15th order resonance terms using the decaying orbit of TETR-3

The orbit of TETR-3 (1971-83B), inclination: 33°, passed through resonance with 15th order geopotential terms in February 1972. The resonance caused the orbit inclination to increase by 0.015°. Analysis of 48 sets of mean Kepler elements for this satellite in 1971–1972 (across the resonance) has established the following strong constraint for high degree, 15th order gravitational terms (normalized):

$\text{10}{}^9\text{(}\text{C, S}\text{)}{}_{15}\text{= (28.3 ± 3.0, 7.4 ± 3.0) =}\text{0.001(}\text{C, S}\text{)}{}_{\mathrm{15,15}}\text{?0.015(}\text{C, S}\text{)}{}_{\mathrm{17,15}}\text{+0.073(}\text{C, S}\text{)}{}_{\mathrm{19,15}}\text{?0.219(}\text{C, S}\text{)}{}_{\mathrm{21,15}}\text{+0.477(}\text{C, S}\text{)}{}_{\mathrm{23,15}}\text{?0.781(}\text{C, S}\text{)}{}_{\mathrm{25,15}}\text{+1.000(}\text{C, S}\text{)}{}_{\mathrm{27,15}}\text{?0.0963(}\text{C, S}\text{)}{}_{\mathrm{29,15}}\text{+0.622(}\text{C, S}\text{)}{}_{\mathrm{31,15}}\text{?0.119(}\text{C, S}\text{)}{}_{\mathrm{33,15}}\text{?0.290(}\text{C, S}\text{)}{}_{\mathrm{35,15}}\text{+0.403(}\text{C, S}\text{)}{}_{\mathrm{37,15}}\text{?0.223(}\text{C, S}\text{)}{}_{\mathrm{39,15}}\text{?0.058(}\text{C, S}\text{)}{}_{\mathrm{41,15}}\text{+…}$

This result combined with previous results on high inclination 15th order and other resonant orbits suggests that the coefficients of the gravity field beyond the 15th degree are smaller than Kaula's rule ($\text{10}{}^{\mathrm{?5}}\text{l}{}^2$).     

Evaluation of harmonics in the geopotential of order 15 and odd degree

When a satellite orbit decaying slowly under the action of air drag experiences 15th-order resonance with the Earth's gravitational field, so that the ground track repeats after 15 rev, the orbital inclination suffers appreciable changes due to the perturbations from the harmonics in the geopotential of order 15 and odd degree (15,17,19 …). In this paper the changes in inclination at resonance of 11 satellites at inclinations between 30° and 90° have been analysed to determine values of the geopotential coefficients of order 15 and degree $\text{l,}\text{C}\text{?}{}_{\mathrm{l,15}}$ and $\text{S}\text{?}{}_{\mathrm{l,15}}$ in the usual notation. The recommended solution, going up to l = 31, is:

     

3.

Individual geopotential coefficients of order 15 and 30, from resonant satellite orbits     

D.G. King-Hele  Doreen M.C. Walker 《Planetary and Space Science》1985,33(2):223-238

The analysis of variations in satellite orbits when they pass through 15th-order resonance (15 revolutions per day) yields values of lumped geopotential harmonics of order 15, and sometimes of order 30. The 15th-order lumped harmonics obtained from 24 such analyses over a wide range of orbital inclinations are used here to determine individual harmonic coefficients of order 15 and degree 15,16,…35; and the 30th-order lumped harmonics (from eight of the analyses) are used to evaluate individual coefficients of order 30 and degree 30,32,…40. The new values should be more accurate than any previously obtained. The accuracy of the 15th-order coefficients of degree 15, 16,…23 is equivalent to 1 cm in geoid height, while the 30th-order coefficients of degree 30, 32 and 34 are determined with an accuracy which is equivalent to better than 2 cm in geoid height. The results are used to assess the accuracy of the Goddard Earth Model 10B.     

4.

