Comparison of satellite and terrestrial gravity data

Summary The integral mean values of gravity on the surface W=W ₀ , obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J ₂ ⁽⁰⁾ ] ² , which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly.     

Lunar deflections of the vertical and their elementary interpretation

Summary The selenopotential was determined at the Apollo 12 landing site (A12) using the selenocentric constant, Stokes' constants of the Moon up to n=13, the angular velocity of rotation of the Moon and the value of gravity directly observed at A12. Using and the constants mentioned above, the radius-vector of the equiselenopotential surface passing through A12 was derived. The fundamental selenocentric parameters, based on this surface, were computed, as well as the deflections of the vertical especially in some strongly anomalous regions of the Moon. For some mascons an elementary interpretation has been carried out.Dedicated to Academician Alois Zátopek on His 65th BirthdayPresented at the XVth Plenary Meeting of COSPAR, Madrid, May 10–24, 1972, under the title:Selenocentric Reference Parameters and Deflections of the Vertical Related to the Equipotential Surface Passing through the Apollo 12 Landing Site.     

Parameters of the normal gravity field deduced from satellite observations

Summary The parameters of the normal gravity field were deduced from the harmonic coefficients[3, 4] upto n=6 and compared with the parameters used hitherto. The symbols used are the same as in papers[5, 6, 8] with which this paper connects up.     

Fundamental geodetic parameters of the earth's figure and the structure of the earth's gravity field derived from satellite data

Summary Using the geocentric constant GM=398 601.3 × 10 ⁹ m ³s ^–2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J _n ^(k) and S _n ^(k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid W_o, the scale factor for lengths R_o=GM/W_o, the radius-vector of the surface W=W_o, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.     

Geoidal curvature radii from satellite data for different degrees of smoothing

Summary Radii of curvature and their anomalies of a smoothed geoidal surface are computed using Stokes's constants J _n ^(k) , S _n ^(k) of the Earth's body, obtained from satellite orbit dynamics[2]. Different degrees n of smoothing are used (n = 8, 12, 21). The notations are the same as in[4, 5].     

On some types of gravity anomalies

Summary The gravity anomaly is a matter of convention. So far, only mixed gravity anomalies have been used. However, if in the future we shall have a sufficiently accurate geoid map covering the entire Earth's surface, it might be convenient to apply another type of gravity anomaly, as suggested Pellinen[1]. The object of this paper is to analyse this question with respect to the solution of the problems of physical geodesy.     

Inferences on the lunar temperature from gravity,stress state and flow laws

Inferences on the lunar temperature regime are made from the inversion of gravity for density anomalies and the stress-state of the Moon's interior, and by comparing these results with flow laws and estimates of likely strain-rates.The nature of the spectrum of the lunar gravitational potential indicates that the density anomalies giving rise to the potential are mainly of near-surface origon. The average stress-differences in the lunar mantle required to support these density anomalies are of the order of a few tens of bars and have persisted for more than 3 · 10⁹ years. If current flow laws for dry olivine can be extrapolated to the conditions of the lunar mantle, and the selenotherms based on electrical conductivity models are valid, the strain rates are too high to explain the preservation of the lateral near-surface density anomalies. We suggest that the present temperatures in the Moon are relatively low, of the order of 800°C or less, at a depth of about 300 km. This compares with 1100°C based on electrical conductivity models and is near the lower limit predicted by Keihm and Langseth (1977) from lunar heat-flow observations.     

Gravity potential of the normal body in the outer and inner space

Summary The level rotational ellipsoid, best fitting the actual Earth, rotating with the same angular velocity around a common axis of rotation, is assumed to be a mathematical model of the real Earth. The gravity potential of this body and its derivatives in the outer space are derived by means of the generalized Pizzetti method[1]. For some analyses of the structure of the Earth we need to know the gravity anomaly and thus the gravity potential and its derivatives inside the mathematical model. These values are not defined in the classical conception. In this paper, the normal potential and its derivatives in the inner space are derived up to a certain depth, which is still of significance for gravimetric research.Dedicated to RNDr Jan Pícha, CSc., on his 60th Birthday     

The constant part of the tidal field in the theory of heights

Summary The problem of the constant part of the tidal field is still topical in view of the recommendations of IAG[1, 2] to eliminate the tidal effect of external masses from all geodetic measurements under preservation of the effect of the time-constant tidal deformation of the Earth. The paper discusses the consequences of accepting this recommendation for normal heights, and suggests a solution based on the new definition of the normal gravity field[3].     

