Influence of the Choice of Lunar Gravity Model on Orbit Determination for Lunar Orbiters

We examine the influence of the lunar gravity model on the orbit determination (OD) of a lunar orbiter operating in a 100 km high, lunar polar orbit. Doppler and sequential range measurements by three Deep Space Network antennas and one Korea Deep Space Antenna were used. For measurement simulation and OD analysis, STK11 and ODTK6 were utilized. GLGM2, LP100K, LP150Q, GRAIL420A, and GRAIL660B were used for investigation of lunar gravity model selection effect. OD results were assessed by position and velocity uncertainties with error covariance and an external orbit comparison using simulated true orbit. The effect of the lunar gravity models on the long-term OD, degree and order level, measurement-acquisition condition, and lunar altitude was investigated. For efficiency verification, computational times for the five lunar gravity models were compared. Results showed that significant improvements to OD accuracy are observed by applying a GRAIL-based model; however, applying a full order and degree gravity modeling is not always the best strategy, owing to the computational burden. Consequently, we consider that OD using GRAIL660B with 70 × 70 degree and order is the most efficient strategy for mission preanalysis. This study provides useful guideline for KPLO OD analysis during nominal mission operation.

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THE GRAVITY MODEL FORMALIZATION FOR THE INTERCITY PASSENGER’S CORRESPONDENCES PARAMETER’S ESTIMATION

Science & Technique ◽

10.21122/2227-1031-2017-16-5-437-443 ◽

2017 ◽

Vol 16 (5) ◽

pp. 437-443 ◽

Cited By ~ 2

Author(s):

C. V. Dolya

Keyword(s):

Gravity Model ◽

Transportation System ◽

Gravity Models ◽

Gravity Modeling ◽

Passenger Transport ◽

Passenger Transportation ◽

The Given ◽

Selection Of ◽

Calibration Coefficients

he paper considers a possibility to apply gravity models for calculation of intercity passenger transport corres- pondences which are implemented with the help of public transport. The Ukraine transportation system has been selected as an object of investigation and this approach extends application possibilities of the obtained results. Calibration coefficients used in calculation of the indicated correspondences are rather important and significant in case of forecasting passenger transport correspondences. Formalization of these factors is necessary for every transportation system if a calculation of pas-senger transport correspondences has been made for it. In this case searching for actual calibration parameters and other coef-ficients as components of gravitational models is a relevant objective of the given paper. Selection of the gravity model va- riant plays rather significant role in solution of this problem. The developed methods for calculation of passenger transport correspondences are proposed for their application in respect of various transport and trip types. The executed research works have made it possible to investigate a process pertaining to providing of services for passenger transportation while using public routes. The obtained characteristics on functioning of the studied system have allowed to assess the possibility for ap-plication of the known methods for calculation of passenger correspondences and analyze the quality of their application. Calibration coefficients have been empirically selected for calculation of the indicated correspondences while using method of gravity modeling. Formalization of previously unexplored parameters of gravity model component provides the possibility to apply the considered approach for calculation of passenger correspondences within the framework of the investigated trans-portion system. This makes it possible to plan and arrange interaction of various transport types and provides new data and knowledge on the studied system.

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Orbit determination for Chang’E-2 lunar probe and evaluation of lunar gravity models

Science China Physics Mechanics and Astronomy ◽

10.1007/s11433-011-4596-2 ◽

2012 ◽

Vol 55 (3) ◽

pp. 514-522 ◽

Cited By ~ 20

Author(s):

PeiJia Li ◽

XiaoGong Hu ◽

Yong Huang ◽

GuangLi Wang ◽

DongRong Jiang ◽

...

Keyword(s):

Orbit Determination ◽

Gravity Models ◽

Lunar Gravity

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The improvements of Chang’E series satellites orbit determination from GRAIL lunar gravity model

SCIENTIA SINICA Physica, Mechanica & Astronomica ◽

10.1360/sspma2016-00320 ◽

2017 ◽

Vol 47 (6) ◽

pp. 069502

Author(s):

JianFeng DUAN ◽

JianFeng CAO ◽

Ming CHEN ◽

Yu ZHANG

Keyword(s):

Gravity Model ◽

Orbit Determination ◽

Lunar Gravity

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Effect of lunar gravity models on Chang'E-2 orbit determination using VLBI tracking data

