Search NASA⌕ Search

SEARCH · Search NASA

Results for “Trajectory Tracking”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 919 records · Page 51

Multiple Uplinks Per Antenna (MUPA) Signal Acquisition Schemes

The Deep Space Network (DSN) currently makes use of the technique of Multiple Spacecraft per Antenna (MSPA) where a single antenna is used to track multiple spacecraft downlinks within its beam, such as in the case of multiple spacecraft orbiting Mars at 8.4 GHz (X-band). It is desired to extend this technique to the uplink where a single station is used to send a signal to multiple spacecraft in order to make more efficient use of ground resources. This would be applicable to numerous smallsat constellations being considered for future missions or to future spacecraft at Venus, Mars, or more distant destinations that are all within the half-power beamwidth of a single 34-m diameter antenna. In one scheme, each spacecraft’s command sequences would be time multiplexed onto a single uplink frequency. Each spacecraft would lock onto the uplink signal and would accept only commands intended for it via special identifier codes. Each spacecraft would also emit a downlink signal to the ground that is coherent with the uplink signal but would have its own allocated frequency channel and identifier information. A couple of key challenges associated with using this technique need to be addressed. Because of the single uplink frequency, coherent turnaround for two-way Doppler and ranging would not conform to established ratios, thus the radios employed by the spacecraft would need to be capable of variable turnaround ratios. In addition, because of the different orbits or spacecraft trajectories, the relative Doppler shifts and rates can be large with respect to the common uplink signal whose frequency would lie at the centroid of the frequencies of the expected received signals of the constellation. This would be problematic with standard analog spacecraft radios whose acquisition bandwidths are relatively small (~1.7 kHz) relative to the large frequency offsets (~100 kHz) expected using the single frequency uplink technique. With the advent of software defined radios (SDRs), signal frequency search algorithms can be utilized within the flight software and/or programmable hardware (e.g., FPGAs) that can easily acquire and track signals with large frequency offsets and varying dynamics. Such techniques could include FFT search algorithms, step-and-sweep search algorithms, or onboard frequency steering making use of trajectory vectors uplinked to each member spacecraft. Other challenges include mitigation of potential interference between received signals. We have identified several software defined radios that are in different stages of development and whose key parameters have been tabulated. We have examined each radio’s capabilities with respect to acquiring and tracking signals with large frequency offsets. Such analyses made use of previous studies supplemented with specially designed tests using both simulation tools and/or existing testbeds. We have compared signal acquisition times computed from provided algorithms along with measured values derived from tests using existing hardware and simulation tools for the purpose of conducting tradeoff studies between the various radio designs and software/firmware programming approaches.

Abraham, Douglas S.↗

Prediction of the pattern performance for the Aeroassist Flight Experiment (AFE) spacecraft

In order to provide a set of benchmark flight data for a reusable Aeroassisted Orbit Transfer Vehicle (AOTV) application, NASA undertook the development of an Aeroassisted Flight Experiment (AFE) which will be launched from the Space Shuttle. A representative aeroassist trajectory will be flown and sensor measurements of aerodynamic performance, thermal protection response, and plasma ionization reentry effects will be obtained. Discussed here is the spacecraft antenna. Estimates of signal transmissions from the AFE to the Tracking and Data Relay Satellites (TDRS) during the reentry period are given. The computer modeling of the antennas is presented with and without the reentry plasma.

Yang, C.↗

Steady-State Pursuit Is Driven by Object Motion Rather Than the Vector Average of Local Motions

We have previously shown that humans can pursue the motion of objects whose trajectories can be recovered only by spatio-temporal integration of local motion signals. We now explore the integration rule used to derive the target-motion signal driving pursuit. We measured the pursuit response of 4 observers (2 naive) to the motion of a line-figure diamond viewed through two vertical bar apertures (0.2 cd/square m). The comers were always occluded so that only four line segments (93 cd/square m) were visible behind the occluding foreground (38 cd/square m). The diamond was flattened (40 & 140 degree vertex angles) such that vector averaging of the local normal motions and vertical integration (e.g. IOC) yield very I or different predictions, analogous to using a Type II plaid. The diamond moved along Lissajous-figure trajectories (Ax = Ay = 2 degrees; TFx = 0.8 Hz; TFy = 0.4 Hz). We presented only 1.25 cycles and used 6 different randomly interleaved initial relative phases to minimize the role of predictive strategies. Observers were instructed to track the diamond and reported that its motion was always coherent (unlike type II plaids). Saccade-free portions of the horizontal and vertical eye-position traces sampled at 240 Hz were fit by separate sinusoids. Pursuit gain with respect to the diamond averaged 0.7 across subjects and directions. The ratio of the mean vertical to horizontal amplitude of the pursuit response was 1.7 +/- 0.7 averaged across subjects (1SD). This is close to the prediction of 1.0 from vertical motion-integration rules, but far from 7.7 predicted by vector averaging and infinity predicted by segment- or terminator-tracking strategies. Because there is no retinal motion which directly corresponds to the diamond's motion, steady-state pursuit of our "virtual" diamond is not closed-loop in the traditional sense. Thus, accurate pursuit is unlikely to result simply from local retinal negative feedback. We conclude that the signal driving steady-state pursuit is not the vector average of local motion signals, but rather a more vertical estimate of object motion, derived in extrastriate cortical areas beyond V1, perhaps NIT or MST.

