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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

National Geodetic Satellite Program, Part II: University of California, Los Angeles

Satellite orbit analyses are presented which were undertaken for: (1) reasons of insight and economy; (2) obtaining geophysically interesting tesseral harmonics; (3) comparing effects of tracking station location error drag, radiation pressure, and luni-solar attraction to tesseral harmonic effects; and (4) combination of satellite and terrestrial data. The analyses were divided into the following phases: (1) MINITRACK interferometry; early Baker-Nunn camera directions; (2) late Baker-Nunn camera directions; and (3) combined Baker-Nunn camera and TRANET Doppler data.

Kaula, W. M.↗
NASA NTRS1981

A diurnal resonance in the ocean tide and in the earth's load response due to the resonant free 'core nutation'

The effects of the oceans, which are subject to a resonance due to a free rotational eigenmode of an elliptical, rotating earth with a fluid outer core having an eigenfrequency of (1 + 1/460) cycle/day, on the body tide and nutational response of the earth to the diurnal luni-tidal force are computed. The response of an elastic, rotating, elliptical, oceanless earth with a fluid outer core to a given load distribution on its surface is first considered, and the tidal sea level height for equilibrium and nonequilibrium oceans is examined. Computations of the effects of equilibrium and nonequilibrium oceans on the nutational and deformational responses of the earth are then presented which show small but significant perturbations to the retrograde 18.6-year and prograde six-month nutations, and more important effects on the earth body tide, which is also resonant at the free core notation eigenfrequency.

Wahr, J. M.↗
NASA NTRS1981

Effect of the fluid core on changes in the length of day due to long period tides

The long period luni-solar tidal potential is known to cause periodic changes in the earth's rotation rate. It is found that the effect of a dissipationless fluid outer core is to reduce the amplitudes of these tidal perturbations by about 11 percent. When the fluid core effect is added to Agnew and Farrell's (1978) estimate of the effect of an equilibrium ocean, the result is in accord with observation. The effects of dissipative processes within the fluid core are also examined. Out-of-phase perturbations are found which could be as large as about 10 ms at 18.6 yr. It is concluded, however, that the poorly understood decade fluctuations in the earth's rotation rate will prohibit observation of this effect.

Wahr, J. M.↗
NASA NTRS1986

The implementation of two satellite programs in a microcomputer environment

This paper describes the implementation of two computer programs that predict the motion of artificial satellites. The two programs are developed in a microcomputer environment. The particular microcomputer used is an IBM AT system. The programs can predict the orbital behavior of artificial satellites under the influence of gravity harmonics up to a 21 by 21 field, luni-solar gravity, drag, and solar radiation pressure. One program uses Cowell's method and the other uses variation of parameters with a singly averaging technique. Both programs use commercially available software to post-process trajectory information and to generate graphics display. The programs reside on floppy disks and are available to the general public through NASA's Computer Software Management and Information Center (COSMIC).

Kwok, J. H.↗
NASA NTRS1986

The effects of mantle and anelasticity on nutations, earth tides, and tidal variations in rotation rate

The paper models the effects of mantle anelasticity on luni-solar nutations, on tidal deformation, on tidal variations in rotation rate, and on the eigenfrequency of the free core nutation. The results can be used to invert observations to solve for the anelastic contributions to the shear and bulk moduli of the upper and lower mantle. Specific anelastic models are used to numerically estimate the effects of anelasticity on these geodetic observables. The nutation estimates are compared with observational results. Among the conclusions: (1) mantle anelasticity is likely to be the most important source of damping for the free core nutation; (2) present VLBI nutation results are, in principle, accurate enough to usefully bound anelasticity at diurnal periods. But the discrepancy between the VLBI observed nutations and the 1984 IAU nutation model cannot be explained by anelasticity and is not yet well enough understood to allow anelasticity to be determined from the data.

