection errors and target an outbound lunar swingby in September 1998. The gravity assist from the lunar swingby raised apogee to the vicinity of the weak stability boundary. After three more targeting maneuvers, Nozomi performed an inbound lunar swingby followed immediately by a powered Earth swingby in late December 1998. A 420 m/s Trans Mars Insertion (TMI) burn at the final Earth periapsis was intended to place the spacecraft on a heliocentric trajectory leading to Mars orbit insertion in October 1999. Orbit determination for Nozomi is performed in parallel by both ISAS and the Multi-Mission Navigation (MMNAV) group at JPL. This was an advantage for the mission because each group would generate solutions based on data collected from their respective tracking networks. Spacecraft events, such as sequence uplinks and maneuvers, were generally scheduled during passes at the Usuda tracking station in Japan. As a result, maneuver design and reconstruction was derived from MMNAV solutions based on JPL tracking data obtained immediately prior to or following maneuvers. Data was also exchanged between ISAS and MMNAV so orbit determination could be performed on joint data sets in support of critical targeting late in the cis-lunar phase. In this paper, information regarding the MMNAV orbit determination effort for the first six months of the mission is presented. The spacecraft trajectory is characterized first, followed by a discussion of the orbit determination estimation procedure and models. Results from selected orbit solutions are presented and compared against reconstructed trajectories. One area of emphasis in this paper is orbit determination in the vicinity of the weak stability boundary. Precise navigation was necessary to target the second lunar swingby and the powered Earth swingby. Delivery accuracy of 150 m was required for these critical encounters, but a number of factors contributed to the general degradation of orbit determination accuracy. This included the fact that the spacecraft was at apogee, at a range of 1.7 million km and moving at less than I km/sec perpendicular to the line of sight. Nozomi was also close to zero degrees declination where there are known limitations on orbit determination performance. Finally, S-band tracking data was acquired through the Nozomi backup low gain antenna. This antenna is offset from the axis of this spin stabilized spacecraft and superimposed large signatures in the Doppler and range data. These difficulties were overcome by combining long data arcs, spanning several maneuvers, with a high fidelity solar pressure model. The model included a physically accurate representation of the spacecraft structure and a high time resolution orientation model. Observation modeling included the removal of the spin induced Doppler bias, spin signature and per pass correction of range calibration errors applied for data leading up to critical events. As a result, all orbit determination goals were met. A second area of emphasis in this paper is the JPL tracking and orbit determination effort in support of the TMI maneuver. TMI occurred out of contact with ground stations and the JPL Goldstone tracking complex had the first pass following the bum. As a result, MMNAV had the responsibility to make a rapid assessment of the maneuver performance. MMNAV made the determination that a 100 m/s under bum had occurred and promptly informed ISAS via voice lines. ISAS immediately began preparations for a correction maneuver (TMIc), which had to be performed during the next Usuda pass. The near real time assessment by MMNAV provided accurate antenna frequency and pointing updates for the spacecraft acquisition at Usuda and the close coordination between the two agencies enabled the design and successful execution of the TMc maneuver. Propellant consumption during the correction burn dictated that the mission be redesigned. ISAS developed a new plan which adds 3 full solar orbits, two Earth swingbys and one lunar swingby with arrival at Mars in January 2004. The final Mars orbit will still enable the mission to achieve all of its science objectives.

Ryne, Mark↗

An assessment of gravity model improvements using TOPEX/Poseidon TDRSS observations

The contribution of TOPEX/Poseidon (T/P) TDRSS data to geopotential model recovery is assessed. Simulated TDRSS one-way and Bilateration Ranging Transponder System (BRTS) observations have been generated and orbitally reduced to form normal equations for geopotential parameters. These normals have been combined with those of the latest prelaunch T/P gravity model solution using data from over 30 satellites. A study of the resulting solution error covariance shows that TDRSS can make important contributions to geopotential recovery, especially for improving T/P specific effects like those arising from orbital resonance. It is argued that future effort is desirable both to establish TDRSS orbit determination limits in a reference frame compatible with that used for the precise laser/DORIS orbits, and the reduction of these TDRSS data for geopotential recovery.

Putney, B. H.↗

Voyager 2 orbit determination at Neptune

In August 1989 the Voyager 2 spacecraft encountered Neptune and Triton. Precise knowledge of the trajectory of the spacecraft relative to the Neptunian system was essential to ensure successful observations during the flyby, and to perform trajectory control. Determination of the orbit of Voyager 2 with respect to the Neptunian system was accomplished by the use of radiometric Doppler, range, and VLBI observations of the spacecraft in combination with spacecraft-based optical observations of Neptune, Triton, Nereid, and the Voyager-discovered satellite 1989N1. These data types were used in a new version of the JPL Orbit Determination Program to determine the orbit of the spacecraft as well as Neptunian system ephemerides and dynamical parameters, resulting in accurate delivery of the spacecraft to targeted conditions at Neptune and Triton.