Stone, Leland S.↗

Two Dimensional Wake Vortex Simulations in the Atmosphere: Preliminary Sensitivity Studies

A numerical large-eddy simulation model is currently being used to quantify aircraft wake vortex behavior with meteorological observables. The model, having a meteorological framework, permits the interaction of wake vortices with environments characterized by crosswind shear, stratification, and humidity. The addition of grid-scale turbulence as an initial condition appeared to have little consequence. Results show that conventional nondimensionalizations work very well for vortex pairs embedded in stably stratified flows. However, this result is based on simple environments with constant Brunt-Vaisala frequency. Results presented here also show that crosswind profiles exert important and complex interactions on the trajectories of wake vortices. Nonlinear crosswind profiles tended to arrest the descent of wake vortex pairs. The member of the vortex pair with vorticity of same sign as the vertical change in the ambient along-track vorticity may be deflected upwards.

Proctor, F. H.↗

Deep Impact Autonomous Navigation : the trials of targeting the unknown

On July 4, 2005 at 05:44:34.2 UTC the Impactor Spacecraft (s/c) impacted comet Tempel 1 with a relative speed of 10.3 km/s capturing high-resolution images of the surface of a cometary nucleus just seconds before impact. Meanwhile, the Flyby s/c captured the impact event using both the Medium Resolution Imager (MRI) and the High Resolution Imager (HRI) and tracked the nucleus for the entire 800 sec period between impact and shield attitude transition. The objective of the Impactor s/c was to impact in an illuminated area viewable from the Flyby s/c and capture high-resolution context images of the impact site. This was accomplished by using autonomous navigation (AutoNav) algorithms and precise attitude information from the attitude determination and control subsystem (ADCS). The Flyby s/c had two primary objectives: 1) capture the impact event with the highest temporal resolution possible in order to observe the ejecta plume expansion dynamics; and 2) track the impact site for at least 800 sec to observe the crater formation and capture the highest resolution images possible of the fully developed crater. These two objectives were met by estimating the Flyby s/c trajectory relative to Tempel 1 using the same AutoNav algorithms along with precise attitude information from ADCS and independently selecting the best impact site. This paper describes the AutoNav system, what happened during the encounter with Tempel 1 and what could have happened.

impactor spacecraft↗

The Regolith Biters: A Divide-And-Conquer Architecture for Sample-Return Missions

The collective interaction of simple systems can be leveraged to attain complex goals. Based on this principle, we envision space system architectures where the core functional components are decoupled, autonomous, and cooperative. We aim to pursue this vision in the context of small-body sample-return missions. After all, no experimental study sheds more light into our understanding of the origin and evolution of the Solar System than the analysis of samples from asteroids and comets. We also believe that their study is important from a strategic perspective: meteorite impacts pose a direct and credible threat to life on Earth, and the development of contingency small-body deflection missions presupposes some knowledge of the target body. The current architectural paradigm for sample-return missions is centered around a design where spacecraft and sampling device are merged into a single, complex system. We argue that this monolithic approach couples the navigation and sample-collection problems, making both more difficult. In contrast, we propose a decoupled system based on the coordinated interaction between a spacecraft and a collective of small, simple devices - the Regolith Biters (RBs). A spacecraft carrying a number of RBs would travel to the vicinity of a small body. From a favorable vantage point, and while remaining within a safe distance in a non-colliding trajectory, it would release the RBs towards the target body. Upon encountering the body, they would bite the regolith (thus retaining a sample), and eject back to orbit. The spacecraft, being endowed with appropriate navigation and tracking capabilities, would rendezvous with and collect those RBs within its reach, and bring them back to Earth. Separating the navigation and sampling concerns removes the need for proximity operations with the small body-the stage in current architectures that carries the most challenges and risks. Eliminating the need for proximity operations brings back to the discussion the exploration of exciting prospects, like highly active comets, fast-rotating bodies, and binary systems. Distributing the sampling problem among a collective of agents provides the opportunity to sample multiple regions in a single mission. It also provides robustness to various environmental conditions, and may enable the distributed, in situ characterization of the body. In the search for reliability, current architectures rely on complexity: an elaborate system should succeed at once. We rely on numbers: a given agent may fail at any stage, but success is attained by the collective.

