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NASA NTRS2013

Circular-Orbit Maintenance Strategies for Primitive Body Orbiters

For missions to smaller primitive bodies, solar radiation pressure (SRP) is a significant perturbation to Keplerian dynamics. For most orbits, SRP drives large oscillations in orbit eccentricity, which leads to large perturbations from the irregular gravity field at periapsis. Ultimately, chaotic motion results that often escapes or impacts that body. This paper presents an orbit maintenance strategy to keep the orbit eccentricity small, thus avoiding the destabilizing secondary interaction with the gravity field. An estimate of the frequency and magnitude of the required maneuvers as a function of the orbit and body parameters is derived from the analytic perturbation equations.

comet↗

NASA NTRS1988

Advanced simulation and analysis of a geopotential research mission

Computer simulations have been performed for an orbital gradiometer mission to assist in the study of high degree and order gravity field recovery. The simulations were conducted for a satellite in near-circular, frozen orbit at a 160-km altitude using a gravitational field complete to degree and order 360. The mission duration is taken to be 32 days. The simulation provides a set of measurements to assist in the evaluation of techniques developed for the determination of the gravity field. Also, the simulation provides an ephemeris to study available tracking systems to satisfy the orbit determination requirements of the mission.

Schutz, B. E.↗

NASA NTRS2012

Design of an Extended Mission for GRAIL

The GRAIL extended mission will extend the measurement of the lunar gravity field beyond what was achieved by the primary GRAIL mission this past spring (2012). By lowering the orbits of the two GRAIL spacecraft to less than half the altitude of the primary mission orbits on average, the resolution of the gravity field measurements will be improved by a factor of two, yielding a signicant improvement in our knowledge of the structure of the upper crust of the Moon. The challenges of flying so low and the design which will meet those challenges is presented here.

eccentricty vector↗

NASA NTRS1994

Arctic geodynamics: Arctic science and ERS-1 satellite altimetry

A detailed gravity field map of the mid Arctic Ocean, spreading ridge system was produced on the basis of ERS-1 satellite altimetry data. Areas of special concern, the Barents and Kara Seas, and areas surrounding the islands of Svalbard, Frans Josef Land and Novoya Zemlya are reviewed. ERS-1 altimetry covers unique Arctic and Antarctic latitudes above 72 degrees. Before ERS-1 it was not possible to study these areas with satellite altimetry. Gravity field solutions for the Barents Sea, portions of the Arctic Ocean and the Norwegian sea are shown. The largest gravity anomalies occur along the Greenland fracture zone as well as along transform faults near Svalbard.

Anderson, Allen Joel↗

NASA NTRS1989

Small Mercury Relativity Orbiter

The accuracy of solar system tests of gravitational theory could be very much improved by range and Doppler measurements to a Small Mercury Relativity Orbiter. A nearly circular orbit at roughly 2400 km altitude is assumed in order to minimize problems with orbit determination and thermal radiation from the surface. The spacecraft is spin-stabilized and has a 30 cm diameter de-spun antenna. With K-band and X-band ranging systems using a 50 MHz offset sidetone at K-band, a range accuracy of 3 cm appears to be realistically achievable. The estimated spacecraft mass is 50 kg. A consider-covariance analysis was performed to determine how well the Earth-Mercury distance as a function of time could be determined with such a Relativity Orbiter. The minimum data set is assumed to be 40 independent 8-hour arcs of tracking data at selected times during a two year period. The gravity field of Mercury up through degree and order 10 is solved for, along with the initial conditions for each arc and the Earth-Mercury distance at the center of each arc. The considered parameters include the gravity field parameters of degree 11 and 12 plus the tracking station coordinates, the tropospheric delay, and two parameters in a crude radiation pressure model. The conclusion is that the Earth-Mercury distance can be determined to 6 cm accuracy or better. From a modified worst-case analysis, this would lead to roughly 2 orders of magnitude improvement in the knowledge of the precession of perihelion, the relativistic time delay, and the possible change in the gravitational constant with time.

