On the analysis of lunar occultations of point-like X-ray sources

In view of the scheduled satellite mission EXOSAT (European X-Ray Observatory Satellite) of ESA (European Space Agency) the lunar occultation technique to determine the position of point-like X-ray sources is investigated. In particular, this paper explores the accuracy of the determination of the starting and ending time of an occultation, both of which are directly related to the size of the resulting position error box. An attempt is made to calculate analytically the distribution function of the estimated starting time, and some corresponding numerical evaluations are given. Finally, it is shown by Monte Carlo simulations that a slightly modifiedX ²-minimum method can be used to analyse the X-ray occultation data.     

火星电离层无线电掩星探测仿真研究

对中俄联合火星星-星电离层掩星技术体制进行了分析和介绍,采用三维射线追踪方法对电离层掩星事件的电波观测值进行了模拟计算,并利用模拟的掩星观测数据进行了电子密度廓线反演,结果说明仿真算法可靠.利用仿真的方法,分别对掩星电波相位观测误差和卫星轨道误差等带来的反演误差进行了个例计算和分析,结果得到:5%周的相位测量误差对白天电离层掩星探测结果的影响可以忽略,而夜间电子密度测量的绝对误差小于4×108 m-3;卫星轨道误差对掩星的主要影响是导致电离层高度抬升或下降.结果表明,中俄联合火星电离层掩星探测技术体制先进,可望获得高精度的电子密度廓线;其技术体制也可以用于月球电离层环境的探测.     

Lunar occultation of Saturn. I. The diameters of Tethys,Dione, Rhea,Titan, and Iapetus

The diameters of Tethys, Dione, Rhea, Titan and Iapetus were determined from observations of their March 30, 1974, lunar occultations, made with the Mauna Kea 224 and 61 cm telescopes. Light curves were obtained simultaneously in four colors, and the difference between the time of occultation at the two telescopes provided a direct measurement of the slope of the lunar limb, found to be small in all cases. The satellite diameters were determined by least-squares fits of model occultation light curves to the data. In these fits the diameter and degree of limb darkening of the satellite are correlated variables, requiring the limb darkening to be specified before the diameter can be determined, or vice versa. However, for Titan the signal-to-noise ratio is sufficiently high to allow some assessment of the amount of limb darkening, which was found to be substantial. Titan's diameter must be at least 5800 km, much larger than the currently accepted value of 5000 km, making it the largest satellite in the solar system. This larger diameter implies a low mean density. For the other four satellites arguments are presented in favor of accepting the occultation diameters corresponding to limb darkened disks. Except for Titan, the lunar occultation diameters generally agree with previous diskmeter and radiometric determinations.     

预报大行星,月球掩点源事件的一种方法

以ＪＰＬ提供的太阳系天体数值历表ＤＥ２００／ＬＥ２００和美国海军天文台提供的岁差、章动改正程序为出发点，本文介绍预报大行星、月球掩源的一种方法，本方法分三个步骤：首先给出被掩源所满足的必要条件，并据此进行被掩源的初选；其次预报掩事件的全局情况，即掩发生的始终时刻和比较精确的地球椭球表面上可观测区域边界，在可观测区域边界中，本文发现了文献中未见出现过的出没南北界最后；预报地方见掩情况。     

Electron content near the lunar surface using dual-frequency VLBI tracking data in a single lunar orbiter mission

In VLBI observations of Vstar, a subsatellite of the Japanese lunar mission SELENE, there were opportunities for lunar grazing occultation when Vstar was very close to the limb of the Moon. This kind of chance made it possible to probe the thin plasma layer above the Moon's surface as a meaningful by-product of VLBI,by using the radio occultation method with coherent radio waves from the S/X bands.The dual-frequency measurements were carried out at Earth-based VLBI stations. In the line-of-sight direction between the satellite and the ground-based tracking station where VLBI measurements were made, the effects of the terrestrial ionosphere, interplanetary plasma and the thin lunar ionosphere mixed together in the combined observables of dual-frequency Doppler shift and phase shift. To separate the variation of the ionospheric total electron content(TEC) near the surface of the Moon from the mixed signal, the influences of the terrestrial ionosphere and interplanetary plasma have been removed by using an extrapolation method based on a short-term trend. The lunar TEC is estimated from the dual-frequency observation for Vstar from UT 22:18to UT 22:20 on 2008 June 28 at several tracking stations. The TEC results obtained from VLBI sites are identical, however, they are not as remarkable as the result obtained at the Usuda deep space tracking station.     