Scale factor for lengths of the geopotential model

Summary Using the data in[1], the scale factor for lengths is derived of the geopotential model R ₀ =GM/W ₀ (W ₀ is the potential on a generalized geoid). The resulting value, R ₀ ==6 363 672.9 m, which is2 m less than the original value[5], is practically the same as that in[6].     

On the problem of determining the vertical gradients of gravity anomalies

Summary Green's theorem on harmonic functions makes it possible to determine the integral relationship between the harmonic function and its derivative with respect to the normal on a closed Lyapunov surface. The conditions of solvability are given by Fredholm's theory of integral equations. The solution for a sphere was presented by Molodenskii[3] and the general solution with the help of Molodenskii's parameter k by Ostach[4]. The present paper indicates a possibility of solving this problem with the help of a system of linear algebraic equations, a simplified modification of the Ostach-Molodenskii solution and, finally, a method, based on Eremeev's solution of the fundamental integral equation[5].     

应用LP165P模型分析月球重力场特征及其对绕月卫星轨道的影响

通过现有的最新月球重力场模型LP165P和GLGM 2模型对月球重力场的特征进行了分析,计算了相应重力场的阶方差,给出了两种模型在月球外部空间不同高度上的重力异常分布图,分析比较了截断至不同阶次的月球重力场模型在不同高度上所反映的月球重力场的特征和差异.此外,利用GSFC/NASA/USA的GEODYNⅡ轨道分析软件模拟计算了不同高度处卫星的轨道变化,得出了在进行一定高度的轨道计算时,可以对重力场模型进行适当截断的结论.     

Tidal friction. The effect of oceans on the secular variation of the inclination and eccentricity of the Moon's orbit

Summary Procedures of astrodynamics are used to calculate the actual values of the secular variation of the inclination and eccentricity of the Moon's orbit due to ocean tides. The ocean tide data were taken from the resolution of the ocean tide potential into spherical functions[2] based on cotidal maps[1].     

On the triaxiality of the earth on the basis of satellite data

Summary The evolution of the opinions as to the problem of the triaxiality of the Earth in the period prior to satellite geodesy can be seen, e.g., in[1–18]. Recently the opinion has been voiced that triaxiality is a result of the mathematical treatment of data rather than reality[19–21], especially since this is a comparatively small parameter. This opinion is not in contradiction with the results of satellite observations[22–28], but the non-zero values of the harmonic coefficients of the second degree and second order are a reality, they yield a value of the equatorial flattening of about1/90 000, and the representation of the equatorial section by an ellipse is justified even if the harmonics n=3, k=1 and n=3, k=3 have amplitudes only about half as small, and some other parameters might occur with just as much justification besides triaxiality.     

Dielectric properties of the first 100 meters of the Moon

Reviewing 92 measurements of lunar sample dielectric constant versus density at frequencies above 100 kHz, gives the relationK′ = (1.93 ± 0.17)^p by regression analysis, where K′ is the dielectric constant of a soil or solid at a density ofpg/cm³. This formula is the geometric mean between the dielectric constant of vacuum (1) and the zero porosity dielectric constant of lunar material. Similarly, the loss tangent (D) can be described byD = [(0.00053 ± 0.00056) + (0.00025 ± 0.00009)C]p whereD is the loss tangent at densitypg/cm³ withC percent of total FeO + TiO₂ (approximately proportional to ilmenite content). Using the density versus depth relations derived from lunar surface core tubes, and from laboratory studies of lunar soil compression gives a model of the dielectric properties as a function of depth in the lunar regolith. The dielectric constant increases smoothly with depth, as a function of the soil compaction only. The loss tangent, however, is more sensitive to the ilmenite content than it is to density. Neither dielectric constant nor loss tangent varies significantly with the temperature observed in a lunar day.     