Lumped geopotential harmonics of order 14, from the orbit of 1967-11G     

D.G. King-Hele 《Planetary and Space Science》1985,33(10):1145-1153

The satellite 1967-11G, which had an orbital inclination of 40°, passed through the 14th-order resonance with the Earth's gravitational field in 1974. The changes in its orbital inclination at resonance have been analysed to obtain values for four lumped 14th-order harmonics in the geopotential, with accuracies equivalent to about 5 cm in geoid height. Analysis of the eccentricity was also attempted, but did not yield useful results.As no previous satellite analysed at 14th-order resonance has had an inclination near 40°, the results have proved to be valuable in determining individual 14th-order harmonics in the geopotential.     

5.

Lumped geopotential harmonics of order 29, from analysis of the orbit of Cosmos 837 rocket     

H. Hiller 《Planetary and Space Science》1982,30(1):73-80

The orbit of Cosmos 837 rocket (1976-62E) has been determined at 36 epochs between January and September 1978, using the RAE orbit refinement program PROP 6 with about 3000 observations. The inclination was 62.7° and the eccentricity 0.039. The orbital accuracy achieved was between 30m and 150m, both radial and crosstrack. The orbit was near 29:2 resonance in 1978 (exact resonance occurred on 14 May) and the values of orbital inclination obtained have been analysed to derive lumped 29th-order geopotential harmonic coefficients, namely:

$\text{10}{}^9\text{C}{}^{\mathrm{0,2}}{}_{29}\text{= ? 10 ± 15}$

and

$\text{10}{}^9\text{S}{}^{\mathrm{0,2}}{}_{29}\text{= ?76 ± 12}$

. These will be used in future, when enough results at different inclinations have accumulated, to determine individual coefficients of order 29. The values of lumped harmonics obtained from analysis of the values of eccentricity were not well defined, because of the high correlations between them and the errors in removing the very large perturbation (31 km) due to odd zonal harmonics.     

6.

Higher order curvature terms in theories with creation     

C. Wolf 《Astronomische Nachrichten》1988,309(3):173-175

In two theories involving continuous creation higher order curvature terms are added to the field equations. At high gravitational curvatures the creation of matter depends critically on these extra terms.     

7.

Second order terms of the galactic velocity field. Cycindrical symmetry model     

F. Figueras  J. Núñez 《Astrophysics and Space Science》1991,177(1-2):483-490

One of the most important applications of the Astrometry is the study of the motions in our Galaxy. In this sense, an effort has been made to determine the kinematic parameters of the galactic rotation in the solar neighbourhood when the galactic velocity field is expanded until the second order terms of its Taylor development. For this purpose, it has been necessary to use a larger sample of stars and better distributed in galactic latitude than hitherto. As a first study, we present here the solution method applied and the results obtained when the hypothesis of cylindrical symmetry is made. The small correlations obtained between the second order partial derivatives indicate that some of these parameters can be solved at present. Furthermore, we have obtained a good concordance between our values and the hypothesis made by several previous authors concerning these terms: Trumpler and Weaver (1962), Clube (1974) and Brosche and Schwan (1981).     

8.

On the tidal variation of the geopotential     

José M. Ferrándiz  Juan Getino 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):279-292

In this paper analytical expressions are derived for the temporal variations ofJ ₂ andJ ₂₂ due to the tides of the solid Earth, taking into account only the deformation of the mantle, and employing a procedure already used by the authors in their Hamiltonian theory of the Earth's rotation, which obtain the necessary parameters in a direct way by integration of those provided by a selected model of Earth interior.Numerical tables giving the periodic variation of coefficients are given, as well as a new prediction for UT1. For J ₂ and J ₂₂ the amplitudes reach such a magnitude that both two variations should not be ignored in studies involving the analysis of highly precise satellite tracking data. Moreover, the possibility of improving our knowledge of the value of those harmonic coefficients in only a more exact digit appears as to be strongly dependent on the limitations in the theoretical modeling of the variations of the inertia tensor due to solid tides.     

9.