Forthcoming close angular approaches of planets to radio sources and possibilities to use them as GR tests

During close angular approaches of solar system planets to astrometric radio sources, the apparent positions of these sources shift due to relativistic effects and, thus, these events may be used for testing the theory of general relativity; this fact was successfully demonstrated in the experiments on the measurements of radio source position shifts during the approaches of Jupiter carried out in 1988 and 2002. An analysis, performed within the frames of the present work, showed that when a source is observed near a planet’s disk edge, i.e., practically in the case of occultation, the current experimental accuracy makes it possible to measure the relativistic effects for all planets. However, radio occultations are fairly rare events. At the same time, only Jupiter and Saturn provide noticeable relativistic effects approaching the radio sources at angular distances of about a few planet radii. Our analysis resulted in the creation of a catalog of forthcoming occultations and approaches of planets to astrometric radio sources for the time period of 2008–2050, which can be used for planning experiments on testing gravity theories and other purposes. For all events included in the catalog, the main relativistic effects are calculated both for ground-based and space (Earth-Moon) interferometer baselines.     

An analysis of lunar occultations in the years 1955–1980 using the new lunar ephemeris ELP2000

About 60,000 observations of lunar occultations made during 1955–1980 are analysed using recently-developed semi-analytical solution ELP2000-82 for the Moon's position in order to determine the constants in the lunar theory and to investigate the tidal term in the Moon's mean longitude and the motions of the perigee and node of the lunar orbit. The equinox correction and systematic correction to the fundamental star catalogue and the correction to the datum of the lunar-profile in Watts' charts are also investigated. It is confirmed that the occultation observations do not have inconsistent tidal term with the modern observations and the observed mean motions of the perigee and node coincide with the theoretical ones within the error of observations. Some of the values of the constants in the lunar theory and the equinox correction to the fundamental catalogue FK5 obtained in this paper are significantly different from the values obtained using the Brown's theory. The reason of the difference is almost attributed to the deficiencies in the Brown's theory. The obtained correction to the datum of the lunar-profile in Watts' charts is almost consistent with the results by earlier investigators.     

On the possibility of investigating the galactic center region with the integral observatory by the method of lunar and terrestrial occultations

The possibility of investigating the sky region near the Galactic center with instruments of the INTEGRAL orbital astrophysical gamma-ray observatory by the method of its occultation by the Earth and the Moon is considered. Existing engineering constraints on the observing conditions, such as the admissible orientation of the INTEGRAL satellite relative to the direction to the Sun and the performance of measurements only outside the Earth??s radiation belts, are taken into account. Long time intervals during which the lunar occultation center passes at angular distances of less than 2° from the Galactic center have been found. Such events occur under the adopted constraints two or three times per year without any correction of the INTEGRAL satellite orbit. The orbit can be corrected to reduce the angular distance between the Moon and the Galactic center in occultation events. The required velocity impulses do not exceed several meters per second. The possibility of the Galactic center being occulted by the Earth has been analyzed. In this case, to perform measurements, the admissible (in radiation exposure) height of the working segment of the orbit should be reduced to 25 000 km, which can be problematic. At the same time, part of the Galaxy??s equatorial region is shadowed by the Earth for a time long enough to carry out the corresponding experiments.     

Numerical investigation of collision orbits of lunar satellites

In the present study an investigation of the collision orbits of natural satellites of the Moon (considered to be of finite dimensions) is developed, and the tendency of natural satellites of the Moon to collide on the visible or the far side of the Moon is studied. The collision course of the satellite is studied up to its impact on the lunar surface for perturbations of its initial orbit arbitrarily induced, for example, by the explosion of a meteorite. Several initial conditions regarding the position of the satellite to collide with the Moon on its near (visible) or far (invisible) side is examined in connection to the initial conditions and the direction of the motion of the satellite. The distribution of the lunar craters-originating impact of lunar satellites or celestial bodies which followed a course around the Moon and lost their stability - is examined. First, we consider the planar motion of the natural satellite and its collision on the Moon's surface without the presence of the Earth and Sun. The initial velocities of the satellite are determined in such a way so its impact on the lunar surface takes place on the visible side of the Moon. Then, we continue imparting these velocities to the satellite, but now in the presence of the Earth and Sun; and study the forementioned impacts of the satellites but now in the Earth-Moon-Satellite system influenced also by the Sun. The initial distances of the satellite are taken as the distances which have been used to compute periodic orbits in the planar restricted three-body problem (cf. Gousidou-Koutita, 1980) and its direction takes different angles with the x-axis (Earth-Moon axis). Finally, we summarise the tendency of the satellite's impact on the visible or invisible side of the Moon.     