Bender, Peter L.↗

NASA NTRS1979

Non-linear dynamic response of a wind turbine blade

The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

Chopra, I.↗

NASA NTRS1997

A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and other tracking data

A spherical harmonic model of the lunar gravity field complete to degree and order 70 has been developed from S band Doppler tracking data from the Clementine mission, as well as historical tracking data from Lunar Orbiters 1-5 and the Apollo 15 and 16 subsatellites. The model combines 361,000 Doppler observations from Clementine with 347,000 historical observations. The historical data consist of mostly 60-s Doppler with a noise of 0.25 to several mm/s. The Clementine data consist of mostly 10-s Doppler data, with a data noise of 0.25 mm/s for the observations from the Deep Space Network, and 2.5 mm/s for the data from a naval tracking station at Pomonkey, Maryland. Observations provided Clementine, provide the strongest satellite constraint on the Moon's low-degree field. In contrast the historical data, collected by spacecraft that had lower periapsis altitudes, provide distributed regions of high-resolution coverage within +/- 29 deg of the nearside lunar equator. To obtain the solution for a high-degree field in the absence of a uniform distribution of observations, we applied an a priori power law constraint of the form 15 x 10(exp -5)/sq l which had the effect of limiting the gravitational power and noise at short wavelengths. Coefficients through degree and order 18 are not significantly affected by the constraint, and so the model permits geophysical analysis of effects of the major basins at degrees 10-12. The GLGM-2 model confirms major features of the lunar gravity field shown in previous gravitational field models but also reveals significantly more detail, particularly at intermediate wavelengths (10(exp 3) km). Free-air gravity anomaly maps derived from the new model show the nearside and farside highlands to be gravitationally smooth, reflecting a state of isostatic compensation. Mascon basins (including Imbrium, Serenitatis, Crisium, Smythii, and Humorum) are denoted by gravity highs first recognized from Lunar Orbiter tracking. All of the major mascons are bounded by annuli of negative anomalies representing significant subsurface mass deficiencies. Mare Orientale appears as a minor mascon surrounded by a horseshoe-shaped gravity low centered on the Inner and Outer Rook rings that is evidence of significant subsurface structural heterogeneity. Although direct tracking is not available over a significant part of the lunar farside, GLGM-2 resolves negative anomalies that correlate with many farside basins, including South Pole-Aitken, Hertzsprung, Korolev, Moscoviense, Tsiolkovsky, and Freundlich-Sharonov.

Lemonie, Frank G. R.↗

NASA NTRS1993

Optimal cooperative power-limited rendezvous between neighboring circular orbits

A minimum-fuel rendezvous of two power-limited spacecraft is investigated. Both vehicles are active and provide thrust to complete the rendezvous. Total propellant consumption is minimized. Analytical solutions are obtained for cooperative rendezvous in the linearized Hill-Clohessy-Wiltshire gravity field. The optimal solutions depend in a complicated way on the power-to-mass ratios of the spacecraft, the initial orbits, and the specified transfer time. For comparison purposes, analytical solutions for active-passive rendezvous in the linearized gravity field are also determined. Cooperative rendezvous requires smaller total propellant consumption, resulting in greater payload capability.

Coverstone-Carroll, Victoria↗

NASA NTRS2019

Serendipitous Geodesy from Bennu's Short-Lived Moonlets

The Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx; or OREx) spacecraft arrived at its target, near-Earth asteroid (101955) Bennu, on December 3, 2018. The OSIRIS-REx spacecraft has since collected a wealth of scientific information in order to select a suitable site for sampling. Shortly after insertion into orbit on December 31, 2018, particles were identified in starfield images taken by the navigation camera (NavCam 1). Several groups within the OSlRlS-REx team analyzed the particle data in an effort to better understand this newfound activity of Bennu and to investigate the potential sensitivity of the particles to Bennu's geophysical parameters. A number of particles were identified through automatic and manual methods in multiple images, which could be turned into short sequences of optical tracking observations. Here, we discuss the precision orbit determination (OD) effort focused on these particles at NASA GSFC, which involved members of the Independent Navigation Team (INT) in particular. The particle data are combined with other OSIRIS-REx tracking data (radiometric from OSN and optical landmark data) using the NASA GSFC GEODYN orbit determination and geodetic parameter estimation software. We present the results of our study, particularly those pertaining to the gravity field of Bennu. We describe the force modeling improvements made to GEODYN specifically for this work, e.g., with a raytracing-based modeling of solar radiation pressure. The short-lived, low-flying moonlets enable us to determine a gravity field model up to a relatively high degree and order: at least degree 6 without constraints, and up to degree 10 when applying Kaula-like regularization. We can backward- and forward-integrate the trajectory of these particles to the ejection and landing sites on Bennu. We assess the recovered field by its impact on the OSIRIS-REx trajectory reconstruction and prediction quality in the various mission phases (e.g., Orbital A, Detailed Survey, and Orbital B).

