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1.
Leland E. Cunningham 《Celestial Mechanics and Dynamical Astronomy》1970,2(2):207-216
A method is presented for the accurate and efficient computation of the forces and their first derivatives arising from any number of zonal and tesseral terms in the Earth's gravitational potential. The basic formulae are recurrence relations between some solid spherical harmonics,V
n,m, associated with the standard polynomial ones. 相似文献
2.
Edwin Wnuk 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):179-191
A new formula has been derived for geopotential expressed in terms of orbital elements. The summation sequence was changed so that the terms of the same frequencies would be grouped and the generalized lumped coefficients were derived. The proposed formula has the same form for both odd and evenl-m.Applying Hori's perturbation method, new formulae were derived for tesseral harmonic perturbations in nonsingular orbital elements:l+g, h, e cosg,e sing, L, andH. We show the possibility of effective application of the derived formulae to the calculation of orbits of very low satellites taking into account the coefficients of tesseral harmonics of the Earth's gravitational field up to high orders and degrees. As an example the perturbations up to the order and degree of 90 for the orbit of GRM satellites were calculated. The calculations were carried out on an IBM AT personal computer. 相似文献
3.
Peter J. Melvin 《Celestial Mechanics and Dynamical Astronomy》1985,35(4):345-355
Deprit's approach to the summation of the Legendre series in the geopotential evaluation problem is modified to accomodate normalized spherical harmonics and coefficients. Normalization avoids the floating point overflow encountered with high order geopotential models when the computer floating point arithmetic does not provide for large enough exponent. Deprit's algorithm is then appropriate for trajectory generation on-board an autonomous satellite system or for gravity compensation in an inertial navigation system. 相似文献
4.
Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field
model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS)
mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W
0 = (12,654,875 ± 69) (m2/s2), is used as one of the four fundamental gravity parameters of Mars namely, {W
0, GM, ω, J
20}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic
of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed
reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid
is presented with respect to the computed reference ellipsoid. 相似文献
5.
The formulae for the perturbations in radial, transverse and binormal components of the Earth artificial satellite motion have been derived. Perturbations due to the tesseral part of the geopotential are considered. The geopotential expressed in terms of the orbital elements has the form proposed by Wnuk (1988). The formulae for the perturbations have been obtained using the Hori (1966) method. They can be effectively applied in calculation of the perturbations in the components including the coefficients of the high order and degree tesseral harmonics. The derived formulae reveal no singularities at zero eccentricity. 相似文献
6.
The series in ellipsoidal harmonics for derivatives of the Earth’s gravity potential are used only on the reference ellipsoid enveloping the Earth due to their very complex mathematical structure. In the current study, the series in ellipsoidal harmonics are constructed for first- and second-order derivatives of the potential at satellite altitudes; their structure is similar to the series on the reference ellipsoid. The point P is chosen at a random satellite altitude; then, the ellipsoid of revolution is described, which passes through this point and is confocal to the reference ellipsoid. An object-centered coordinate system with the origin at the point P is considered. Using a sequence of transformations, the nonsingular series in ellipsoidal harmonics is constructed for first and second derivatives of the potential in the object-centered coordinate system. These series can be applied to develop a model of the Earth’s potential, based on combined use of surface gravitational force measurements, data on the satellite orbital position, its acceleration, or measurements of the gravitational force gradients of the first and second order. The technique is applicable to any other planet of the Solar System. 相似文献
7.
本文阐明地球非球形引力位中的高阶次球谐项（ 即“短”波项） 对求解卫星运动微分方程的两类数值方法（ 单步法和多步法） 选择积分步长的不同影响,并以实际算例证实这一点。 相似文献
8.
This paper derives asymptotic expansions of ellipsoidal coordinates in Cartesian coordinates and an expansion in spherical harmonics of the dominant term for the solution of Laplace's equation corresponding to the gravitational force function for a two-dimensional finite body.On comparing the expansion of the dominant term derived here with known expansions of the force functions of the Earth's and Moon's gravitation the author obtains values for the semimajor axes and eccentricities of the singular ellipses of these bodies in terms of the second degree harmonic coefficientsc
20 andc
22. 相似文献
9.
