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"Gravitational fields."
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Satellite Gravimetry: A Review of Its Realization
Since Kepler, Newton and Huygens in the seventeenth century, geodesy has been concerned with determining the figure, orientation and gravitational field of the Earth. With the beginning of the space age in 1957, a new branch of geodesy was created, satellite geodesy. Only with satellites did geodesy become truly global. Oceans were no longer obstacles and the Earth as a whole could be observed and measured in consistent series of measurements. Of particular interest is the determination of the spatial structures and finally the temporal changes of the Earth's gravitational field. The knowledge of the gravitational field represents the natural bridge to the study of the physics of the Earth's interior, the circulation of our oceans and, more recently, the climate. Today, key findings on climate change are derived from the temporal changes in the gravitational field: on ice mass loss in Greenland and Antarctica, sea level rise and generally on changes in the global water cycle. This has only become possible with dedicated gravity satellite missions opening a method known as satellite gravimetry. In the first forty years of space age, satellite gravimetry was based on the analysis of the orbital motion of satellites. Due to the uneven distribution of observatories over the globe, the initially inaccurate measuring methods and the inadequacies of the evaluation models, the reconstruction of global models of the Earth's gravitational field was a great challenge. The transition from passive satellites for gravity field determination to satellites equipped with special sensor technology, which was initiated in the last decade of the twentieth century, brought decisive progress. In the chronological sequence of the launch of such new satellites, the history, mission objectives and measuring principles of the missions CHAMP, GRACE and GOCE flown since 2000 are outlined and essential scientific results of the individual missions are highlighted. The special features of the GRACE Follow-On Mission, which was launched in 2018, and the plans for a next generation of gravity field missions are also discussed.
Journal Article
Gravity Field and Internal Structure of Mercury from MESSENGER
Radio tracking of the MESSENGER spacecraft has provided a model of Mercury's gravity field. In the northern hemisphere, several large gravity anomalies, including candidate mass concentrations (mascons), exceed 100 mi Hi-Galileos (mgal). Mercury's northern hemisphere crust is thicker at low latitudes and thinner in the polar region and shows evidence for thinning beneath some impact basins. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia CIMR² = 0.353 ± 0.017, where M and R are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of CJC = 0.452 ± 0.035. A model for Mercury's radial density distribution consistent with these results includes a solid silicate crust and mantle overlying a solid iron-sulfide layer and an iron-rich liquid outer core and perhaps a solid inner core.
Journal Article
The Tides of Titan
We have detected in Cassini spacecraft data the signature of the periodic tidal stresses within Titan, driven by the eccentricity (e = 0.028) of its 16-day orbit around Saturn. Precise measurements of the acceleration of Cassini during six close flybys between 2006 and 2011 have revealed that Titan responds to the variable tidal field exerted by Saturn with periodic changes of its quadrupole gravity, at about 4% of the static value. Two independent determinations of the corresponding degree-2 Love number yield k 2 = 0.589 ± 0.150 and k 2 = 0.637 ± 0.224 (2σ). Such a large response to the tidal field requires that Titan's interior be deformable over time scales of the orbital period, in a way that is consistent with a global ocean at depth.
Journal Article
Dynamical response of Bose-Einstein condensates to oscillating gravitational fields
A description of the dynamical response of uniformly trapped Bose-Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime.
Journal Article
Fixed-Magnetization Ising Model with a Slowly Varying Magnetic Field
The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is seen as a particular instance of an Ising model with a slowly varying magnetic field in the fixed magnetization ensemble. We first characterize the typical magnetization profiles in the regime in which the contribution of the magnetic field competes with the bulk energy term. We then discuss in more detail the particular case of a gravitational field and the arising interfacial phenomena. In particular, we identify the macroscopic profile and propose several conjectures concerning the interface appearing in the phase coexistence regime. The latter are supported by explicit computations in an effective model. Finally, we state some conjectures concerning equilibrium crystal shapes in the presence of a gravitational field, when the latter contributes to the energy only to surface order.