Asteroids↗

Pterodactyl: Non-Propulsive Control System Designs for Future Planetary Missions

Advances in deployable entry vehicle (DEV) technology, entry guidance, woven thermal protection systems, and affordable launch services make it possible to conceive of entry vehicles that optimize maneuverability, usable payload mass and volume, and operational costs. NASA's Space Technology Mission Directorate is currently funding the authors on a project, Pterodactyl, that is using on-the-fly trajectory design and integrated software and hardware development to investigate non-propulsive entry control systems for precision targeting of mechanical DEVs. The authors recently reported developments of these control systems for an asymmetric DEV to track bank commands for a lunar return entry. For this presentation, the authors will highlight key findings from their studies and propose rapid investigations of applications to future Mars missions such as sample return and asset delivery. Pterodactyl entry vehicle designs are suited to handle sensitive payloads and poised to achieve greater payload mass and volume compared to heritage entry vehicles given a particular launch vehicle. Furthermore, these designs could be adapted to launch on less costly launch vehicles as secondary payloads and could enable missions with high-frequency deployment requirements.

Alunni, Antonella↗

Flight test results for the Digital Integrated Automatic Landing Systems (DIALS): A modern control full-state feedback design

The Digital Integrated Automatic Landing System (DIALS) is discussed. The DIALS is a modern control theory design performing all the maneuver modes associated with current autoland systems: localizer capture and track, glideslope capture and track, decrab, and flare. The DIALS is an integrated full-state feedback system which was designed using direct-digital methods. The DIALS uses standard aircraft sensors and the digital Microwave Landing System (MLS) signals as measurements. It consists of separately designed longitudinal and lateral channels although some cross-coupling variables are fed between channels for improved state estimates and trajectory commands. The DIALS was implemented within the 16-bit fixed-point flight computers of the ATOPS research aircraft, a small twin jet commercial transport outfitted with a second research cockpit and a fly-by-wire system. The DIALS became the first modern control theory design to be successfully flight tested on a commercial-type aircraft. Flight tests were conducted in late 1981 using a wide coverage MLS on Runway 22 at Wallops Flight Center. All the modes were exercised including the capture and track of steep glidescopes up to 5 degrees.

Hueschen, R. M.↗

Ice Cloud Formation and Dehydration in the Tropical Tropopause Layer

Stratospheric water vapor is important not only for its greenhouse forcing, but also because it plays a significant role in stratospheric chemistry. several recent studies have focused on the potential for dehydration due to ice cloud formation in air rising slowly through the tropical tropopause layer. Holton and Gettelman showed that temperature variations associated with horizontal transport of air in the tropopause layer can drive ice cloud formation and dehydration, and Gettelman et al. recently examined the cloud formation and dehydration along kinematic trajectories using simple assumptions about the cloud properties. In this study, we use a Lagrangian, one-dimensional cloud model to further investigate cloud formation and dehydration as air is transported horizontally and vertically through the tropical tropopause layer. Time-height curtains of temperature are extracted from meteorological analyses. The model tracks the growth and sedimentation of individual cloud particles. The regional distribution of clouds simulated in the model is comparable to the subvisible cirrus distribution indicated by SAGE II. The simulated cloud properties depend strongly on the assumed ice supersaturation threshold for ice nucleation. with effective nuclei present (low supersaturation threshold), ice number densities are high (0.1--10 cm(circumflex)-3), and ice crystals do not grow large enough to fall very far, resulting in limited dehydration. With higher supersaturation thresholds, ice number densities are much lower (less than 0.01 cm(circumflex)-3), and ice crystals grow large enough to fall substantially; however, supersaturated air often crosses the tropopause without cloud formation. The clouds typically do not dehydrate the air along trajectories down to the temperature minimum saturation mixing ratio. Rather the water vapor mixing ratio crossing the tropopause along trajectories is typically 10-50% larger than the saturation mixing ratio.