Efficient Determination of Global Gravity Field from Satellite-to-satellite Tracking Mission 总被引：2，自引：0，他引：2
Shin-Chan Han 《Celestial Mechanics and Dynamical Astronomy》2004,88(1):69-102
The gravity field dedicated satellite missions like CHAMP, GRACE, and GOCE are supposed to map the Earth's global gravity field with unprecedented accuracy and resolution. New models of the Earth's static and time-variable gravity fields will be available every month as one of the science products from GRACE. A method for the efficient gravity field recovery is presented using in situ satellite-to-satellite observations at altitude and results on static as well as temporal gravity field recovery are shown. Considering the energy relationship between the kinetic energy of the satellite and the gravitational potential, the disturbing potential observations can be computed from the orbital state vector, using high-low GPS tracking data, low–low satellite-to-satellite GRACE measurements, and data from 3-axis accelerometers. The solution method is based on the conjugate gradient iterative approach to efficiently recover the gravity field coefficients and approximate error covariance up to degree and order 120 every month. Based on the monthly GRACE noise-only simulation, the geoid was obtained with an accuracy of a few cm and with a resolution (half wavelength) of 160 km. However, the geoid accuracy can become worse by a factor of 6–7 because of spatial aliasing. The approximate error covariance was found to be a very good accuracy measure of the estimated coefficients, geoid, and gravity anomaly. The temporal gravity field, representing the monthly mean continental water mass redistribution, was recovered in the presence of measurement noise and high frequency temporal variation. The resulting recovered temporal gravity fields have about 0.3 mm errors in terms of geoid height with a resolution of 670 km. 相似文献
10.
Florent Deleflie Gilles Métris Pierre Exertier 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):105-134
This paper presents an analytic solution of the equations of motion of an artificial satellite, obtained using non singular
elements for eccentricity. The satellite is under the influence of the gravity field of a central body, expanded in spherical
harmonics up to an arbitrary degree and order. We discuss in details the solution we give for the components of the eccentricity
vector. For each element, we have divided the Lagrange equations into two parts: the first part is integrated exactly, and
the second part is integrated with a perturbation method. The complete solution is the sum of the so-called “main” solution
and of the so-called “complementary” solution. To test the accuracy of our method, we compare it to numerical integration
and to the method developed in Kaula (Theory of Satellite Geodesy, Blaisdell publ. Co., New York. 1966), expressed in classical
orbital elements. For eccentricities which are not very small, the two analytical methods are almost equivalent. For low eccentricities,
our method is much more accurate. 相似文献
11.
对北京天文台动态频谱仪1996～1999年观测到的68群Ⅲ型爆发作了统计分析,并对这些事件的频率漂移、持续时间、偏振和带宽的基本特性作了定性分析. 相似文献
12.
The scalar equations of infinitesimal elastic gravitational motion for a rotating, slightly elliptical Earth are always used
to study the Earth's nutation and tides theoretically, while the determination of the integration of the equations depends,
to a certain extent, on the choice of a set of appropriate boundary conditions. In this paper, a continuity quantity related
to the displacement is first transformed from the elliptical reference boundary to the corresponding effective spherical domain,
and then converted from a vector (or tensor) form to a scalar form by generalized surface spherical harmonics expansion. All
the related components, including the displacement vector field (or the stress tensor field), are then decomposed into the
poloidal and toroidal field using the symmetry restrictions on the normal mode eigenfunctions. After truncation, the boundary
conditions are finally derived, in a scalar ordinary differential form. The process of the derivation is second order in ellipticity
and in full detail. Moreover, the other boundary conditions are also presented as second order in ellipticity at the end of
this paper.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Theory of the motion of an artificial Earth satellite 总被引：1，自引：0，他引：1
Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):307-363
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ
4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions. 相似文献
14.
The spatial and temporal variations of the Earth deformation and the gravitational field are important both in the theoretical research and in the construction of geospatial database. The Earth deforms due to various mechanisms and the deformation further induces changes in the gravitational potential of the Earth, i.e. the deformation-induced additional potential or the Euler gravitational increment. Based on the theory of vector spherical harmonics, we discuss in this paper the Earth deformation and gravitational increment resulting from the tidal force, loading force and the stress of the Earth's surface. We write out the expression for the Euler gravitational potential increment and the relations between different Love numbers. These are all important points in the research on Earth deformation. 相似文献
15.