Journal Article
Recursive Analytical Formulae of Gravitational Fields and Gradient Tensors for Polyhedral Bodies with Polynomial Density Contrasts of Arbitrary Non-negative Integer Orders
Exact computation of the gravitational field and gravitational gradient tensor for a general mass body is a core routine to model the density structure of the Earth. In this study, we report on the existence of closed-form solutions of the gravitational potential, gravitational field and gravitational gradient tensor for a general polyhedral mass body with a polynomial density function of arbitrary non-negative integer orders that can simultaneously vary in both horizontal and vertical directions. Our closed-form solutions of the gravitational potential and the gravitational field are singularity-free, which implies that the observation sites can have arbitrary geometric relationships with polyhedral mass source bodies. However, weak logarithmic singularities exist on the edges of polyhedra for the gravitational gradient tensor. A simple prismatic mass body with polynomial density contrast varying in the vertical direction and a complicated dodecahedral mass body with quartic-order density contrasts were tested to verify the accuracy of the newly derived closed-form solutions. For the gravitational potential, gravitational fields and gradient tensors, our closed-form solutions are in excellent agreement with previously published analytical solutions and Gaussian numerical quadrature solutions.
Journal Article
Information Storage in a Black Hole’s Gravitational Field
The key to resolving the black hole information loss paradox lies in clarifying the origin of black hole entropy and the mechanism by which black holes store information. By applying thermodynamic principles, we demonstrate that the entropy of a gravitational field is negative and proportional to the strength of the field, indicating that gravitational fields possess information storage capacity. For Schwarzschild black holes, we further demonstrate that information conventionally attributed to the black hole’s interior is in fact encoded within its external gravitational field. During black hole evaporation, the emitted particles transmit this information via gravitational correlations. This study advances our understanding of gravitational field entropy and provides valuable insights toward resolving the black hole information loss problem.
Journal Article
Modeling and stability analysis of a tethered asteroid probe system based on multi flexible body dynamics
The tethered asteroid probe system refers to a method of connecting a probe to an asteroid using a tether. This system allows the probe to hover near the asteroid’s surface without consuming fuel, making it valuable for conducting high-precision exploration, sampling, and other exploration tasks. However, various physical characteristics, such as the tether length, flexibility, gravity, internal tension, and the initial velocity state of the probe, affect the probe’s hovering position and stability. In this article, the dynamic model and stability of tether probes near irregular asteroids are investigated. By considering the mass and elasticity of the tether, a multi-flexible body dynamic equation is established to describe the behavior of the probe and tether under the influence of the gravitational field of the asteroid. Dynamic equations can describe the dynamical response of the probe when switching between the tensed and relaxed states. Moreover, the changes in the position and stability of the stable range caused by the tether are analyzed. The findings suggest that connecting the probe to the asteroid through tethers significantly expands the stable operation range of the probe. The length of the tether and the amplitude of the tension significantly impact the dynamic characteristics of the probe and the stable range. Additionally, compared with the assumption that the tether is assumed to be massless and rigid, the initial range in which the tethered system can be stable is significantly reduced. Hence, the influence of the tether mass, elasticity, and damping should not be overlooked. The research presented in this article holds great significance for asteroid proximity exploration and sampling tasks that utilize tether systems. By understanding the dynamics and stability of tethered probes near irregular asteroids, human capabilities in exploring and studying these celestial bodies can be enhanced.
Journal Article
Tachyonic Field Coupled with Global Monopole
As the early universe expanded, phase transitions occurred which resulted in the formation of different types of topological defects. Specifically, the self-coupling scalar field triplet
ϕ
a
was responsible for the creation of global monopoles, which are massive objects that arise during these phase transitions. The initial global symmetry of
O
(3) undergoes a process of spontaneous breaking, resulting in U(1) symmetry. In this paper we describe a model of global monopole consisting of the Higgs triplet of scalar fields with Tachyonic fluid described by the relativistic Lagrangian
L
Tach
=
-
V
(
ϕ
a
)
1
+
g
μ
ν
∂
μ
ϕ
a
∂
ν
ϕ
a
. In the weak field approximation, we were able to discover the solution for the scalar field and space-time produced by the global monopole and the Einstein equation that emerges from these scenario exhibits a high degree of non-linearity. Our investigation focused on determining whether the global monopole produces gravitational pull on a test particle that is in motion within its spacetime. Finally, we have calculated the bending of light due to gravitational field of this global monopole.
Journal Article