Geodesy and Geodynamics ◽

10.1016/j.geog.2016.09.001 ◽

2016 ◽

Vol 7 (6) ◽

pp. 406-415

Author(s):

Erhu Wei ◽

Xuechuan Li ◽

Shuanggen Jin ◽

Jingnan Liu

Keyword(s):

Orbit Determination ◽

Gravity Models ◽

Tracking Data ◽

Lunar Gravity

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Randomness in modified general relativity theory: The stochastic f(R) gravity model

Canadian Journal of Physics ◽

10.1139/cjp-2017-0938 ◽

2018 ◽

Vol 96 (11) ◽

pp. 1173-1177

Author(s):

Tomer Shushi

Keyword(s):

Gravity Field ◽

Gravity Model ◽

Gravity Models ◽

Relativity Theory ◽

Field Equations ◽

Important Special Case ◽

Proposed Model ◽

Stochastic Space ◽

Wavefunction Collapse ◽

New Interpretation

We consider a stochastic modification of the f(R) gravity models, and provide its important properties, including the gravity field equations for the model. We show a prediction in which particles are localized by a system of random gravitational potentials. As an important special case, we investigate a gravity model in the presence of a small stochastic space–time perturbation and provide its gravity field equations. Using the proposed model we examine the stochastic quantum mechanics interpretation, and obtain a novel Schrödinger equation with gravitational potential that is based on diffusion in a gravitational field. Furthermore, we provide a new interpretation to the wavefunction collapse. It seems that the stochastic f(R) gravity model causes decoherence of the spatial superposition state of particles.

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A fast quadrature-based gravity model for the homogeneous polyhedron

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3461 ◽

2019 ◽

Vol 492 (1) ◽

pp. 420-430

Author(s):

Jason M Pearl ◽

Darren L Hitt

Keyword(s):

Gravitational Field ◽

Gravity Model ◽

Approximate Model ◽

Edge Length ◽

Gravity Models ◽

Surface Topology ◽

Constant Density ◽

Bulk Properties ◽

Average Edge Length ◽

Computationally Expensive

ABSTRACT To date several probes have been sent to explore the Solar system’s asteroids and comets. These bodies are often irregular in shape and to safely navigate probes in their vicinity accurate gravity models are required. For an arbitrarily shaped constant-density body, the gravitational field can be determined from the surface topology and bulk properties. This is achieved by replacing the body’s true geometry with a polyhedron that closely resembles it and for which analytic equations for the gravitational field exist. For some applications however, these equations are too computationally expensive and it can be beneficial to replace them with numerically amenable approximations. In this work, a numerical-quadrature-based model for the gravitational field of a polyhedron consisting of triangular facets is derived. The proposed approximate model is found to be faster than its analytic counterpart. The error of the approximation is found to be negligible for the potential and Laplacian calculations. The approximate model introduces singularities to the surface of the acceleration calculation degrading the solution at altitudes less than the average edge length of the polyhedron.

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Crustal structure of the offshore Labrador margin into deep water from combined seismic reflection interpretation and gravity modeling

Interpretation ◽

10.1190/int-2019-0068.1 ◽

2020 ◽

Vol 8 (2) ◽

pp. SH1-SH17 ◽

Cited By ~ 1

Author(s):

J. Kim Welford ◽

Deric Cameron ◽

Erin Gillis ◽

Victoria Mitchell ◽

Richard Wright

Keyword(s):

Late Cretaceous ◽

Seismic Reflection ◽

Gravity Data ◽

Gravity Models ◽

Gravity Modeling ◽

Data Set ◽

Shelf Slope ◽

Gravity Forward Modeling ◽

Thickness Variations ◽

Similar Density

A regional long-offset 2D seismic reflection program undertaken along the Labrador margin of the Labrador Sea, Canada, and complemented by the acquisition of coincident gravity data, has provided an extensive data set with which to image and model the sparsely investigated outer shelf, slope, and deepwater regions. Previous interpretation of the seismic data revealed the extent of Mesozoic and Cenozoic basins and resulted in the remapping of the basin configuration for the entire margin. To map the synrift package and improve understanding of the geometry and extent of these basins, we have undertaken joint seismic interpretation and gravity forward modeling to reduce uncertainty in the identification of the prerift basement, which varies between Paleozoic shelfal deposits and Precambrian crystalline rocks, with similar density characteristics. With this iterative approach, we have obtained new depth to basement constraints and have deduced further constraints on crustal thickness variations along the Labrador margin. At the crustal scale, extreme localized crustal thinning has been revealed along the southern and central portions of the Labrador margin, whereas a broad, margin-parallel zone of thicker crust has been detected outboard of the continental shelf along the northern Labrador margin. Our final gravity models suggest that Late Cretaceous rift packages from further south extend along the entire Labrador margin and open the possibility of a Late Cretaceous source rock fairway extending into the Labrador basins.