On the analytic lunar and solar perturbations of a near Earth satellite

The disturbing function of the Moon (Sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the Moon (Sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elementsl, l′, F, D and Γ of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements ω and Ω of the satellite so that analytic integration is simple and the results accurate over a long period of time.     

Scintillations during occultations by planets I. An approximate theory

Fluctuations are observed during occultations of both stars and spacecraft by planetary atmospheres. Existing treatments of spacecraft scintillations ignore a major effect unique to occultations: the severe flattening of the Fresnel zone or source image by defocusing. Other large effects, due to “saturation” of the scintillation, have also been ignored. The deeper portions of atmospheric temperature and density profiles inferred from occultation data are seriously in error if other planets' atmospheres are as turbulent as our own. Thus, profiles obtained from entry probes (e.g., the Soviet Venera series) are probably more accurate than those from radio occultation (Mariner 5 and 10) data. Scintillation greatly reduces the information obtainable from occultation observations; much of the detail attributed to layering in published profiles is probably due to aliasing of turbulence. This paper gives an approximately correct theoretical treatment that is a substantial improvement over published theories, and shows how a more accurate theory could be constructed. Some methods for a more accurate determination of atmospheric structure are proposed.     

Independent selenocentric system of coordinates by large-scale star-calibrated lunar photography

The selenocentric coordinates of 263 craters and one mountain are given. The scale and orientation of the selenocentric coordinates system is determined by star-calibrated lunar photographs obtained with the long-focus horizontal telescope. The origin of the system is defined by the theory of the motion of the Moon. The physical libration is taken into account for the reduction of the coordinates system to the principal axes of the lunar inertia. The reference stars coordinates are reduced to the FK4 system. The position of the lunar mass centre is determined by LURE-2 theory, the rotation parameters are taken from the Migus tables (Migus, 1980).     

The improvement of the lunar ephemeris

At present the fundamental lunar ephemeris is based on Brown's theory of the motion of the Moon with improvements based on the bypassing of Brown's Tables, the removal of the great empirical term, the substitution of the relevant constants of the IAU system of astronomical constants and the retransformation of Brown's series in rectangular coordinates to spherical coordinates. Even so this ephemeris does not represent adequately the recent range and range-rate radio observations, and it will be inadequate for use in the analysis of laser observations of corner reflectors on the Moon. Numerical integrations for these purposes have already been made at the Jet Propulsion Laboratory, but improved theoretical developments are also required; new solutions of the main problem are in hand elsewhere. Work at H.M. Nautical Almanac Office is aimed at obtaining improved values of the constants of the lunar orbit by a rediscussion of occultation observations made since 1943 and at the redevelopment of the series for the planetary perturbations using more precise theories of the motion of the Sun and planets. The techniques and preliminary results of exploratory numerical integrations were briefly described.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, 17–23 August, 1969.     

System of absolute elevations in the marginal zone of the moon derived from stellar occultations

The present paper contains an outline of the method for a determination of the altitudes in the lunar marginal zone from occultations of the stars by the Moon; and the limb charts of this zone were constructed from such altitudes.     

Lunar occultation of Saturn: IV. Astrometric results from observations of the satellites

The method of determining local lunar limb slopes, and the consequent time scale needed for diameter studies, from accurate occultation timings at two nearby telescope is described. The results for the photoelectric observations made at Mauna Kea Observatory during the occultation of Saturn's satellites on March 30, 1974, are discussed. Analysis of all observations of occultations of Saturn's satellites during 1974 indicates possible errors in the ephemerides of Saturn and its satellites.     