The accuracy of geopotential models     

C. A. Wagner  F. J. Lerch 《Planetary and Space Science》1978,26(12):1081-1140

Extensive tests of two recent geopotential models (GEM 7 and 8) have been made with observations not used in the solutions. Several other recent models are also evaluated. These tests show the accuracy of the satellite derived model (GEM 7, with 400 coefficients) to be about 4.3 m (r.m.s.) with respect to the global geoid surface. The corresponding accuracy of the combined satellite and surface gravimetry model (GEM 8, with 706 coefficients) is found to be 3.9m (r.m.s.). These results include a calibration for the commission errors of the coefficients in the models and an estimate of the errors from omitted coefficients. For GEM 7, the formal precision (commission errors) of the solution gives 0.7 m for the geoid error which after calibration increases to 2.4 m.

Independent observations used in this assessment include: 159 lumped coefficients from 35 resonant orbits of 1 and 9 through 15 revolutions per day, two sets of (8, 8) fields derived from optical-only and laser-only data, sets of zonal and resonant coefficients derived from largely independent sources and geoid undulations measured by satellite altimetry. In addition, the accuracy of GEM 7 has been judged by the gravimetry in GEM 8. The ratio of estimated commission to formal error in GEM 7 and 8 ranges from 2 to 5 in these tests.     

10.

Orbit determination and analysis for Cosmos 58 at 15th-order resonance, to evaluate geopotential harmonics of order 15 and 30     

Doreen M. C. Walker 《Planetary and Space Science》1986,34(12):1307-1318

The orbital parameters of Cosmos 58 have been determined at 65 epochs from some 4500 observations, between March 1982 and September 1983, using the RAE orbit refinement program, PROP. During this time, the satellite passed slowly through 15th-order resonance, and the orbital inclination and eccentricity have been analysed. Six lumped 15th-order geopotential harmonic coefficients have been evaluated, with an accuracy equivalent to between 0.8 and 2.0cm in geoid height. Six 30th-order coefficients have also been determined, with accuracies between 2 and 7 cm in geoid height. The coefficients have been compared with those from the GEM 10B and 10C models. There is good agreement for nine of the twelve coefficients.     

11.

The elimination of the critical terms of a first order Uranus-Neptune theory through Hori's method     

Osman M. Kamel 《Earth, Moon, and Planets》1982,27(4):407-415

An outline for the elimination of the critical terms of a first order Uranus-Neptune theory is presented with a stress on the application of Hori's procedure to the problem.     

12.

Refinement of the geopotential scale factorR 0 on     

David Nesvorný  Zdislav Šíma 《Earth, Moon, and Planets》1994,65(1):79-88

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.     

13.

The elimination of the critical terms of a first order Uranus-Neptune theory by Hori's method     

Osman M. Kamel 《Earth, Moon, and Planets》1983,28(3):221-245

In this part we determine the value ofS ₁, and in terms of the canonical variables of H. Poincaré. A complete solution of the auxiliary system of equations generated by the Hamiltonian is presented.     

14.

Evaluation of 14th-order harmonics in the geopotential     

D.G. King-Hele  Doreen M.C. Walker  R.H. Gooding 《Planetary and Space Science》1979,27(1):1-18

The Earth's gravitational potential is now usually expressed in terms of a double series of tesseral harmonics with several hundred terms, up to order and degree at least 20. The harmonics of order 14 can be evaluated by analysing changes in satellite orbits which experience 14th-order resonance, when the track over the Earth repeats after 14 revolutions.In this paper we describe our first evaluation of individual 14th-order coefficients in the geopotential from analysis of the variations in inclination and eccentricity of satellite orbits passing through 14th-order resonance under the action of air drag. Using results from eleven satellites, we find the following values for normalized coefficients of harmonics of order 14 and degree l, C?_{l, 14} and S?_{l, 14}, for l=14, 154. 22:

l	109C?l,15	109S?l,15
15	?21.5 ± 0.9	?8.4 ± 0.9
17	4.4 ± 1.6	9.0 ± 1.5
19	?15.6 ± 2.6	?14.1 ± 2.7
21	10.4 ± 3.0	7.3 ± 3.5
23	22.5 ± 2.8	1.2 ± 4.4
25	?0.9 ± 4.7	?3.8 ± 5.3
27	?11.2 ±3.3	9.1 ± 3.2
29	?20.5 ± 5.4	?1.2 ± 6.1
31	17.7 ± 6.6	?1.0 ± 7.1

     

15.