Wahr, John↗
NASA NTRS1987

Simulation and analysis of a geopotential research mission

Methods for the determination of the initial conditions for the two satellites that will satisfy Geopotential Research Mission (GRM) requirements are investigated. For certain gravitational recovery techniques, the satellites must remain close to a specified separation distance and their groundtracks must repeat after a specified interval of time. Since the objective of the GRM mission is to improve the gravity model, any pre-mission orbit predicted using existing gravity models will be in error. A technique has been developed to eliminate the drift between the two satellites caused by gravitational modeling errors and return them to repeating groundtracks. The concept of frozen orbits, which minimize altitude variations over given latitudes, was investigated. Finally, the effects of temporal perturbations on the relative range-rate signal were studied. At the proposed altitude of 160 km, the range-rate signal produced by perturbations other than the static geopotential field are dominated by the luni-solar effect. This study demonstrates that the combined effects of all the temporal perturbations does not prevent the orbit from being frozen or the satellites from obtaining a repeating groundtrack to within a specified closure distance.

White, Lisa K.↗
NASA NTRS1990

TOPEX/POSEIDON orbit maintenance maneuver design

The Ocean Topography Experiment (TOPEX/POSEIDON) mission orbit requirements are outlined, as well as its control and maneuver spacing requirements including longitude and time targeting. A ground-track prediction model dealing with geopotential, luni-solar gravity, and atmospheric-drag perturbations is considered. Targeting with all modeled perturbations is discussed, and such ground-track prediction errors as initial semimajor axis, orbit-determination, maneuver-execution, and atmospheric-density modeling errors are assessed. A longitude targeting strategy for two extreme situations is investigated employing all modeled perturbations and prediction errors. It is concluded that atmospheric-drag modeling errors are the prevailing ground-track prediction error source early in the mission during high solar flux, and that low solar-flux levels expected late in the experiment stipulate smaller maneuver magnitudes.

Bhat, R. S.↗
NASA NTRS1991

Ocean tide models for satellite geodesy and Earth rotation

A theory is presented which predicts tides in turbulent, self-gravitating, and loading oceans possessing linearized bottom friction, realistic bathymetry, and continents (at coastal boundaries no-flow conditions are imposed). The theory is phrased in terms of spherical harmonics, which allows the tide equations to be reduced to linear matrix equations. This approach also allows an ocean-wide mass conservation constraint to be applied. Solutions were obtained for 32 long and short period luni-solar tidal constituents (and the pole tide), including the tidal velocities in addition to the tide height. Calibrating the intensity of bottom friction produces reasonable phase lags for all constituents; however, tidal amplitudes compare well with those from observation and other theories only for long-period constituents. In the most recent stage of grant research, traditional theory (Liouville equations) for determining the effects of angular momentum exchange on Earth's rotation were extended to encompass high-frequency excitations (such as short-period tides).

Dickman, Steven R.↗
NASA NTRS1991

Libration in the earth's rotation

External luni-solar torque exerted on the difference (B-A) of the earth's two equatorial principal moments of inertia gives rise to two types of librational motions in the earth's rotation: the semidiurnal libration in spin and the prograde diurnal libration in polar motion. Formulas for the librations considering a realistic earth model and their tidal decompositions are derived and evaluated. The spin libration has a maximum peal-to-peak amplitude of 0.90 milliarcseconds, that of the polar libration is 0.06 milliarcseconds. Implications concerning their detectability and role in the tidal variation of earth rotation are discussed.

Chao, B. F.↗
NASA NTRS1990

Ocean tides for satellite geodesy

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Dickman, S. R.↗
NASA NTRS1994

Computing Satellite Maneuvers For A Repeating Ground Track

TOPEX/POSEIDON Ground Track Maintenance Maneuver Targeting Program (GTARG) assists in designing maneuvers to maintain orbit of TOPEX/POSEIDON satellite. Targeting strategies used either maximize time between maneuvers or force control band exit to occur at specified intervals. Runout mode allows for ground-track propagation without targeting. GTARG incorporates analytic mean-element propagation algorithm accounting for all perturbations known to cause significant variations in ground track. Perturbations include oblateness of Earth, luni-solar gravitation, drag, thrusts associated with impulsive maneuvers, and unspecified fixed forces acting on satellite in direction along trajectory. Written in VAX-FORTRAN.