Mazarico, Erwan↗

NASA NTRS2005

The Space Technology 7 disturbance reduction system

The NASA New Millennium Program Space Technology 7 (ST7) project was selected for the purpose of flight validation of technology for minimizing disturbances on spacecraft and freely-floating test masses. Measurements of the motion of test masses are used for determining the gravitational field in its location, providing information on the nearby mass distribution or looking gravitational waves generated by distant star systems. Any unmeasured forces acting on the test mass cause a deviation from a purely gravitational trajectory and so limit the accuracy of the gravity field estimation. The ST7 project will validate the capability to eliminate unwanted forces to a level 3000 times lower than the current state of the art. The ST7 design is based on the concept of a freely-floating test mass surrounded by a spacecraft which shields the test mass from unwanted disturbances. since some disturbance of the test mass can be caused by motion of the spacecraft itself with respect to the test mass, the disturbance reduction system includes the capability of precisely measuring the position of the spacecraft with respect to the test mass and control of the spacecraft position to within 1/100 of a wavelength of light.. The overall system performance of the ST7 project will be infused into space observatories for gravitational waves such as the Laser Interferometer Space Antenna project, and into future mission for mapping the time-variable Earth gravity field. The ST7 precision control capability also has applications for separated-spacecraft interferometric imaging projects. ST7 will consist of an instrument package and a set of microthrusters, which will be attached to the European Space Agency’s LISA Pathfinder spacecraft with launch scheduled for 2008.

Folkner, W. M.↗

NASA NTRS2016

Determination of Ceres Physical Parameters Using Radiometric and Optical Data

The Dawn spacecraft was launched on September 27th, 2007. Its mission is to rendezvous with and observe the two largest bodies in the main asteroid belt, Vesta and Ceres. It has completed over a year’s worth of direct observations of Vesta from early 2011 through late 2012. In the spring of 2015, the Dawn spacecraft entered orbit around the asteroid Ceres for the start of what is expected to be more than a year of science operations. The science data collected from this encounter consist of infrared (IR) images and spectra, visible images through a number of color filters, gamma ray detections and measurements of the Ceres gravity field. These data will be collected during several science phases: an Approach phase (1500000-4860 km from Ceres), a Survey orbit (4860 km radius), a High Altitude Mapping Orbit (HAMO) (1940 km radius) and a Low Altitude Mapping Orbit (LAMO) (855 km radius). The Approach phase included three Rotational Characterization (RC) opportunities. Designing each science orbit and successfully transferring into that orbit requires a sufficiently accurate estimate of Ceres physical parameters (body fixed frame, GM and harmonics). This paper focuses on work performed to estimate Ceres physical parameters using Deep Space Network (DSN) radiometric tracking data and optical measurements derived from science camera imagery. This paper describes planning for the data acquisition, as well as processing techniques and methodology. The trajectories predicted by the gravity field estimations are also compared with the actual as-flown trajectories. Observations of the gravity at high altitudes are found to be sufficient to design precision orbits at lower altitudes. Follow-up analysis after successfully reaching LAMO is included, as is a discussion of lessons learned.

Kennedy, Brian M.↗

NASA NTRS1987

Surface deformation, gravity and the geoid from a three-dimensional convection model at low Rayleigh numbers

The two-dimensional surface deformation, gravity field, and geoid are calculated from the temperature fields of a number of numerical models of constant-viscosity three-dimensional convective flows, heated from within and from below. The surface deformation and the geoid are insensitive to the short-wavelength features of the temperature variation; the gravity field is less smooth, although it still does not clearly indicate the narrowness of the upwelling and downwelling regions at large Rayleigh numbers. The results indicate that the convective upwelling beneath regions showing positive geoid and residual depth anomalies is more localized than the horizontal extent of these features would suggest. The results are relevant to attempts to understand the behavior of the earth mantle.