新53阶次月球重力场及其精细结构

月球重力场是了解月球内部结构的重要信息之一.日本SELENE卫星首次获得月球背面卫星轨道的直接探测数据并建立了更高精度的全月球重力场模型.本文根据日本公布的采样间隔为60 s、轨道高度为100 km的SELENE卫星观测资料并利用作者移植的GEODYN-II微机版本软件求解出新53阶次月球球谐场模型LG-53.经过测试表明移植后的微机版本比原始工作站版本的计算效率提高了5到10倍.理论上表明60 s采样间隔、100 km高度的轨道数据能够计算出60阶次的月球球谐系数模型,但是作者在实际计算过程中发现:在接近理论阶次(60阶次)的一系列模型中出现了平行于经线的高频噪声,且模型越接近理论阶次其噪声越高.因此本文将53阶次月球球谐系数模型LG-53作为最后的解算结果并建立各种月球重力异常场,并将其与美国GLGM-2 (70阶次)模型和利用嫦娥1号数据解算出的CEGM-01(50阶次)模型对比,发现新53阶次重力场模型LG-53在高纬度和月球背面都显示出了更高分辨率的异常特征;与美国LP165P(165阶次)模型对比发现LG-53所建立的自由空气重力异常在月球背面不存在LP165P中所出现的高频噪声.与日本90阶次SGM90d模型对比后发现新模型的精度较日本模型还有所差距.主要是由于两者参与计算的数据采样率不同所致.53阶次的模型LG-53能够反映100 km尺度的重力异常,而日本90阶次模型则可以反映60 km尺度的异常.利用新53阶次模型计算的自由空气重力异常图并结合月球地形图探讨了四种类型的Mascon重力异常特征及其地形特征.     

Lunar perturbations in geomagnetic field and in the characteristics ofF-region over huancayo

Summary The lunar daily (L) and lunar monthly (M) variations in horizontal magnetic field (H), maximum electron density (N _max ), height of peak ionisation (h _max ), semi-thickness (y _m ) of theF ₂ layer and total electron content (N _t ) at Huancayo for the period January 1960 to December 1961 are described. The lunar tidal variations inh _max follow sympathetically the variations inH such that an increase of magnetic field causes the raising of height of peak ionisation. Lunar tides inN _max are opposite in phase to that ofh _max with a delay of about 1–2 hours, suggesting that an increase of height causes a decrease in maximum electron density. The lunar tides in semi-thickness are very similar in phase to that inh _max . The lunar tidal effects in any of the parameters are largest inD-months and least inJ-months. The amplitude of lunar tides in maximum electron density seems to increase with increasing height whereas the phase seems to be constant with height. It is concluded that lunar tides in the ionospheric parameters at magnetic equator are greatly controlled by the corresponding geomagnetic variations.Presented at the Third International Symposium on Equatorial Aeronomy, Ahmedabad, 3–10 February 1969.     

Berechnung der Funktionen einfacher Streuung auf Trübungsteilchen in der Atmosphäre

Summary In 1967, a series of observations were carried out at Lomnický tít of the intensity of light of the clear sky. Using the de Bary method[1], the observations were used to determine the function of simple dispersion on turbind particles in the atmosphere and compared with theoretical functions, which hold for Jung's power distribution of the particles according to size[7] and for the logarithmic Gauss distribution of the particles[8].     

A note on the effect of the ground on the convective temperature field in the atmospheric surface layer

Summary The paper presents the solution of the equation of heat conduction with density of heat sources given generally. For two special cases the computed central temperature excesses of model[5] are compared with the results of some authors[1, 6] who deal with convection in the surface layer.     

The sunspot cycle and solar and lunar daily variations inH

Summary Results of sunspot cycle influence on solar and lunar ranges at a low latitude station, Alibag, outside the equatorial electrojet belt, show that the sunspot cycle association in solar ranges is three times that of the lunar ranges in thed- andj-seasons. This is in general agreement with the earlier results for non-polar latitude stations. The association with sunspot number of individual lunar amplitudes is greatest for lunar semidiurnal harmonic in thej-season. During this season, the sunspot cycle influence on lunar variations is more than that on solar variations, thereby indicating that the lunar current is situated at a level more favourable for sunspot cycle influence than the level of the current associated with solar variations. With the increase in solar activity a shift appears in the times of maxima of semidiurnal lunar variation towards a later lunar hour ine- andj-seasons and in the year.