第十三批天文学名词的推荐译名     

中国天文学会天文学名词审定委员会 《天文学进展》2006,24(1):89-92

中国天文学会名词审定委员会从1985年起开始在《天文学进展》发表天文学名词的推荐译名,到2004 年已公布了12批共2025个名词。现再推荐第13批126个名词,其中大多数是近年出现的天文学新词。希望读者在使用过程中对译名提出改进意见。     

16.

Reformulation of the Brouwer geopotential theory for improved computational efficiency   总被引：1，自引：1，他引：0  

Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,24(4):367-375

The theory, as derived by Brouwer and later modified by Lyddane, of the motion of an artificial Earth satellite perturbed by the first five zonal harmonics is reformulated in terms of an alternate set of variables. This alternate set of variables produces an equivalent solution, has no small eccentricity or small inclination restrictions, and allows calculation of position and velocity with considerably fewer algebraic and trigonometric operations. In addition, the alternate set of variables avoids one solution of Kepler's equation.     

17.

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.     

18.

The sun's rotation and perturbations of geopotential height and temperature fields in the stratosphere     

A. Ebel  B. Schwister 《Solar physics》1981,74(2):385-398

The morphology of a solar activity effect apparently connected with the Sun's rotation and showing up in 25-day and 13.6-day oscillations of stratospheric geopotential and temperature fields is analysed in this study. The used data cover the height range between roughly 20 and 30 km and a timespan from July 1965 to October 1971. Most prominent responses are found for zonal harmonic wave number 1 at the oscillation period of 25 days (solar rotation period modulated by seasonal changes) and for the zonally averaged meteorological quantities at the oscillation period of 13.6 days. Additional statistically significant effects show up in the zonal harmonics with wave number 1 and 3 at half the solar rotation period and in the zonal means with periodicities near 25–27 days. The results point towards a modulation of the quasistationary stratospheric planetary wave with a positive geopotential anomaly around roughly 180° longitude by solar activity changes. The direct physical mechanisms of this Sun-climate relationship are not yet clear, but it can be concluded that atmospheric dynamics is an important factor for its morphology and that downward propagation of such effects seems possible and should be investigated in future studies.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

19.

A series expansion of the solid Earth tide effect on geopotential     

Sergey M. Kudryavtsev 《Celestial Mechanics and Dynamical Astronomy》2013,115(4):353-364

We develop analytical series representing the main part of corrections to the geopotential coefficients caused by the solid Earth tides, where Love numbers are assumed to be frequency-independent. The series are compact, precise and valid over 1800 A.D.–2200 A.D. The maximum difference between the corrections given by the analytical series and their numerical values, obtained with use of the DE/LE-423 planetary/lunar ephemerides, does not exceed $0.7\times 10^{-12}$ . A new algorithm is proposed for calculating amplitudes of the additional variations of the geopotential coefficients for frequency dependence of Love numbers. It uses the representation of the Earth tide-generating potential in the standard HW95 format and takes into account the phase of tidal waves. Corrections of up to $2\times 10^{-12}$ to the published by the IERS Conventions (2010) amplitudes of the additional variations of the geopotential coefficients are suggested. Examples of use of the obtained series in analytical theories of motion of low-altitude STARLETTE and high-altitude ETALON-1 satellites are given.     

20.

Radial,transverse and normal satellite position perturbations due to the geopotential   总被引：1，自引：0，他引：1  

G. W. Rosborough  B. D. Tapley 《Celestial Mechanics and Dynamical Astronomy》1987,40(3-4):409-421

Perturbations in the position of a satellite due to the Earth's gravitational effects are presented. The perturbations are given in the radial, transverse (or alongtrack) and normal (or cross-track) components. The solution is obtained by projecting the Kepler element perturbations obtained by Kaula [Kaula, 1966] into each of the three components. The resulting perturbations are presented in a form analogous to the form of Kaula's solution which facilitates implementation and interpretation.     