Craig, Claire Harvey↗

NASA NTRS2026

Tidal Tomography Reveals a Thermal Anomaly Beneath Mars’s Crustal Dichotomy

Mars undergoes seasonal tidal forcing as a result of its eccentric orbit and the tilt of its rotation axis relative to the Sun1. Response to this forcing produces temporal variations in the Martian gravity field and is sensitive to the internal structure of the planet2,3,4. Using tracking data from the Mars Global Surveyor (MGS), Mars Odyssey (ODY) and Mars Reconnaissance Orbiter (MRO) spacecraft5,6,7, we demonstrate that degree-3 components of the time-variable gravity field of Mars differ by up to 300% from predictions for a spherically symmetric planet8,9,10. These deviations can be explained if the effective shear modulus of the mantle varies by >20% over a roughly north–south pattern that closely aligns with the surface expression of the Martian crustal dichotomy11. On the basis of this correlation, we infer preservation of a 200–400 °C thermal anomaly in the present-day mantle below the southern highlands of Mars. This temperature variation could reflect regional mantle convection12,13 or insulation by the thick southern highlands crust of Mars that has persisted over several billion years14,15.

Mars↗

NASA NTRS1974

Benefits to the study of oceanic tectonics expected from Seasat-A

A more detailed gravity field such as provided by the SEASAT-A altimeter would help resolve several problems of marine geology, such as the relationship of spreading rises to convective upstreams and the tectonics of subduction zones and the associated marginal basins. In addition, the gravity field should be measured in more detail over continental shelves accessible to mineral exploration. A secondary contribution of SEASAT-A would be to sedimentation processes, through its influence on models of ocean currents.

Kaula, W. M.↗

NASA NTRS1973

Gravity model improvement investigation

This investigation was undertaken to improve the gravity model and hence the ocean geoid. A specific objective is the determination of the gravity field and geoid with a space resolution of approximately 5 deg and a height resolution of the order of five meters. The concept of the investigation is to utilize both GEOS-C altimeter and satellite-to-satellite tracking data to achieve the gravity model improvement. It is also planned to determine the geoid in selected regions with a space resolution of about a degree and a height resolution of the order of a meter or two. The short term objectives include the study of the gravity field in the GEOS-C calibration area outlined by Goddard, Bermuda, Antigua, and Cape Kennedy, and also in the eastern Pacific area which is viewed by ATS-F.

Siry, J. W.↗

NASA NTRS1991

Toward a global lunar resource survey - The Lunar Observer mission

The present status of NASA's Lunar Observer study effort at JPL is discussed in the context of an ongoing 20-year series of studies focused on defining a robotic, low-altitude, polar-orbiting mission to the moon. The primary emphasis of the discussion is a review of the various systems-level factors that drive the overall mission plan. Selected top-level project and science requirements are summarized and the current mission and science objectives are presented. A brief description of the candidate science instrument complement is included. Several significant orbital effects caused by the lunar gravity field are explained and the variety of trajectory and maneuver options considered for both getting to the moon and orbiting there are described. The baseline mission scenario that results is a single-spacecraft, single-launch scenario which includes a small subsatellite for lunar gravity field determination.

Ridenoure, Rex W.↗

NASA NTRS1994

Satellite Laser Ranging in the 1990s: Report of the 1994 Belmont Workshop

An international network of 43 stations in 30 countries routinely collects satellite ranging data which is used to study the solid Earth and its interactions with the oceans, atmosphere, and Moon. Data products include centimeter accuracy site positions on a global scale, tectonic plate motions, regional crustal deformation, long wavelength gravity field and geoid, polar motion, and variations in the Earth's spin rate. By calibrating and providing precise orbits for spaceborne microwave altimeters, satellite laser ranging also enables global measurement of sea and ice surface topography, mean sea level, global ocean circulation, and short wavelength gravity fields and marine geoids. It provides tests of general relativity and a means or subnanosecond time transfer. This workshop was convened to define future roles and directions in satellite laser ranging.

Degnan, John J.↗

NASA NTRS1993

Gravity recovery analysis using GPS for STEP and a low-low satellite mission

Global Positioning System (GPS) receivers on low Earth orbiting satellites can provide three-dimensional global tracking with sub-decimeter orbit accuracy. The precise GPS data can additionally be used to refine the Earth's gravity field. Satellite Test of the Equivalence Principle (STEP) is a proposed European Space Agency mission which will carry a flight GPS receiver. Using a realistic scenario for processing 5 days of GPS data, a covariance analysis is performed to obtain the expected improvement in the gravity field. Additionally, a similar analysis is then repeated for two low Earth orbiting satellites, each equipped with GPS receivers and with precise ranging measurements between them.

Muellerschroen, Ronald J.↗