scholarly journals A new formulation of Stokes’ approach in determining the global gravimetric geoid

2013 ◽  
Vol 56 (3) ◽  
Author(s):  
Wen-Bin Shen
Keyword(s):  
Potential Function ◽  
Normal Gravity ◽  
Major Axis ◽  
Gravity Potential ◽  
Semi Major Axis ◽  
Disturbing Potential ◽  
Fundamental Parameters ◽  
Ellipsoidal Surface ◽  
New Formulation ◽  
Two Parameters

<p>According to Stokes’ approach, given the gravity anomaly on the geoid as the boundary, a disturbing potential function satisfying some boundary conditions should be solved. The basic requirement is that the disturbing potential function should be harmonic in the region outside the geoid. However, since the normal gravity potential is not defined inside the reference ellipsoid (taking the WGS84 ellipsoid as an example), when the geoid is below the ellipsoidal surface, the disturbing potential function is not harmonic in the whole region outside the geoid, and is not defined on the whole geoid itself. These are theoretical difficulties in Stokes’ approach. To remove these difficulties from Stokes’ approach, this study provides a new formulation of Stokes’ approach. An inner ellipsoid with four fundamental parameters is chosen, two of which, the geocentric gravitational constant and the rotational angular velocity, coincide with the corresponding parameters of the WGS84 ellipsoid. The other two parameters, the semi-major axis and flattening, are different from the corresponding ones of the ellipsoid. Then, the normal gravity potential generated by the inner ellipsoid is determined, by requiring that it holds a constant on the surface of the inner ellipsoid or on the surface of the ellipsoid. With this new formulation, the disturbing potential function is harmonic in the whole region outside the geoid, and the difficulties in Stokes’ approach disappear. The new formulation proposed in this study is also adequate for analogous geodetic boundary-value problems.</p>

Subtleties in spherical harmonic synthesis of the gravity field

2020 ◽  
Author(s):  
Ropesh Goyal ◽  
Sten Claessens ◽  
Will Featherstone ◽  
Onkar Dikshit
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Gravitational Constant ◽  
Angular Rate ◽  
Physical Geodesy ◽  
Major Axis ◽  
Gravity Potential ◽  
Semi Major Axis ◽  
The Earth ◽  
Spherical Harmonic Synthesis

&lt;p&gt;Spherical harmonic synthesis (SHS) can be used to compute various gravity functions (e.g., geoid undulations, height anomalies, deflections of vertical, gravity disturbances, gravity anomalies, etc.) using the 4pi fully normalised Stokes coefficients from the many freely available Global Geopotential Models (GGMs). &amp;#160;This requires a normal ellipsoid and its gravity field, which are defined by four parameters comprising (i) the second-degree even zonal Stokes coefficient (J2) (aka dynamic form factor), (ii) the product of the mass of the Earth and universal gravitational constant (GM) (aka geocentric gravitational constant), (iii) the Earth&amp;#8217;s angular rate of rotation (&amp;#969;), and (iv) the length of the semi-major axis (a). GGMs are also accompanied by numerical values for GM and a, which are not necessarily identical to those of the normal ellipsoid.&amp;#160; In addition, the value of W&lt;sub&gt;0,&lt;/sub&gt; the potential of the geoid from a GGM, needs to be defined for the SHS of many gravity functions. W&lt;sub&gt;0&lt;/sub&gt; may not be identical to U&lt;sub&gt;0&lt;/sub&gt;, the potential on the surface of the normal ellipsoid, which follows from the four defining parameters of the normal ellipsoid.&amp;#160; If W&lt;sub&gt;0&lt;/sub&gt; and U&lt;sub&gt;0&lt;/sub&gt; are equal and if the normal ellipsoid and GGM use the same value for GM, then some terms cancel when computing the disturbing gravity potential.&amp;#160; However, this is not always the case, which results in a zero-degree term (bias) when the masses and potentials are different. &amp;#160;There is also a latitude-dependent term when the geometries of the GGM and normal ellipsoids differ.&amp;#160; We demonstrate these effects for some GGMs, some values of W&lt;sub&gt;0&lt;/sub&gt;, and the GRS80, WGS84 and TOPEX/Poseidon ellipsoids and comment on its omission from some public domain codes and services (isGraflab.m, harmonic_synth.f and ICGEM).&amp;#160; In terms of geoid heights, the effect of neglecting these parameters can reach nearly one metre, which is significant when one goal of modern physical geodesy is to compute the geoid with centimetric accuracy.&amp;#160; It is also important to clarify these effects for all (non-specialist) users of GGMs.&lt;/p&gt;