$\text{l}$	109C?$\text{l,14}$	109S?l,14
-	-	-
14	?38.5 ±2.9	?7.8 ±2.2
15	4.5 ±1.1	?23.8 ±0.3
16	?22.3 ±3.6	?36.0 ±3.8
17	?15.0 ±2.6	16.8 ±1.2
18	?24.0±4.9	?3.2 ±3.7
19	?1.6 ±2.8	?7.6 ±1.0
20	8.8 ±5.8	?15.4 ±4.6
21	18.2 ±3.6	?10.6 ±1.9
22	?14.5 ±8.1	9.9 ±6.4

Individual geopotential coefficients of order 15 and 30, from resonant satellite orbits

The analysis of variations in satellite orbits when they pass through 15th-order resonance (15 revolutions per day) yields values of lumped geopotential harmonics of order 15, and sometimes of order 30. The 15th-order lumped harmonics obtained from 24 such analyses over a wide range of orbital inclinations are used here to determine individual harmonic coefficients of order 15 and degree 15,16,…35; and the 30th-order lumped harmonics (from eight of the analyses) are used to evaluate individual coefficients of order 30 and degree 30,32,…40. The new values should be more accurate than any previously obtained. The accuracy of the 15th-order coefficients of degree 15, 16,…23 is equivalent to 1 cm in geoid height, while the 30th-order coefficients of degree 30, 32 and 34 are determined with an accuracy which is equivalent to better than 2 cm in geoid height. The results are used to assess the accuracy of the Goddard Earth Model 10B.     

Lumped geopotential harmonics of order 14, from the orbit of 1967-11G

The satellite 1967-11G, which had an orbital inclination of 40°, passed through the 14th-order resonance with the Earth's gravitational field in 1974. The changes in its orbital inclination at resonance have been analysed to obtain values for four lumped 14th-order harmonics in the geopotential, with accuracies equivalent to about 5 cm in geoid height. Analysis of the eccentricity was also attempted, but did not yield useful results.As no previous satellite analysed at 14th-order resonance has had an inclination near 40°, the results have proved to be valuable in determining individual 14th-order harmonics in the geopotential.     

Lumped geopotential harmonics of order 29, from analysis of the orbit of Cosmos 837 rocket

The orbit of Cosmos 837 rocket (1976-62E) has been determined at 36 epochs between January and September 1978, using the RAE orbit refinement program PROP 6 with about 3000 observations. The inclination was 62.7° and the eccentricity 0.039. The orbital accuracy achieved was between 30m and 150m, both radial and crosstrack. The orbit was near 29:2 resonance in 1978 (exact resonance occurred on 14 May) and the values of orbital inclination obtained have been analysed to derive lumped 29th-order geopotential harmonic coefficients, namely:

$\text{10}{}^9\text{C}{}^{\mathrm{0,2}}{}_{29}\text{= ? 10 ± 15}$

and

$\text{10}{}^9\text{S}{}^{\mathrm{0,2}}{}_{29}\text{= ?76 ± 12}$

. These will be used in future, when enough results at different inclinations have accumulated, to determine individual coefficients of order 29. The values of lumped harmonics obtained from analysis of the values of eccentricity were not well defined, because of the high correlations between them and the errors in removing the very large perturbation (31 km) due to odd zonal harmonics.     

Higher order curvature terms in theories with creation

In two theories involving continuous creation higher order curvature terms are added to the field equations. At high gravitational curvatures the creation of matter depends critically on these extra terms.     