Lewis, G. D.↗

Extremely Accurate On-Orbit Position Accuracy using TDRSS

NASA is planning to launch a new service for Earth satellites providing them with precise GPS differential corrections and other ancillary information enabling decimeter level orbit determination accuracy and nanosecond time-transfer accuracy, onboard, in real-time. The TDRSS Augmentation Service for Satellites (TASS) will broadcast its message on the S-band multiple access forward channel of NASA s Tracking and Data Relay Satellite System (TDRSS). The satellite's phase array antenna has been configured to provide a wide beam, extending coverage up to 1000 km altitude over the poles. Global coverage will be ensured with broadcast from three or more TDRSS satellites. The GPS differential corrections are provided by the NASA Global Differential GPS (GDGPS) System, developed and operated by JPL. The GDGPS System employs global ground network of more than 70 GPS receivers to monitor the GPS constellation in real time. The system provides real-time estimates of the GPS satellite states, as well as many other real-time products such as differential corrections, global ionospheric maps, and integrity monitoring. The unique multiply redundant architecture of the GDGPS System ensures very high reliability, with 99.999% demonstrated since the inception of the system in early 2000. The estimated real time GPS orbit and clock states provided by the GDGPS system are accurate to better than 20 cm 3D RMS, and have been demonstrated to support sub-decimeter real time positioning and orbit determination for a variety of terrestrial, airborne, and spaceborne applications. In addition to the GPS differential corrections, TASS will provide real-time Earth orientation and solar flux information that enable precise onboard knowledge of the Earth-fixed position of the spacecraft, and precise orbit prediction and planning capabilities. TASS will also provide 5 seconds alarms for GPS integrity failures based on the unique GPS integrity monitoring service of the GDGPS System.

Stocklin, Frank↗

NASA's global differential GPS system and the TDRSS augmentation service for satellites

NASA is planning to launch a new service for Earth satellites providing them with precise GPS differential corrections and other ancillary information enabling decimeter level orbit determination accuracy, and nanosecond time-transfer accuracy, onboard, in real-time. The TDRSS Augmentation Service for Satellites (TASS) will broadcast its message on the S-band multiple access channel of NASA's Tracking and Data Relay Satellite System (TDRSS). The satellite's phase array antenna has been configured to provide a wide beam, extending coverage up to 1000 km altitude over the poles. Global coverage will be ensured with broadcast from three or more TDRSS satellites. The GPS differential corrections are provided by the NASA Global Differential GPS (GDGPS) System, developed and operated by NASA's Jet Propulsion Laboratory. The GDGPS System employs a global ground network of more than 70 GPS receivers to monitor the GPS constellation in real time. The system provides real-time estimates of the GPS satellite states, as well as many other real-time products such as differential corrections, global ionospheric maps, and integrity monitoring. The unique multiply redundant architecture of the GDGPS System ensures very high reliability, with 99.999% demonstrated since the inception of the system in Early 2000. The estimated real time GPS orbit and clock states provided by the GDGPS system are accurate to better than 20 cm 3D RMS, and have been demonstrated to support sub-decimeter real time positioning and orbit determination for a variety of terrestrial, airborne, and spaceborne applications. In addition to the GPS differential corrections, TASS will provide real-time Earth orientation and solar flux information that enable precise onboard knowledge of the Earth-fixed position of the spacecraft, and precise orbit prediction and planning capabilities. TASS will also provide 5 seconds alarms for GPS integrity failures based on the unique GPS integrity monitoring service of the GDGPS System.

Global Postitioning Satellite (GPS)↗

What perturbs the gamma and delta rings of Uranus?

Since the discovery of the Uranian rings in 1977, it has been possible to determine the orbits of the rings with remarkable precision. It has been found that seven of the nine known rings follow well-behaved Keplerian ellipses. However, two adjacent rings, gamma and delta, deviate significantly from simple ellipses, with residuals of up to 10 km. The present report is concerned with a test of two possible causes of the observed perturbations in the case of the gamma and delta rings, taking into account shepherd satellites which are presumed to confine the sharp-edged narrow rings, and low-order Lindblad resonances.

French, R. G.↗

GPS orbit determination at the National Geodetic Survey

The National Geodetic Survey (NGS) independently generates precise ephemerides for all available Global Positioning System (GPS) satellites. Beginning in 1991, these ephemerides were produced from double-differenced phase observations solely from the Cooperative International GPS Network (CIGNET) tracking sites. The double-difference technique combines simultaneous observations of two satellites from two ground stations effectively eliminating satellite and ground receiver clock errors, and the Selective Availability (S/A) signal degradation currently in effect. CIGNET is a global GPS tracking network whose primary purpose is to provide data for orbit production. The CIGNET data are collected daily at NGS and are available to the public. Each ephemeris covers a single week and is available within one month after the data were taken. Verification is by baseline repeatability and direct comparison with other ephemerides. Typically, an ephemeris is accurate at a few parts in 10(exp 7). This corresponds to a 10 meter error in the reported satellite positions. NGS is actively investigating methods to improve the accuracy of its orbits, the ultimate goal being one part in 10(exp 8) or better. The ephemerides are generally available to the public through the Coast Guard GPS Information Center or directly from NGS through the Geodetic Information Service. An overview of the techniques and software used in orbit generation will be given, the current status of CIGNET will be described, and a summary of the ephemeris verification results will be presented.