Detection and Characterization of earth-like Planets

1997 ◽  
Vol 161 ◽  
pp. 299-311 ◽  
Author(s):  
Jean Marie Mariotti ◽  
Alain Léger ◽  
Bertrand Mennesson ◽  
Marc Ollivier
Keyword(s):  
Direct Detection ◽  
Contrast Ratio ◽  
Angular Size ◽  
Physical Nature ◽  
Major Axis ◽  
Infrared Emission ◽  
Space Technology ◽  
Semi Major Axis ◽  
Earth Like Planets ◽  
Visible Wavelengths

AbstractIndirect methods of detection of exo-planets (by radial velocity, astrometry, occultations,...) have revealed recently the first cases of exo-planets, and will in the near future expand our knowledge of these systems. They will provide statistical informations on the dynamical parameters: semi-major axis, eccentricities, inclinations,... But the physical nature of these planets will remain mostly unknown. Only for the larger ones (exo-Jupiters), an estimate of the mass will be accessible. To characterize in more details Earth-like exo-planets, direct detection (i.e., direct observation of photons from the planet) is required. This is a much more challenging observational program. The exo-planets are extremely faint with respect to their star: the contrast ratio is about 10−10at visible wavelengths. Also the angular size of the apparent orbit is small, typically 0.1 second of arc. While the first point calls for observations in the infrared (where the contrast goes up to 10−7) and with a coronograph, the latter implies using an interferometer. Several space projects combining these techniques have been recently proposed. They aim at surveying a few hundreds of nearby single solar-like stars in search for Earth-like planets, and at performing a low resolution spectroscopic analysis of their infrared emission in order to reveal the presence in the atmosphere of the planet of CO H2O and O3. The latter is a good tracer of the presence of oxygen which could be, like on our Earth, released by biological activity. Although extremely ambitious, these projects could be realized using space technology either already available or in development for others missions. They could be built and launched during the first decades on the next century.

scholarly journals Some Special Types of Orbits around Jupiter

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 183
Author(s):  
Yongjie Liu ◽  
Yu Jiang ◽  
Hengnian Li ◽  
Hui Zhang
Keyword(s):  
Gravity Model ◽  
Small Perturbation ◽  
Equilibrium Points ◽  
Major Axis ◽  
Semi Major Axis ◽  
Ground Track ◽  
The Earth ◽  
Degenerate Equilibrium ◽  
The Mean ◽  
Element Theory

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

scholarly journals Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis

2021 ◽  
Author(s):  
Jérôme Daquin ◽  
Elisa Maria Alessi ◽  
Joseph O’Leary ◽  
Anne Lemaitre ◽  
Alberto Buzzoni
Keyword(s):  
Major Axis ◽  
Long Term Evolution ◽  
Semi Major Axis ◽  
Satellite Constellation ◽  
Term Evolution ◽  
Dynamical Properties

scholarly journals The surface layer integral method for the modelling of the radial gravity gradient component over sea surface

2019 ◽  
Vol 9 (1) ◽  
pp. 127-132
Author(s):  
D. Zhao ◽  
Z. Gong ◽  
J. Feng
Keyword(s):  
Surface Layer ◽  
Integral Method ◽  
Integral Formula ◽  
Radial Component ◽  
Second Order ◽  
Sea Surface ◽  
Gravity Potential ◽  
Gravity Gradient ◽  
Disturbing Potential ◽  
Gradient Component