Shapiro, Bruce↗
NASA NTRS1994

Measuring temporal gravitational variations using SLR data

Redistribution of mass within the Earth system changes its gravitational field, and thus changes the orbits of Earth satellites. While these variations are small, Satellite Laser Ranging (SLR) to precise geodetic satellites such as Lageos-1, Lageos-2, Starlette, Ajisai, and Stella can detect these changes at their broadest spatial scales (currently greater than 10,000 km). The satellites sense only the combined variation in the solid Earth-ocean-atmosphere system; however, modeling of these different components has led to detection of long-wavelength variations in the distribution of atmospheric mass, changes in the amplitudes of atmospheric and oceanic tides, and secular variations caused by the post-glacial adjustment of the Earth's crust. The unambiguous detection of ocean mass redistribution by SLR has not been verified due largely to inadequacies in current ocean models. Great progress has been made in recent years in the determination of luni-solar tides and the braking they induce in the Earth-Moon-Sun system (leading to secular changes in the length-to-day and lengthening of the lunar orbit period) using a wide variety of techniques including ocean tide gauges, satellite altimetry, Lunar Laser Ranging, and near-Earth satellite orbit modeling. Recent investigations of the more complex and less predictable non-tidal temporal variations in the gravity field have generally proceeded along two fronts: 1) the determination of long-wavelength variations in the gravity field through the changing perturbations seen in the orbits of near-Earth satellites, and 2) the prediction of temporal variations in gravity using geophysical, atmospheric, and oceanic models. A convergence of these efforts is sought to better understand the source of observed changes in the Earth's gravitational field.

Nerem, Robert S.↗
NASA NTRS1994

Obliquity-oblateness feedback: Are climatically sensitive values of obliquity dynamically unstable?

A new model is presented for feedback between rotational and climatic variations, operative on time scales of 10(exp 4) - 10(exp 7) years. Due to the combined effect of planetary perturbations to the Earth's orbit plane and luni-solar torques on the oblate figure of the Earth, the obliquity varies by approximately 1 deg on a 4 x 10(exp 4) year time scale. Associated changes in the seasonal and latitudinal pattern of incident solar radiation cause major glaciations. Mass transport from the oceans to the polar ice sheets during these glaciations can change the gravitational oblateness of the Earth by amounts approaching 1%. As the rate of spin axis precession is directly proportional to the oblateness, the climatically forced mass transport can by dynamically significant. A simple parameterization of this coupled orbital-rotational-climatic system suggests that there is a strong tendency for the system to evolve away from climatically sensitive values of the obliquity. This may explain the mid-Pleistocene transition from an obliquity dominated regime to the present regime in which most climatic variability is concentrated at longer (10(exp 5) year) periods.

Bills, Bruce G.↗
NASA NTRS1999

Impact of Eccentricity on East-west Stationkeeping for GPS Class of Orbits

There exists a strong relationship between eccentricity and the potential for a repeating groundtrack orbit to exhibit chaotic motion. This is true at all values of eccentricity, but, perhaps most dramatic, is that it is true even for orbits that are nearly circular. These complex motions can have a significant impact on the east-west stationkeeping process for maintaining the repeating groundtrack property of a commensurate orbit. Ely and Howell have shown that traditional stationkeeping (SK) methods are unable to maintain a repeating groundtrack in the presence of complex dynamics, such as with chaotic motion. They developed an alternate SK method that is able to maintain a repeating groundtrack for eccentric, commensurate orbits. The focus of the current study is to investigate orbits with characteristics that are similar to GPS satellites except with modestly larger eccentricities. It will be shown that at eccentricities larger than approx. .01 the chaotic regions become significant, and the need arises for a robust stationkeeping approach, such as developed in. FurtheRmore, the investigation will reveal that the influence of luni-solar perturbations contributes to the growth of eccentricity, thus increasing the probability of encountering chaotic motion during a typical satellite lifetime.