Jensen, Eric↗

Giotto Extended Mission (GEM)

The primary objectives of the Giotto Extended Mission (GEM), are to determine the composition and physical state of the Grigg Skjellerup Comet's nucleus; to determine the processes that govern the composition and distribution of neutral and ionized species in the cometary atmosphere. Giotto consists of a single European Space Agency (ESA) spacecraft that was launched in 1985 from Center Spatial Guyanis in French Guiana on an Ariane launch vehicle. After a successful launch into geostationary orbit and a heliocentric transfer trajectory, the spacecraft successfully encountered Halley's Comet in 1986. One month after encountering Halley's Comet, Mar. 1986, the spacecraft was placed in hibernation in a heliocentric orbit slightly less than 1 AU. Between Feb. and Jul. 1990 the spacecraft was successfully reactivated, checked out, and placed on a trajectory course to intercept comet Grigg Skjellerup. The spacecraft has been in hibernation since Jul. 1990. Information is presented in tabular form in the following areas: coverage goals, Deep Space Network Support, frequency assignments, telemetry, command, and tracking support responsibility.

Wilkins, D. E. B.↗

Pterodactyl: Non-propulsive Control Systems for Future Planetary Missions

This white paper presents an assessment of control systems as it relates to state-of-the-art hypersonic entry vehicles and addresses technological advances that enable new control systems for future hypersonic entry vehicles. Advancements in deployable entry vehicle (DEV) technology, entry guidance, woven thermal protection systems, and affordable launch services make it possible to conceive of entry vehicles that optimize entry loads, maneuverability, usable payload mass and volume, and operational costs. NASA’s Space Technology Mission Directorate (STMD) is currently funding the authors on a project, Pterodactyl, that is using on-the-fly trajectory design and integrated software and hardware development to investigate non-propulsive entry control systems for precision targeting of mechanical DEVs. The authors recently reported key findings of these control systems for an asymmetric DEV to track bank commands for a lunar sample return entry.

Sarah D'Souza↗

Management of Operations under Visual Flight Rules in UTM for Disaster Response Missions

The disaster response domain has experienced an increased focus in recent years due to the rise in number and scale of events, lessons learned from past experience, and emerging technologies that make possible a more coordinated and effective response. As part of this focus, JAXA and NASA have been collaborating on the integration of manned and unmanned aircraft in support of disaster response operations through integrated testing of their respective mission planning and optimization system (Disaster Relief Aircraft Information Sharing Network, or D-NET) and an automated UAS traffic management system (e.g., UTM). In 2018, JAXA and NASA jointly participated in a large-scale disaster drill in Japan where the integration of systems was successfully demonstrated through real-time data exchanges, visualization, and decision making as part of the coordinated airspace management of a manned helicopter in VFR conditions and unmanned small UAS operating in common areas. This work details a flight test consisting of two flights that were conducted December 2019 near the Chofu Aerodrome in Tokyo, which focused on the evaluation of pilots operating under Visual Flight Rules (VFR) communicating through D-NET and sharing intent and position information within UTM. This work contributes to defining the necessary requirements for digital coordination between manned and unmanned operations. UTM requires the use of operation volumes, which are spatial and temporal volumes that encompass UAS flight trajectories and account for technical performance errors and deviations due to disturbances (e.g., wind). A series of flights, representing different missions, used landmark-based operation volumes and conformance of the aircraft to those operation volumes were tracked within UTM. Experienced disaster response helicopter pilots provided insight on the development of the operation plans and their usability during disaster response operations. Results from the flight test supported the suggested benefits of using landmarks for planning and positional awareness and highlighted the need for future research in advanced visualization capabilities to support operations that consider both system constraints and flight deck/airspace management interaction.

disaster response↗

Chaotic Motion in the Solar System and Beyond

The motion of planetary bodies is the archetypal clockwork system. Indeed, clocks and calendars were developed to keep track of the relative motions of the Earth, the Sun and the Moon. However, studies over the past few decades imply that this predictable regularity does not extend to small bodies, nor does it apply to the precise trajectories of the planets themselves over long timescale.s. Various examples of chaotic motion within our Solar System and, extrasolar planetary systems will be discussed.