Abstract For the modelling and determination of the Earth’s external gravity potential as well as its second-order radial derivatives in the space near sea surface, the surface layer integral method was discussed in the paper. The reasons for the applicability of the method over sea surface were discussed. From the original integral formula of disturbing potential based on the surface layer method, the expression of the radial component of the gravity gradient tensor was derived. Furthermore, an identity relation was introduced to modify the formula in order to reduce the singularity problem. Numerical experiments carried out over the marine area of China show that, the modi-fied surface layer integral method effectively improves the accuracy and reliability of the calculation of the second-order radial gradient component of the disturbing potential near sea surface.

scholarly journals Creation/destruction of ultra-wide binaries in tidal streams

2020 ◽  
Author(s):  
Jorge Peñarrubia
Keyword(s):  
Globular Clusters ◽  
Galactic Halo ◽  
Local Density ◽  
Formation Rate ◽  
Semimajor Axis ◽  
Major Axis ◽  
Binding Energies ◽  
Semi Major Axis ◽  
The Mean ◽  
Tidal Streams

Abstract This paper uses statistical and N-body methods to explore a new mechanism to form binary stars with extremely large separations (≳ 0.1 pc), whose origin is poorly understood. Here, ultra-wide binaries arise via chance entrapment of unrelated stars in tidal streams of disrupting clusters. It is shown that (i) the formation of ultra-wide binaries is not limited to the lifetime of a cluster, but continues after the progenitor is fully disrupted, (ii) the formation rate is proportional to the local phase-space density of the tidal tails, (iii) the semimajor axis distribution scales as p(a)da ∼ a1/2da at a ≪ D, where D is the mean interstellar distance, and (vi) the eccentricity distribution is close to thermal, p(e)de = 2ede. Owing to their low binding energies, ultra-wide binaries can be disrupted by both the smooth tidal field and passing substructures. The time-scale on which tidal fluctuations dominate over the mean field is inversely proportional to the local density of compact substructures. Monte-Carlo experiments show that binaries subject to tidal evaporation follow p(a)da ∼ a−1da at a ≳ apeak, known as Öpik’s law, with a peak semi-major axis that contracts with time as apeak ∼ t−3/4. In contrast, a smooth Galactic potential introduces a sharp truncation at the tidal radius, p(a) ∼ 0 at a ≳ rt. The scaling relations of young clusters suggest that most ultra-wide binaries arise from the disruption of low-mass systems. Streams of globular clusters may be the birthplace of hundreds of ultra-wide binaries, making them ideal laboratories to probe clumpiness in the Galactic halo.

EFFECTS OF INITIAL INHOMOGENEOUS DENSITY DISTRIBUTION AND VOID SHAPE ON POWDER FORGING OF POROUS METAL

2013 ◽  
Vol 27 (19) ◽  
pp. 1341008
Author(s):  
TAIQING DENG ◽  
LIANXI HU ◽  
YU SUN ◽  
XIAOYA LIU
Keyword(s):  
Density Distribution ◽  
Initial Density ◽  
Porous Metal ◽  
Major Axis ◽  
Average Density ◽  
Semi Major Axis ◽  
Punch Force ◽  
Inhomogeneous Density ◽  
Void Shape ◽  
Initial Density Distribution

The deformation behavior during axisymmetric upsetting of sintered metals has been studied based on the finite-element method. The investigation on the effects of the initial density distribution, void shape and die friction on the density distribution and punch force during deformation have been conducted. It was found that under low-friction conditions, the initial density distribution affects the deformation geometry and the density distribution. However, the effect of the initial density distribution was found to be negligible under high-friction conditions. The initial density distribution did not affect the punch force or the average density, regardless of the friction conditions. When the force is perpendicular to semi-major axis of elliptical void, it is not only good for densification but also decrease the punch force in forging of porous metal.

