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1.
Position and velocity perturbations for the determination of geopotential from space geodetic measurements 总被引：10，自引：0，他引：10
Peiliang Xu 《Celestial Mechanics and Dynamical Astronomy》2008,100(3):231-249
Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting
(LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods
for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based
method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable
mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical
integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite
gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In
order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology
for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the
corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order
approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values,
our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In
particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and
resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform
the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly
outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic
measurements for the determination of geopotential. 相似文献
2.
We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines”
such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that
the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small
size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn.
For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces
accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions
we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic
solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions
and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric
periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation
which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their
stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families
of three dimensional symmetric periodic orbits. 相似文献
3.
The first aim of the present work is to compute a more accurate and recent model for the Earth’s magnetic field. The second
aim is to determine the effects of the Earth’s magnetic field on the motion of a charged artificial satellite to evaluate
the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time
have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential
field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow
the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results
concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1
satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis. 相似文献
4.
The possibility of using a trap with ultracold neutrons as a detector of dark matter particles with long-range forces is considered.
The main advantage of the proposed method lies in the possibility of detecting a recoil energy of ∼10−7 eV. Constraints on the parameters of an interaction potential of the form φ (r) = ae
−r/b
/r between dark matter particles and a neutron are presented at various dark matter densities on Earth. The assumption about
the long-range interaction of dark matter particles and ordinary matter is shown to lead to a significant increase in the
elastic scattering cross section at low energies. As a consequence, it becomes possible to capture and accumulate dark matter
in the Earth’s gravitational field. The accumulated dark matter in the Earth’s gravitational field is roughly estimated. The
first experimental constraints on the existence of dark matter with long-range forces on Earth are presented. 相似文献
5.
B.A. Conway 《Icarus》1982,51(3):610-622
A frequency-dependent model of tidal friction is used in the determination of the time rate of change of the lunar orbital elements and the angular velocity of the Earth. The variational equations consider eccentricity, the solar tide on the Earth, Earth oblateness, and higher-order terms in the Earth's tidal potential. A linearized solution of the equations governing the precission of the Earth's rotational angular momentum and the lunar ascending node is found. This allows the analytical averaging of the variational equations over the period of relative precession which, though large, is necessarily small in comparison to the time step of the numerical integrator that yields the system history over geological time. Results for this history are presented and are identified as consistent with origin of the Moon by capture. This model may be applied to any planet-satellite system where evolution under tidal friction is of interest. 相似文献
6.
Using trajectory calculations of cosmic rays in the geomagnetic field, the changes of vertical cutoff rigidities in the past
are discussed. The computations are done for selected positions at the Earth’s surface using the IGRF model data for 1900–2000.
The contour maps of vertical cutoff rigidities using the set of ten Gauss coefficients for the period of years between 0 and
1600 are obtained. The trends in long-term variability of cutoffs at different positions on the Earth’s surface are described. 相似文献
7.
Based on some additional clarifications of the cosmological model of the formation of the Solar System it was shown that the
main source of the Earth’s energy are thermonuclear processes in the inner Earth’s core consisting of metallic hydrides. This
energy is quite significant, but it is substantially smaller (by about three orders of magnitude) than the energy received
from the Sun. The proposed hypothesis suggests a presence of hydrogen fluxes or deep fluids propagating from the Earth’s core
and transporting thermal energy from the thermonuclear reactions to the Earth’s surface. This energy has been a primary reason
for the endogenic, geodynamic and tectonic processes over the course of the Earth’s whole history. 相似文献
8.
Yuan Ren Pierpaolo Pergola Elena Fantino Bianca Thiere 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):1-21
Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon
system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular
restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific
transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered
the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use
of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body
model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute
the invariant tori and their manifolds in this dynamical model. 相似文献
9.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):169-217
Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δ
c, δ
i responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd for the angles of nutation θ and precession are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms. 相似文献
10.