M. S. Schenewerk↗

Time transfer using geostationary satellites: Implementation of a Kalman filter

Since 1988, various experiments have shown that the TV signals transmitted by direct TV satellites may easily be used to perform time transfers at the level of a few tens of nanoseconds, the main source of error being the uncertainty on the satellite position. We first present the two methods used in our experiment to reduce the effects of the satellite residual motion: the first one consists in estimating the longitude variations of the satellite and then using this information to improve other measurements. This allows reducing the uncertainty to values between 9 and 50 nanoseconds according to the position of the involved stations. In the second method we determine the satellite position by using the data collected by three calibrated stations. Time transfer between each of these stations and a fourth one has been shown to be achievable at the precision level of ten nanoseconds. A new approach based on the use of a Kalman filter is proposed in order to take into account the dynamics of the geostationary satellite. The precisions on orbital elements and clock differences and rates determination given by the first simulated applications of the Kalman filter are presented and compared to those obtained by the other methods.

Meyer, F.↗

RXJ0440.9+4431: a Persistent Be-x-ray Binary in Outburst

The persistent Be/X-ray binary RXJ0440.9+4431 flared in 2010 and 2011 and has been followed by various X-ray facilities (Swift, RXTE, XMM-Newton, and INTEGRAL).We studied the source timing and spectral properties as a function of its X-ray luminosity to investigate the transition from normal to flaring activity and the dynamical properties of the system. We have determined the orbital period from the long-term Swift/BAT light curve, but our determinations of the spin-period are not precise enough to constrain any orbital solution. The source spectrum can always be described by a bulk-motion Comptonization model of black body seed photons attenuated by a moderate photoelectric absorption. At the highest luminosity, we measured a curvature of the spectrum, which we attribute to a significant contribution of the radiation pressure in the accretion process. This allows us to estimate that the transition from a bulk-motion-dominated flow to a radiatively dominated one happens at a luminosity of approx 2 × 10(exp 36) erg/ s. The luminosity dependency of the size of the black body emission region is found to be r(sub BB) varies as L(sub x) (exp 0.39 +/- 0.02). This suggests that either matter accreting onto the neutron star hosted in RXJ0440.9+4431 penetrates through closed magnetic field lines at the border of the compact object magnetosphere or that the structure of the Neutron star magnetic field is more complicated than a simple dipole close to the surface.

binary↗

Highly transparent and rugged sensor for velocity determinations of cosmic dust particles

In order to understand the evolution of interplanetary dust, numerous dust particles have been collected and analyzed. An analysis of the composition often provides information on the particle's origin. So does its origin. Composition and orbit data complement each other and should be determined together. If the last orbit of a particle can be determined, its orbital history can often be calculated backward in time and associated with its parent body. To determine the last orbit, the velocity needs to be measured before the particle is collected. The precision required in determining the velocity components relative to the spacecraft should be 1 percent or better. A sensor for naturally charged cosmic dust particles is discussed. Two models of the sensor were tested, one with a free-falling steel ball and the other with particles accelerated to high speed. Analytic expressions of the sensor signals are presented and compared with the test results. The errors in speed and angle were estimated to be about 0.3 percent and 0.2 degrees respectively.

Auer, Siegfried↗

Astrometric Detection of a Low Mass Companion Orbiting the Star AB Doradus

We report submilliarcsecond--precise astrometric measurements for the late-type star AB Doradus via a combination of VLBI(very long baseline interferometry) and Hipparcos satellite data. Our astrometric analysis results in the precise determination of the kinematics of this star, that reveals an orbital motion readily explained as caused by the gravitational interaction with a low-mass companion.

astrometry interferometric kinematics low-mass bro↗

Astrometric Detection of a Low Mass Companion Orbiting the Star AB Doradus

We report submilliarsecond-precise astrometric measurement for the late-type star AB Doradus via a combination of VLBI (very long baseline interferometry) and Hipparos satellite data. Our astrometric analysis results in the precise determination of the kinematics of this star, that reveals an orbital motion readily explained as caused by the gravitational interaction with a low-mass companion.

kinematics low-mass companion astrometry interfero↗

The effect of clock, media, and station location errors on Doppler measurement accuracy

Doppler tracking by the Deep Space Network (DSN) is the primary radio metric data type used by navigation to determine the orbit of a spacecraft. The accuracy normally attributed to orbits determined exclusively with Doppler data is about 0.5 microradians in geocentric angle. Recently, the Doppler measurement system has evolved to a high degree of precision primarily because of tracking at X-band frequencies (7.2 to 8.5 GHz). However, the orbit determination system has not been able to fully utilize this improved measurement accuracy because of calibration errors associated with transmission media, the location of tracking stations on the Earth's surface, the orientation of the Earth as an observing platform, and timekeeping. With the introduction of Global Positioning System (GPS) data, it may be possible to remove a significant error associated with the troposphere. In this article, the effect of various calibration errors associated with transmission media, Earth platform parameters, and clocks are examined. With the introduction of GPS calibrations, it is predicted that a Doppler tracking accuracy of 0.05 microradians is achievable.

Miller, J. K.↗