Ely, Todd A.↗
NASA NTRS2004

Oceanic Tidal Mixing As a Contributor to Milankovitch-scale Climate Change

We propose that changes in the magnitude of oceanic tidal mixing on long time scales is an important, but previously unrecognized, contributor to global climate change. it is well known that Earth's orbital and rotational state changes significantly on 10(exp 4)-10(exp 5) year time scales, and that this influences the spatial and temporal pattern of incident radiation. It is widely supposed that climatic variations on these same time scales are, in large part, a response of the ocean-atmosphere-cryosphere system to this radiative forcing. Our proposal is that variations in the luni-solar tidal potential, induced by these same orbital and rotational variations, influences oceanic mixing and thus modulates meridional heat transport, by amounts which are competitive with the radiative forcing. There are some obvious differences between tidal potential and insolation. First is that the Sun and Moon both contribute to tides, whereas the radiation is entirely of solar origin. Second is that the Earth is transparent to gravity but opaque to radiation. Clipping associated with this opacity makes the radiation pattern temporal spectrum rather more complex than the tidal spectrum. A third point is that solar radiation directly delivers energy to Earth's surface whereas tidal mixing will only expedite lateral transport of heat in association with oceanic thermohaline circulation. The diurnal average insolation pattern is best parameterized via a Fourier series in time of year and Legendre polynomials in sine of latitude. Our present focus will be on the annual average terms. The Legendre degree n=0 term describes the global average insolation, and is nearly constant. The degree n=l term describes differences between northern and southern hemispheres, and the annual mean is zero. The degree n=2 term is the main contributor to the equator to pole variations, and varies with obliquity and orbital eccentricity, with the obliquity variation dominating. The lowest order decomposition of the tidal potential recognizes 3 constituents: semi-diurnal, diurnal, and long period, with solar and lunar contributions to each. Our present focus will be on long term variations in the mean square amplitude of the semi-diurnal constituent, with averaging over all the short period variations. For the solar tide that includes the day and year. For the lunar tide it includes the day, month, year, and the apsidal (8.85 year) and nodal (18.6 year) periods. We present calculations of the variations in radiative and tidal forcing for the past 3 million years. The two signals are quite similar. Both vary by approximately 1% of their respective mean values, are dominated by obliquity variations, and exhibit only secondary influence from orbital eccentricity.

Munk, Walter↗
NASA NTRS2006

Application of the Convolution Formalism to the Ocean Tide Potential: Results from the Gravity and Recovery and Climate Experiment (GRACE)

A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment (GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright (1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4-5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

models↗
NASA NTRS2017

Decadal Polar Motion of the Earth Excited by the Convective Outer Core From Geodynamo Simulations

Long time geodetic observation records show that the orientation of the Earth's rotation axis with respect to the terrestrial reference frame, or polar motion, changes on a broad range of timescales. Apart from external torques from the luni-solar tides, these changes are excited by interactions among different components of the Earth system. The convective fluid outer core has long been conjectured a likely contributor to the observed polar motion on timescales upward of decades, such as the 30 year Markowitz wobble. We investigated the electromagnetic coupling scenario across the core-mantle boundary via numerical geodynamo simulation for different geodynamo parameters (Rayleigh numbers and magnetic Rossby numbers). Our simulated polar motion varies strongly with the dynamo parameters, while its excitation on decadal timescales appear to converge asymptotically within the adopted range of numerical Rossby numbers. Three strongest asymptotic modes emerge from numerical results, with periods around 30, 40, and 60 years for the prograde excitation and around 24, 30, and 60 years for the retrograde excitation. Their amplitudes are all larger than 5 times 10 (sup minus 8), or approximately 10 milliseconds of arc.The results suggest that the electromagnetic core-mantle coupling could explain a substantial portion, if not all, of the observed decadal polar motion. In particular, the predicted 60 year polar motion deserves special attention for future observations and studies.

Kuang, W.↗