G. Mingotti F. Topputo F. Bernelli-Zazzera 《Celestial Mechanics and Dynamical Astronomy》2011,110(2):169-188
In this paper novel Earth–Mars transfers are presented. These transfers exploit the natural dynamics of n-body models as well as the high specific impulse typical of low-thrust systems. The Moon-perturbed version of the Sun–Earth
problem is introduced to design ballistic escape orbits performing lunar gravity assists. The ballistic capture is designed
in the Sun–Mars system where special attainable sets are defined and used to handle the low-thrust control. The complete trajectory
is optimized in the full n-body problem which takes into account planets’ orbital inclinations and eccentricities. Accurate, efficient solutions with
reasonable flight times are presented and compared with known results. 相似文献
11.
12.
R.D. Schuiling 《Earth, Moon, and Planets》2006,99(1-4):33-49
In this paper we discuss the Herndon hypothesis that a nuclear reactor is operating at the center of the Earth. Recent experimental
evidence shows that some uranium can have partitioned into the core. There is no viable mechanism for the small amount of
uranium that is dissolved in the molten metal to crystallize as a separate uranium phase (uranium metal or uranium sulfide)
and migrate to the center of the core.
There is no need for an extra heat source, as the total heat leaving the core can be easily provided by “classical” heat sources,
which are also more than adequate to maintain the Earth’s magnetic field. It is unlikely that nuclear georeactors (fast breeder
reactors) are operating at the Earth’s center. 相似文献
13.
The relation between gravity anomalies, topography and volcanism can yield important insights about the internal dynamics of planets. From the power spectra of gravity and topography on Earth, Venus and Mars we infer that gravity anomalies have likely predominantly sources below the lithosphere up to about spherical harmonic degree l=30 for Earth, 40 for Venus and 5 for Mars. To interpret the low-degree part of the gravity spectrum in terms of possible sublithospheric density anomalies we derive radial mantle viscosity profiles consistent with mineral physics. For these viscosity profiles we then compute gravity and topography kernels, which indicate how much gravity anomaly and how much topography is caused by a density anomaly at a given depth. With these kernels, we firstly compute an expected gravity-topography ratio. Good agreement with the observed ratio indicates that for Venus, in contrast to Earth and Mars, long-wavelength topography is largely dynamically supported from the sublithospheric mantle. Secondly, we combine an empirical power spectrum of density anomalies inferred from seismic tomography in Earth’s mantle with gravity kernels to model the gravity power spectrum. We find a good match between modeled and observed gravity power spectrum for all three planets, except for 2?l?4 on Venus. Density anomalies in the Venusian mantle for these low degrees thus appear to be very small. We combine gravity kernels and the gravity field to derive radially averaged density anomaly models for the Martian and Venusian mantles. Gravity kernels for l?5 are very small on Venus below ≈800 km depth. Thus our inferences on Venusian mantle density are basically restricted to the upper 800 km. On Mars, gravity anomalies for 2?l?5 may originate from density anomalies anywhere within its mantle. For Mars as for Earth, inferred density anomalies are dominated by l=2 structure, but we cannot infer whether there are features in the lowermost mantle of Mars that correspond to Earth’s Large Low Shear Velocity Provinces (LLSVPs). We find that volcanism on Mars tends to occur primarily in regions above inferred low mantle density, but our model cannot distinguish whether or not there is a Martian analog for the finding that Earth’s Large Igneous Provinces mainly originate above the margins of LLSVPs. 相似文献
14.
Giovanni Federico Gronchi 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):301-326
Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of
preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to
take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized
theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s
limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s:
they may change according to the value of a parameter that depends on the observations. 相似文献
15.
