Gravitational field modeling of irregularly shaped bodies by solving the coupled interior-exterior boundary value problem

Earth gravitational model 2008

On the use of spherical harmonic series inside the minimum Brillouin sphere: Theoretical review and evaluation by GRAIL and LOLA satellite data

Gravitational models have been widely used to study the effects of fields on particle motion. The advantages of such models are: (1) They are often easier or cheaper to construct and use than the system which they represent. (2) Particle motion is readily seen and may be photographed. (3) Events lasting for a fraction of a microsecond as, for example, with electrons moving in electrostatic fields, may be demonstrated in models as events which take a few seconds. The article describes the use of a tilted plane as a two-dimensional, uniform gravitational field. It has been used successfully as a sixth-form physics experiment to demonstrate the motion of projectiles fairly close to the Earth over a limited range. Thus it shows the motion of artillery shells (ignoring air resistance) but not of artificial satellites or long-range rockets, for which a simple uniform field model is not valid.

Crustal density and global gravitational field estimation of the Moon from GRAIL and LOLA satellite data

Firstly, the GRACE Level 1B measured data including the orbital position and velocity of GPS receiver, intersatellite range rate of K‐band ranging system, nonconservative force of accelerometer and attitude of star camera assembly between 2007‐06‐01~2007‐12‐31 provided by the American Jet Propulsion Laboratory (JPL) are processed effectively by orbital connection, gross error detection, linear interpolation, recalibration, coordinate transformation, error analysis, and so on. Secondly, the GRACE Earth's gravitational field complete up to degree and order 120 is recovered based on the improved energy conservation principle, the cumulative geoid height error is 25.313 cm at degree 120. Finally, the dependability of the Earth's gravitational field model IGG‐GRACE is verified in the paper, and the reasons why the accuracy of IGG‐GRACE is a little superior to the Earth's gravitational field model EIGEN‐GRACE02S provided by the German GeoForschungsZentrum Potsdam (GFZ) in the low frequency range and is slightly lower than that in the medium‐high frequency band are analyzed.

Effective interaction among workers at electrical work sites can help prevent accidents and improve work efficiency. The existing interaction measurement methods for electrical workers mainly use visual observation, which is inefficient, slow, and easily influenced by subjectivity, resulting in low measurement accuracy. To improve the measurement speed and accuracy, in this paper, a method for measuring the interaction behavior of electrical workers based on the gravitational field model is proposed by using video surveillance and computer vision technology. Firstly, based on this technology, four features, namely interaction distance, interaction emotion, posture openness, and interaction duration, are extracted. Then, a measurement model for interaction between the four features and workers is established using the gravitational field in physics. Finally, a video dataset of interaction behavior is constructed to verify the accuracy of the model. The results show that the average relative error of this method is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.199\pm 0.0129$</tex> . This article can provide a new idea for enriching interaction behavior measurement methods. It also provides new technologies for feature extraction.

Evaluation of Gravitational Field Models Based on the Laser Range Observation of Low Earth Orbit Satellites

Gravitational features are a fundamental source of information to learn more about the interior structure and composition of planets, moons, asteroids, and comets. Gravitational field modeling typically approximates the target body with a sphere, leading to a representation in spherical harmonics. However, small celestial bodies are often irregular in shape and hence poorly approximated by a sphere. A much better suited geometrical fit is achieved by a triaxial ellipsoid. This is also mirrored in the fact that the associated harmonic expansion (ellipsoidal harmonics) shows a significantly better convergence behavior as opposed to spherical harmonics. Unfortunately, complex mathematics and numerical problems (arithmetic overflow) so far severely limited the applicability of ellipsoidal harmonics. In this paper, we present a method that allows expanding ellipsoidal harmonics to a considerably higher degree compared to existing techniques. We apply this novel approach to model the gravitational field of comet 67P, the final target of the Rosetta mission. The comparison of results based on the ellipsoidal parameterization with those based on the spheroidal and spherical approximations reveals that the latter is clearly inferior; the spheroidal solution, on the other hand, is virtually just as accurate as the ellipsoidal one. Finally, in order to generalize our findings, we assess the gravitational field modeling performance for some 400 small bodies in the Solar System. From this investigation we generally conclude that the spheroidal representation is an attractive alternative to the complex ellipsoidal parameterization, on the one hand, and the inadequate spherical representation, on the other hand.