Lissauer, Jack↗

Stereo-Optic High Definition Imaging: A New Technology to Understand Bird and Bat Avoidance of Wind Turbines

There is a critical need to develop monitoring tools to track aerofauna (birds and bats) in three dimensions around wind turbines. New monitoring systems will reduce permitting uncertainty by increasing the understanding of how birds and bats are interacting with wind turbines, which will improve the accuracy of impact predictions. Biodiversity Research Institute (BRI), The University of Maine Orono School of Computing and Information Science (UMaine SCIS), HiDef Aerial Surveying Limited (HiDef), and SunEdison, Inc. (formerly First Wind) responded to this need by using stereo-optic cameras with near-infrared (nIR) technology to investigate new methods for documenting aerofauna behavior around wind turbines. The stereo-optic camera system used two synchronized high-definition video cameras with fisheye lenses and processing software that detected moving objects, which could be identified in post-processing. The stereo- optic imaging system offered the ability to extract 3-D position information from pairs of images captured from different viewpoints. Fisheye lenses allowed for a greater field of view, but required more complex image rectification to contend with fisheye distortion. The ability to obtain 3-D positions provided crucial data on the trajectory (speed and direction) of a target, which, when the technology is fully developed, will provide data on how animals are responding to and interacting with wind turbines. This project was focused on testing the performance of the camera system, improving video review processing time, advancing the 3-D tracking technology, and moving the system from Technology Readiness Level 4 to 5. To achieve these objectives, we determined the size and distance at which aerofauna (particularly eagles) could be detected and identified, created efficient data management systems, improved the video post-processing viewer, and attempted refinement of 3-D modeling with respect to fisheye lenses. The 29-megapixel camera system successfully captured 16,173 five-minute video segments in the field. During nighttime field trials using nIR, we found that bat-sized objects could not be detected more than 60 m from the camera system. This led to a decision to focus research efforts exclusively on daytime monitoring and to redirect resources towards improving the video post- processing viewer. We redesigned the bird event post-processing viewer, which substantially decreased the review time necessary to detect and identify flying objects. During daytime field trials, we determine that eagles could be detected up to 500 m away using the fisheye wide-angle lenses, and eagle-sized targets could be identified to species within 350 m of the camera system. We used distance sampling survey methods to describe the probability of detecting and identifying eagles and other aerofauna as a function of distance from the system. The previously developed 3-D algorithm for object isolation and tracking was tested, but the image rectification (flattening) required to obtain accurate distance measurements with fish-eye lenses was determined to be insufficient for distant eagles. We used MATLAB and OpenCV to improve fisheye lens rectification towards the center of the image, but accurate measurements towards the image corners could not be achieved. We believe that changing the fisheye lens to rectilinear lens would greatly improve position estimation, but doing so would result in a decrease in viewing angle and depth of field. Finally, we generated simplified shape profiles of birds to look for similarities between unknown animals and known species. With further development, this method could provide a mechanism for filtering large numbers of shapes to reduce data storage and processing. These advancements further refined the camera system and brought this new technology closer to market. Once commercialized, the stereo-optic camera system technology could be used to: a) research how different species interact with wind turbines in order to refine collision risk models and inform mitigation solutions; and b) monitor aerofauna interactions with terrestrial and offshore wind farms replacing costly human observers and allowing for long-term monitoring in the offshore environment. The camera system will provide developers and regulators with data on the risk that wind turbines present to aerofauna, which will reduce uncertainty in the environmental permitting process.

Adams, Evan↗

First Results from a Hardware-in-the-Loop Demonstration of Closed-Loop Autonomous Formation Flying

A closed-loop system for the demonstration of autonomous satellite formation flying technologies using hardware-in-the-loop has been developed. Making use of a GPS signal simulator with a dual radio frequency outlet, the system includes two GPS space receivers as well as a powerful onboard navigation processor dedicated to the GPS-based guidance, navigation, and control of a satellite formation in real-time. The closed-loop system allows realistic simulations of autonomous formation flying scenarios, enabling research in the fields of tracking and orbit control strategies for a wide range of applications. The autonomous closed-loop formation acquisition and keeping strategy is based on Lyapunov's direct control method as applied to the standard set of Keplerian elements. This approach not only assures global and asymptotic stability of the control but also maintains valuable physical insight into the applied control vectors. Furthermore, the approach can account for system uncertainties and effectively avoids a computationally expensive solution of the two point boundary problem, which renders the concept particularly attractive for implementation in onboard processors. A guidance law has been developed which strictly separates the relative from the absolute motion, thus avoiding the numerical integration of a target trajectory in the onboard processor. Moreover, upon using precise kinematic relative GPS solutions, a dynamical modeling or filtering is avoided which provides for an efficient implementation of the process on an onboard processor. A sample formation flying scenario has been created aiming at the autonomous transition of a Low Earth Orbit satellite formation from an initial along-track separation of 800 m to a target distance of 100 m. Assuming a low-thrust actuator which may be accommodated on a small satellite, a typical control accuracy of less than 5 m has been achieved which proves the applicability of autonomous formation flying techniques to formations of satellites as close as 50 m.