We consider a model that describes the evolution of distant satellite orbits and that refines the solution of the doubly averaged
Hill problem. Generally speaking, such a refinement was performed previously by J. Kovalevsky and A.A. Orlov in terms of Zeipel’s
method by constructing a solution of the third order with respect to the small parameter m, the ratio of the mean motions of the planet and the satellite. The analytical solution suggested here differs from the solutions
obtained by these authors and is closest in form to the general solution of the doubly averaged problem (∼m
2). We have performed a qualitative analysis of the evolutionary equations and conditions for the intersection of satellite
orbits with the surface of a spherical planet with a finite radius. Using the suggested solution, we have obtained improved
analytical time dependences of the elements of evolving orbits for a number of distant satellites of giant planets compared
to the solution of the doubly averaged Hill problem and, thus, achieved their better agreement with the results of our numerical
integration of the rigorous equations of perturbed motion for satellites. 相似文献
16.
17.
A comparison of the internal structure of Earth-like planets is unavoidable to understand the formation and evolution of the solar system, and the differences between Earth’s, Mars’, and Venus’ atmospheres, surfaces and tectonic behaviors. Recent studies point at the role of core structure and dynamics in the evolution of the atmosphere, mantle and crust. On Earth, the crust thickness and the radius and physical state of the cores are known for almost one century, since the advent of seismological observations, but the lack of long-term surface-based geodetic, electromagnetic and seismological observations on the other planets, results in very large uncertainties on the crust thickness, on the temperature and composition of their mantle, and on the size and physical state of their cores. According to the currently available geodetic data, Mars’ dimensionless mean-moment-of-inertia ratio is equal to 0.3653±0.0008. When combined with geochemical observations and with the inputs of laboratory experiments on planetary materials at high pressure and high temperature, this result constrains a narrow range of density values for Mars’ mantle and favors a light [6200-6765 kg m−3] sulfur-rich core, but it still allows for a 1600-1750 km range for the core radius, i.e. an uncertainty at least ten times larger than the precision obtained in 1913 by Gutenberg for the Earth’s core. Mars’ mantle density distribution may be explained by a large range of temperatures and mineralogical compositions, either olivine- or pyroxene-rich. The unknown mean thickness of Mars’ crust makes necessary a number of working assumptions for the interpretation of gravimetric and magnetic data. The situation is worse for Venus, and the most conservative model of its deep interior is a transposition of the Earth’s structure scaled to Venus’ radius and mass. The temperature conditions at the surface of this planet hardly make possible long-term ground-based measurements, but this is indeed feasible at the surface of Mars. Precise measurements of Mars’ crust thickness, core radius and structure, and the proof of the existence or absence of an inner core, would put tight constraints on mantle dynamics and thermal evolution, and on possible scenarios leading to the extinction of Mars’ magnetic field about 4.0 Ga ago. Long-lasting surface-based geodetic, seismological and magnetic observations would provide this information, as well as the distributions as a function of depth of the density, elastic and anelastic parameters, and electrical conductivity. Current studies on the structure of Earth’s deep interior demonstrate that the latter data set, when constrained by laboratory experiments, may be inverted in terms of temperature, chemical, and mineralogical compositions. 相似文献
18.
This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and
at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit
radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points
is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand
differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal
direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the
transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the
two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees
closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an
Earth–Moon collinear libration point. 相似文献
19.
Evidence of asteroid surface features as regolith grains and larger boulders implies resurfacing possibility due to external
forces such as gravitational tidal force during close planet encounters. Motion of a meteoroid released from an asteroid in
the gravitational fields of the asteroid and the Earth is modeled. We are interested mainly in a distance between the meteoroid
and the asteroid as a function of the time. Applications to Itokawa and some close approaching NEAs are presented. 相似文献
20.
A second order atmospheric drag theory based on the usage of TD88 model is constructed. It is developed to the second order
in terms of TD88 small parameters K
n,j
. The short periodic perturbations, of all orbital elements, are evaluated. The secular perturbations of the semi-major axis
and of the eccentricity are obtained. The theory is applied to determine the lifetime of the satellites ROHINI (1980 62A),
and to predict the lifetime of the microsatellite MIMOSA. The secular perturbations of the nodal longitude and of the argument
of perigee due to the Earth’s gravity are taken into account up to the second order in Earth’s oblateness. 相似文献