Second order terms of the galactic velocity field. Cycindrical symmetry model

One of the most important applications of the Astrometry is the study of the motions in our Galaxy. In this sense, an effort has been made to determine the kinematic parameters of the galactic rotation in the solar neighbourhood when the galactic velocity field is expanded until the second order terms of its Taylor development. For this purpose, it has been necessary to use a larger sample of stars and better distributed in galactic latitude than hitherto. As a first study, we present here the solution method applied and the results obtained when the hypothesis of cylindrical symmetry is made. The small correlations obtained between the second order partial derivatives indicate that some of these parameters can be solved at present. Furthermore, we have obtained a good concordance between our values and the hypothesis made by several previous authors concerning these terms: Trumpler and Weaver (1962), Clube (1974) and Brosche and Schwan (1981).     

On the tidal variation of the geopotential

In this paper analytical expressions are derived for the temporal variations ofJ ₂ andJ ₂₂ due to the tides of the solid Earth, taking into account only the deformation of the mantle, and employing a procedure already used by the authors in their Hamiltonian theory of the Earth's rotation, which obtain the necessary parameters in a direct way by integration of those provided by a selected model of Earth interior.Numerical tables giving the periodic variation of coefficients are given, as well as a new prediction for UT1. For J ₂ and J ₂₂ the amplitudes reach such a magnitude that both two variations should not be ignored in studies involving the analysis of highly precise satellite tracking data. Moreover, the possibility of improving our knowledge of the value of those harmonic coefficients in only a more exact digit appears as to be strongly dependent on the limitations in the theoretical modeling of the variations of the inertia tensor due to solid tides.     

The accuracy of geopotential models

Extensive tests of two recent geopotential models (GEM 7 and 8) have been made with observations not used in the solutions. Several other recent models are also evaluated. These tests show the accuracy of the satellite derived model (GEM 7, with 400 coefficients) to be about 4.3 m (r.m.s.) with respect to the global geoid surface. The corresponding accuracy of the combined satellite and surface gravimetry model (GEM 8, with 706 coefficients) is found to be 3.9m (r.m.s.). These results include a calibration for the commission errors of the coefficients in the models and an estimate of the errors from omitted coefficients. For GEM 7, the formal precision (commission errors) of the solution gives 0.7 m for the geoid error which after calibration increases to 2.4 m.

Independent observations used in this assessment include: 159 lumped coefficients from 35 resonant orbits of 1 and 9 through 15 revolutions per day, two sets of (8, 8) fields derived from optical-only and laser-only data, sets of zonal and resonant coefficients derived from largely independent sources and geoid undulations measured by satellite altimetry. In addition, the accuracy of GEM 7 has been judged by the gravimetry in GEM 8. The ratio of estimated commission to formal error in GEM 7 and 8 ranges from 2 to 5 in these tests.     

Orbit determination and analysis for Cosmos 58 at 15th-order resonance, to evaluate geopotential harmonics of order 15 and 30

The orbital parameters of Cosmos 58 have been determined at 65 epochs from some 4500 observations, between March 1982 and September 1983, using the RAE orbit refinement program, PROP. During this time, the satellite passed slowly through 15th-order resonance, and the orbital inclination and eccentricity have been analysed. Six lumped 15th-order geopotential harmonic coefficients have been evaluated, with an accuracy equivalent to between 0.8 and 2.0cm in geoid height. Six 30th-order coefficients have also been determined, with accuracies between 2 and 7 cm in geoid height. The coefficients have been compared with those from the GEM 10B and 10C models. There is good agreement for nine of the twelve coefficients.     

The elimination of the critical terms of a first order Uranus-Neptune theory through Hori's method

An outline for the elimination of the critical terms of a first order Uranus-Neptune theory is presented with a stress on the application of Hori's procedure to the problem.     

Refinement of the geopotential scale factorR 0 on

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.     

The elimination of the critical terms of a first order Uranus-Neptune theory by Hori's method

In this part we determine the value ofS ₁, and in terms of the canonical variables of H. Poincaré. A complete solution of the auxiliary system of equations generated by the Hamiltonian is presented.     