Some aspects for efficient computation of the tidal perturbation due to the ellipticity effects of the Earth, the luni-solar potential on an Earth-orbiting satellite and the perturbations of the satellite's radial, transverse and normal position components due to the effects of the Earth's gravitational and ocean tide fields are presented. A straightforward method for computing the spectrum of the geopotential and the tidal-induced perturbations of the orbit elements and the radial, transverse and normal components is described. 相似文献
16.
Spherical harmonics are the natural parameters for the Earth's gravity field as sensed by orbiting satellites, but problems of resolution arise because the spectrum of effects is narrow and unique to each orbit. Comprehensive gravity models now contain many hundreds of thousands of observations from more than thirty different near-Earth artificial satellites. With refinements in tracking systems, newer data is capable of sensing the spherical harmonics of the field experienced by these satellites to very high degree and order. For example, altimeter, laser and satellite-tracking-satellite systems contain gravitational information well above present levels of satellite gravity field recovery (l = 20), but significant aliasing results because the orbital parameters are too restricted compared to the large number of spherical harmonics.It is shown however that the unique spectrum of information for each satellite contained within a comprehensive spherical harmonic model can be represented by simple gravitational constraint equations (lumped harmonics). All such constraints are harmonic in the argument of perigee (ω) with constants determinable directly from tracking data or reconstituted from the comprehensive solution: . The constants are simple linear combinations of the geopotential harmonics. Through these lumped harmonics any satellite gravity field can be decomposed and then uniformly extended to any degree or tailored to a given orbit without reintegration of the trajectory and variational equations. They also make possible the inclusion of information into the field from special deep resonance passages, long arc zonal analyses, and satellites unique to other models. Numerous examples of the derivation, combination, extension and tailoring of the harmonics are presented. The importance of using data spanning an apsidal period is emphasized. 相似文献
17.
Mohamed Adel Sharaf Mervat El-Sayed Awad Mona A. Banaja 《Astrophysics and Space Science》1987,133(2):339-353
In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for the KS regularized theory will be established for any numberN of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulae is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding toN=2 andN=36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm. 相似文献
18.
卫星重力梯度测量任务将获取全球范围内高精度重力场信息。为利用重力梯度测量数据来提高重力场模型的精度,本文从球谐函数谱分析理论出发,导出了重力梯度场球谐谱分析的迭代算法公式。数值模拟结果表明：该迭代算法的收敛性极好,且高阶次位系数的收敛趋势较低阶次的收敛趋势要好得多。 相似文献
19.
Global and regional satellite navigation systems are constellations orbiting the Earth and transmitting radio signals for determining position and velocity of users around the globe. The state-of-the-art navigation satellite systems are located in medium Earth orbits and geosynchronous Earth orbits and are characterized by high launching, building and maintenance costs. For applications that require only regional coverage, the continuous and global coverage that existing systems provide may be unnecessary. Thus, a nano-satellites-based regional navigation satellite system in Low Earth Orbit (LEO), with significantly reduced launching, building and maintenance costs, can be considered. Thus, this paper is aimed at developing a LEO constellation optimization and design method, using genetic algorithms and gradient-based optimization. The preliminary results of this study include 268 LEO constellations, aimed at regional navigation in an approximately 1000 km \(\times \) 1000 km area centered at the geographic coordinates [30, 30] degrees. The constellations performance is examined using simulations, and the figures of merit include total coverage time, revisit time, and geometric dilution of precision (GDOP) percentiles. The GDOP is a quantity that determines the positioning solution accuracy and solely depends on the spatial geometry of the satellites. Whereas the optimization method takes into account only the Earth’s second zonal harmonic coefficient, the simulations include the Earth’s gravitational field with zonal and tesseral harmonics up to degree 10 and order 10, Solar radiation pressure, drag, and the lunisolar gravitational perturbation. 相似文献
20.
In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36.A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.Dept. of Astronomy, KAU 相似文献