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A new f(R) gravity model and properties of gravitational waves in it

The European Physical Journal C ◽

10.1140/epjc/s10052-020-08684-3 ◽

2020 ◽

Vol 80 (12) ◽

Author(s):

Dhruba Jyoti Gogoi ◽

Umananda Dev Goswami

Keyword(s):

Gravitational Waves ◽

Gravity Model ◽

Longitudinal Mode ◽

Mass Scale ◽

Gravity Models ◽

Jordan Frame ◽

New Model ◽

Existing Problems ◽

Pulsar Timing ◽

New Directions

AbstractIn this paper, we have introduced a new f(R) gravity model as an attempt to have a model with more parametric control, so that the model can be used to explain the existing problems as well as to explore new directions in physics of gravity, by properly constraining it with recent observational data. Here basic aim is to study the properties of Gravitational Waves (GWs) in this new model. In f(R) gravity metric formalism, the model shows the existence of scalar degree of freedom as like other f(R) gravity models. Due to this reason, there is a scalar mode of polarization of GWs present in the theory. This polarization mode exists in a mixed state, of which one is transverse massless breathing mode with non-vanishing trace and the other is massive longitudinal mode. The longitudinal mode being massive, travels at speed less than the usual tensor modes found in General Relativity (GR). Moreover, for a better understanding of the model, we have studied the potential and mass of scalar graviton in both Jordan frame and Einstein frame. This model can pass the solar system tests and can explain primordial and present dark energy. Also, we have put constraints on the model. It is found that the correlation function for the third mode of polarization under certain mass scale predicted by the model agrees well with the recent data of Pulsar Timing Arrays. It seems that this new model would be useful in dealing with different existing issues in the areas of astrophysics and cosmology.

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A Gravity-Based Food Flow Model to Identify the Source of Foodborne Disease Outbreaks

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph17020444 ◽

2020 ◽

Vol 17 (2) ◽

pp. 444 ◽

Cited By ~ 1

Author(s):

Tim Schlaich ◽

Abigail L. Horn ◽

Marcel Fuhrmann ◽

Hanno Friedrich

Keyword(s):

Gravity Model ◽

Food Supply ◽

Food Item ◽

Disease Outbreaks ◽

Gravity Models ◽

Shopping Behavior ◽

Foodborne Disease ◽

Inference Models ◽

Computational Approaches ◽

Home Location

Computational traceback methodologies are important tools for investigations of widespread foodborne disease outbreaks as they assist investigators to determine the causative outbreak location and food item. In modeling the entire food supply chain from farm to fork, however, these methodologies have paid little attention to consumer behavior and mobility, instead making the simplifying assumption that consumers shop in the area adjacent to their home location. This paper aims to fill this gap by introducing a gravity-based approach to model food-flows from supermarkets to consumers and demonstrating how models of consumer shopping behavior can be used to improve computational methodologies to infer the source of an outbreak of foodborne disease. To demonstrate our approach, we develop and calibrate a gravity model of German retail shopping behavior at the postal-code level. Modeling results show that on average about 70 percent of all groceries are sourced from non-home zip codes. The value of considering shopping behavior in computational approaches for inferring the source of an outbreak is illustrated through an application example to identify a retail brand source of an outbreak. We demonstrate a significant increase in the accuracy of a network-theoretic source estimator for the outbreak source when the gravity model is included in the food supply network compared with the baseline case when contaminated individuals are assumed to shop only in their home location. Our approach illustrates how gravity models can enrich computational inference models for identifying the source (retail brand, food item, location) of an outbreak of foodborne disease. More broadly, results show how gravity models can contribute to computational approaches to model consumer shopping interactions relating to retail food environments, nutrition, and public health.

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