Gill, E.↗

Tracking seasonal variability in plant traits from spaceborne PRISMA and NEON AOP across forest types and ecoregions

Plant traits serve as critical indicators of how plants adapt to environmental changes and influence ecosystem functions. While airborne hyperspectral remote sensing effectively maps plant traits through detailed reflectance properties, it is limited by cost and scale, making large-scale and temporal studies challenging. The recently launched spaceborne hyperspectral imager, PRecursore IperSpettrale della Missione Applicativa (PRISMA), offers frequent, large scale and high-fidelity observations on a spatial resolution of 30 m and a revisit time of around 29 days, making it suitable for large-scale seasonal trait mapping. However, their potential remains largely unexplored. This study developed a multi-stage framework by leveraging the PRISMA spaceborne hyperspectral data and National Ecological Observatory Network (NEON) Airborne Observation Platform (AOP) hyperspectral data to investigate the seasonal dynamics of four key plant traits — chlorophyll content, carotenoid content, equivalent water thickness, and nitrogen content — across eleven NEON sites representing diverse forest types and ecoregions in the contiguous U.S. Our results demonstrated that PRISMA hyperspectral data can reliably track seasonal variability in plant traits, achieving overall R 2 values ranging from 0.78 to 0.88 and normalized root mean square error (NRMSE) values ranging from 5.4% to 8.4% for the four traits. Seasonal patterns revealed bell-shaped trajectories for chlorophyll and carotenoids, while equivalent water thickness decreased steadily across most sites, driven by structural changes during leaf maturation and senescence. Nitrogen content exhibited less pronounced seasonal variation but followed expected nutrient resorption patterns. Analysis of environmental drivers showed that seasonal variability is primarily controlled by solar radiation and day length in northern sites, vapor pressure in semi-arid regions, and temperature in mid-southeastern sites. Spatial variability, meanwhile, was primarily driven by soil properties, particularly during the peak growing season. However, the influence of soil variables slightly declines toward the end of the season at several sites, as climatic factors become more prominent. This study highlights the capability of PRISMA, and potentially other similar spaceborne hyperspectral data for large-scale, time-series plant trait mapping and provides valuable insights into the interactions between plant traits and environmental factors. In conclusion, these findings contribute to advancing our understanding of plant functional ecology and improving predictions of ecosystem responses to environmental changes.

Environmental drivers↗

S band transponder experiment

It is reported that this experiment measures the lunar gravitational field, which in turn provides information on the distribution of lunar mass and its correlation with surface features such as craters, mountains, and maria. The lunar gravitational field is measured by observing the dynamical motion of spacecraft in free-fall orbits. Effective detection of mass variations is greatly enhanced by low-altitude trajectories, such as the eccentric orbits during revolutions 3 to 16 of the Apollo 16 spacecraft and the 11 km periapsis of the Apollo 16 subsatellite during May 1972. The observational data are the precise earth-based radio tracking measurements initially used for real-time navigation.

Sjogren, W. L.↗

Gravity field of Jupiter and its satellite from Pioneer 10 and Pioneer 11 tracking data

Accurate two-way Doppler tracking data obtained from Pioneers 10 and 11 during their Jupiter encounters are analyzed to yield significantly improved values for the masses of the Galilean satellites, the harmonic coefficients of Jupiter, and the mass of the planet. The spacecraft trajectories relative to Jupiter are discussed, and nongravitational spacecraft accelerations are taken into account. Gravity results are derived from a simultaneous iterative weighted least-squares solution for the orbital elements of seven bodies, the masses of Jupiter and the Galilean satellites, the right ascension and declination of Jupiter's instantaneous pole relative to the 1950.0 mean earth equator and equinox, the Jovian gravity harmonic coefficients, the mass of a hypothetical mascon at the Great Red Spot, and the nongravitational-acceleration parameters. Four separate solutions are determined, and the best numerical values are given for the ratios of the masses of the four Galilean satellites to the mass of Jupiter; the ratio of the sun's mass to that of the Jupiter system; the second, third, fourth, fifth, and sixth zonal harmonic coefficients of Jupiter; the sectoral harmonics; and the ratio of the hypothetical mascon's mass to that of Jupiter.

Null, G. W.↗