Evaluation of 14th-order harmonics in the geopotential

The Earth's gravitational potential is now usually expressed in terms of a double series of tesseral harmonics with several hundred terms, up to order and degree at least 20. The harmonics of order 14 can be evaluated by analysing changes in satellite orbits which experience 14th-order resonance, when the track over the Earth repeats after 14 revolutions.In this paper we describe our first evaluation of individual 14th-order coefficients in the geopotential from analysis of the variations in inclination and eccentricity of satellite orbits passing through 14th-order resonance under the action of air drag. Using results from eleven satellites, we find the following values for normalized coefficients of harmonics of order 14 and degree l, C?_{l, 14} and S?_{l, 14}, for l=14, 154. 22:

第十三批天文学名词的推荐译名

中国天文学会名词审定委员会从1985年起开始在《天文学进展》发表天文学名词的推荐译名,到2004 年已公布了12批共2025个名词。现再推荐第13批126个名词,其中大多数是近年出现的天文学新词。希望读者在使用过程中对译名提出改进意见。     

Reformulation of the Brouwer geopotential theory for improved computational efficiency

The theory, as derived by Brouwer and later modified by Lyddane, of the motion of an artificial Earth satellite perturbed by the first five zonal harmonics is reformulated in terms of an alternate set of variables. This alternate set of variables produces an equivalent solution, has no small eccentricity or small inclination restrictions, and allows calculation of position and velocity with considerably fewer algebraic and trigonometric operations. In addition, the alternate set of variables avoids one solution of Kepler's equation.     

Position and velocity perturbations for the determination of geopotential from space geodetic measurements

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.     

The sun's rotation and perturbations of geopotential height and temperature fields in the stratosphere

The morphology of a solar activity effect apparently connected with the Sun's rotation and showing up in 25-day and 13.6-day oscillations of stratospheric geopotential and temperature fields is analysed in this study. The used data cover the height range between roughly 20 and 30 km and a timespan from July 1965 to October 1971. Most prominent responses are found for zonal harmonic wave number 1 at the oscillation period of 25 days (solar rotation period modulated by seasonal changes) and for the zonally averaged meteorological quantities at the oscillation period of 13.6 days. Additional statistically significant effects show up in the zonal harmonics with wave number 1 and 3 at half the solar rotation period and in the zonal means with periodicities near 25–27 days. The results point towards a modulation of the quasistationary stratospheric planetary wave with a positive geopotential anomaly around roughly 180° longitude by solar activity changes. The direct physical mechanisms of this Sun-climate relationship are not yet clear, but it can be concluded that atmospheric dynamics is an important factor for its morphology and that downward propagation of such effects seems possible and should be investigated in future studies.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

A series expansion of the solid Earth tide effect on geopotential

We develop analytical series representing the main part of corrections to the geopotential coefficients caused by the solid Earth tides, where Love numbers are assumed to be frequency-independent. The series are compact, precise and valid over 1800 A.D.–2200 A.D. The maximum difference between the corrections given by the analytical series and their numerical values, obtained with use of the DE/LE-423 planetary/lunar ephemerides, does not exceed $0.7\times 10^{-12}$ . A new algorithm is proposed for calculating amplitudes of the additional variations of the geopotential coefficients for frequency dependence of Love numbers. It uses the representation of the Earth tide-generating potential in the standard HW95 format and takes into account the phase of tidal waves. Corrections of up to $2\times 10^{-12}$ to the published by the IERS Conventions (2010) amplitudes of the additional variations of the geopotential coefficients are suggested. Examples of use of the obtained series in analytical theories of motion of low-altitude STARLETTE and high-altitude ETALON-1 satellites are given.     

Radial,transverse and normal satellite position perturbations due to the geopotential

Perturbations in the position of a satellite due to the Earth's gravitational effects are presented. The perturbations are given in the radial, transverse (or alongtrack) and normal (or cross-track) components. The solution is obtained by projecting the Kepler element perturbations obtained by Kaula [Kaula, 1966] into each of the three components. The resulting perturbations are presented in a form analogous to the form of Kaula's solution which facilitates implementation and interpretation.