Design, Modeling, and Experimental Drag Characterization of a Bio-Inspired, Shape-Adapting Underwater Vehicle

2018 ◽  
Author(s):  
Levi D. DeVries ◽  
Michael D. M. Kutzer ◽  
Rebecca E. Richmond ◽  
Archie C. Bass
Keyword(s):  
Spatial Scales ◽  
Autonomous Underwater Vehicles ◽  
Major Axis ◽  
Underwater Vehicle ◽  
Great Promise ◽  
Hydrodynamic Drag ◽  
Control Input ◽  
Semi Major Axis ◽  
Generative Modeling

Autonomous underwater vehicles (AUVs) have shown great promise in fulfilling surveillance, scavenging, and monitoring tasks, but can be hindered in expansive, cluttered or obstacle ridden environments. Traditional gliders and streamlined AUVs are designed for long term operational efficiency in expansive environments, but are hindered in cluttered spaces due to their shape and control authority; agile AUVs can penetrate cluttered or sensitive environments but are limited in operational endurance at large spatial scales. This paper presents the prototype testbed design, modeling, and experimental hydrodynamic drag characterization of a novel self-propelled underwater vehicle capable of actuating its shape morphology. The vehicle prototype incorporates flexible, buckled fiberglass ribs to ensure a rigid shape that can be actuated by modulating the length of the semi-major axis. Tools from generative modeling are used to represent the vehicle shape by using a single control input actuating the vehicles length-to-diameter ratio. By actuating the length and width characteristics of the vehicle’s shape to produce a desired drag profile, we derive the feasible speeds achievable by shape actuation control. Tow-tank experiments with an experimental proto-type suggest shape actuation can be used to manipulate the drag by a factor between 2.15 and 5.8 depending on the vehicle’s operating speed.

scholarly journals Determining the AMSR-E SST Footprint from Co-located MODIS SSTs

2018 ◽  
Author(s):  
Brahim Boussidi ◽  
Peter Cornillon ◽  
Gavino Puggioni ◽  
Chelle Gentemann
Keyword(s):  
Aspect Ratio ◽  
Ground Truth ◽  
Major Axis ◽  
Sampling Procedure ◽  
Least Square ◽  
Gaussian Kernel ◽  
Bootstrap Sampling ◽  
Semi Major Axis ◽  
Linear Inversion ◽  
Precise Knowledge

This study was undertaken to derive and analyze the Advanced Microwave Scanning Radiometer - EOS (AMSR-E) sea surface temperature (SST) footprint associated with the Remote Sensing Systems (RSS) Level-2 (L2) product. The footprint, in this case, is characterized by the weight attributed to each 4 4 km square contributing to the SST value of a given AMSR-E pixel. High-resolution L2 SST fields obtained from the MODerate-resolution Imaging Spectroradiometer (MODIS), carried on the same spacecraft as AMSR-E, are used as the sub-resolution &ldquo;ground truth&ldquo; from which the AMSR-E footprint is determined. Mathematically, the approach is equivalent to a linear inversion problem, and its solution is pursued by means of a constrained least square approximation based on the bootstrap sampling procedure. The method yielded an elliptic-like Gaussian kernel with an aspect ratio 1.58, very close to the AMSR-E 6.93GHz channel aspect ratio, 1.7. (The 6.93GHz channel is the primary spectral frequency used to determine SST.) The semi-major axis of the estimated footprint is found to be alignedwith the instantaneous field-of-view of the sensor as expected fromthe geometric characteristics of AMSR-E. Footprintswere also analyzed year-by-year and as a function of latitude and found to be stable &ndash; no dependence on latitude or on time. Precise knowledge of the footprint is central for any satellite-derived product characterization and, in particular, for efforts to deconvolve the heavily oversampled AMSR-E SST fields and for studies devoted to product validation and comparison. A preliminarly analysis suggests that use of the derived footprint will reduce the variance between AMSR-E and MODIS fields compared to the results obtained.

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