Gravitational field modelling is an important tool for inferring past and present dynamic processes of the Earth. Functions on the sphere such as the gravitational potential are usually expanded in terms of either spherical harmonics or radial basis functions (RBFs). The (Regularized) Functional Matching Pursuit and its variants use an overcomplete dictionary of diverse trial functions to build a best basis as a sparse subset of the dictionary. They also compute a model, for instance, of the gravitational field, in this best basis. Thus, one advantage is that the best basis can be built as a combination of spherical harmonics and RBFs. Moreover, these methods represent a possibility to obtain an approximative and stable solution of an ill-posed inverse problem. The applicability has been practically proven for the downward continuation of gravitational data from the satellite orbit to the Earth’s surface, but also other inverse problems in geomathematics and medical imaging. A remaining drawback is that, in practice, the dictionary has to be finite and, so far, could only be chosen by rule of thumb or trial-and-error. In this paper, we develop a strategy for automatically choosing a dictionary by a novel learning approach. We utilize a non-linear constrained optimization problem to determine best-fitting RBFs (Abel–Poisson kernels). For this, we use the Ipopt software package with an HSL subroutine. Details of the algorithm are explained and first numerical results are shown.

The experiment on tying the relative gravity measurements at sea to the values of the gravitational field model is described. It is shown that under the appropriate conditions, tying the marine measurements to the model can be applied instead of tying them to land stations.

In this paper, firstly, the new combined error model of cumulative geoid height influenced by three error sources including the inter‐satellite range‐rate of K‐band ranging system, orbital position of GPS receiver and non‐conservative force of accelerometer from GRACE satellites is established using the semi‐analytical method. Secondly, the dependability of error models is demonstrated based on matching relationship among the accuracy indexes of key payloads. Finally, the accuracy of global gravitational field up to degree and order 120 is effectively and rapidly estimated from GRACE Level 1B measured observation errors of the year 2006 publicized by the Jet Propulsion Laboratory (JPL) in the USA, and the cumulative geoid height error is 18.368 cm at degree 120, which preferably accords with the Earth's gravitational field model EIGEN‐GRACE02S provided by the Geo‐ForschungsZentrum Potsdam (GFZ) in Germany. This work can provide theoretical foundation and calculational guarantee for the efficient and rapid estimation of the accuracy of high‐degree global gravitational field model in the future international satellite gravity measurement mission (e.g. GRACE Follow‐On, degree 360).

Simulating urban expansion by incorporating an integrated gravitational field model into a demand-driven random forest-cellular automata model

Construction of Earth's gravitational field model from CHAMP, GRACE and GOCE data

Modeling the urban landscape dynamics in a megalopolitan cluster area by incorporating a gravitational field model with cellular automata

We present a comprehensive numerical analysis of spherical, spheroidal, and ellipsoidal harmonic series for gravitational field modeling near small moderately irregular bodies, such as the Martian moons. The comparison of model performances for these bodies is less intuitive and distinct than for a highly irregular object, such as Eros. The harmonic series models are each associated with a distinct surface, i.e., the Brillouin sphere, spheroid, or ellipsoid, which separates the regions of convergence and possible divergence for the parent infinite series. In their convergence regions, the models are subject only to omission errors representing the residual field variations not accounted for by the finite degree expansions. In the regions inside their respective Brillouin surfaces, the models are susceptible to amplification of omission errors and possible divergence effects, where the latter can be discerned if the error increases with an increase in the maximum degree of the model. We test the harmonic series models on the Martian moons, Phobos and Deimos, with moderate oblateness of $$<$$ 0.4. The possible divergence effects and amplified omission errors of the models are illustrated and quantified. The three models yield consistent results on a bounding sphere of Phobos in their common convergence region, with relative errors in potential of $$\sim $$ 0.01 and $$\sim $$ 0.001 % for expansions up to degree 10 and degree 20 respectively. On the surface of Phobos, the spherical and spheroidal models up to degree 10 both have maximum relative errors of $$\sim $$ 1 % in potential and $$\sim $$ 100 % in acceleration due ostensibly to divergence effect. Their performances deteriorate more severely on the more irregular Deimos. The ellipsoidal model exhibits much less distinct divergence behavior and proves more reliable in modeling both potential and acceleration, with respective maximum relative errors of $$\sim $$ 1 and $$\sim $$ 10 %, on both bodies. Our results show that for the Martian moons and other such moderately irregular bodies, the ellipsoidal harmonic series should be considered preferentially for gravitational field modeling.