Coordinate systems and lunar observing station positions

Satellite geodesy has yielded the locations of more than fifty stations in a single coordinate system referred to the Earth's center of mass with accuracies in the five to ten meter range. The following different methods have been used at Goddard to accomplish this.Dynamical solutions have been obtained for the locations of some fifty key stations using data from the GEOS satellite program. The distribution of observations about the stations is illustrated in terms of the data obtained for a typical station such as the one at Edinburg, Texas. Geopotential coefficients were held fixed in these solutions. The results of these dynamical determinations implied geodetic datum shifts which were then used to arrive at positions for some two hundred additional stations.Another approach involved the adjustment of the coordinates of seventeen stations on the basis of observations of short arcs of GEOS satellite orbits. These results were found to be consistent with those obtained through ground surveys to about five meters rms in each coordinate.Simultaneous solutions for station locations and geopotential coefficients have also yielded values for positions of some sixty stations, again in a coordinate system defined in terms of the Earth's center of mass.Lunar laser ranging and lunar occultation observing programs involve knowledge of the positions of the observing sites. In some cases the lunar observing program itself yields station coordinate information. In other cases greater reliance is placed upon independent determinations of site locations. The location of an occultation observation site at Olifantsfontein, for example, has been obtained in a center-of-mass system in both the dynamical and simultaneous satellite solutions. It is anticipated that a dynamical satellite solution will be extended in 1973 to obtain center-of-mass coordinates for a station in New Zealand. This will make it possible to tie an occultation site in that region to a dynamically determined coordinate system referred to the mass center. Coordinates for stations at Organ Pass, New Mexico, determined in both the dynamical and simultaneous solutions, and Edinburg, Texas, found in both the dynamical and short-arc adjustments, provide the basis for referring the location of a facility such as the McDonald Observatory to a center-of-mass system either through accurate ground surveying techniques or by means of a satellite geodesty tie. The latter approach has already been used, for example, to fix the position of an isolated site on Madagascar relative to a reference point in Africa and, in turn, to a center-of-mass coordinate system.Estimates of the accuracies of the satellite determinations are discussed.Theoretical aspects of coordinate systems associated with the Earth and the Moon are also considered.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

Future possibilities for lunar occultation studies of faint X-ray sources

Lunar occultation can be considered of interest for future missions dedicated to X-ray astronomy only if instruments with a large enough collecting area are used. In this case, observations of the numerous, faint X-ray sources occulted by the moon during a typical satellite lifetime of several years, can, in principle, add good source positioning as a free bonus to a high-throughput, medium-imaging mission. In the practical case of the EPIC instrument aboard the XMM ESA satellite, a simple calculation shows the potential usefulness of this technique.     

Lunar perturbations of artificial satellites of the earth

Lunisolar perturbations of an artificial satellite for general terms of the disturbing function were derived by Kaula (1962). However, his formulas use equatorial elements for the Moon and do not give a definite algorithm for computational procedures. As Kozai (1966, 1973) noted, both inclination and node of the Moon's orbit with respect to the equator of the Earth are not simple functions of time, while the same elements with respect to the ecliptic are well approximated by a constant and a linear function of time, respectively. In the present work, we obtain the disturbing function for the Lunar perturbations using ecliptic elements for the Moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The Moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the Earth. We can then apply the results to numerical integration by using coordinates of the Moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the Moon's motion represented by a precessing and rotating elliptical orbit.     

The McDonald photoelectric occultation observation program

Since 1968 an assiduous program of photoelectric observation of occultations of stars by the Moon has been pursued at McDonald Observatory. A total of about 600 events has been observed of which 254 have been published and a second list is in preparation. Timings derived from the reductions have errors of the order of 1 ms corresponding to a positional uncertainty in the lunar limb of typically 80 cm. Results are routinely communicated to the ephemerides offices.In about 140 events the fringe pattern due to diffraction by the lunar limb is sufficiently well defined to permit a determination of the slope near the point of occultation. A statistical discussion of these data is given. In all except a few cases, the slopes are numerically less than 15°, though 7 cases with slopes between 30° and 40° have been found. The relations between numbers of observations and contact angle, and between errors of slope determination and contact angle are discussed. The distribution of slope data with contact angle seems adequately explained. When slope data are collected by position angle consistently large and consistently small values show a tendency to group in a pattern suggesting a connection with observed large scale features on the lunar limb.The influence of lunar limb irregularities of a scale of a few meters on observed diffraction patterns and inferred timings is discussed. Multichannel observations should be of value in removing ambiguities. The use of occultation observations for the discovery of multiple stars and for the measurement of angular diameters of stars is mentioned. Future developments proposed for the project are considered.The project has involved contributions by a considerable number of individuals from the staff and student body at Austin, Texas, from the staff at McDonald Observatory, from visiting scientists and from the Laser Ranging Group. These contributions are acknowledged in the paper. The work has been supported by NSF Grants GP-21204 and GP-32263X.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

An Emulation Research on the Radio Occultation Exploration of Martian Ionosphere

The technical system of the Sino-Russian joint satellite-to-satellite Mars ionosphere occultation is analyzed and introduced. The analogue computation of the observed values of the radio waves of the ionosphere occultation event is carried out by adopting the three-dimensional ray tracking method and the electron density profile inversion is conducted by means of the simulated occultation observational data, with the result showing that the emulation algorithm is reliable. By taking advantage of the emulation method the case computation and analysis of the inversion errors caused by the observational error of the occultation radio wave phase and the satellite orbital error are respectively carried out, and it is obtained from the result that the effect of the phase measuring error of the 5% circle on the result of the daytime ionosphere occultation exploration may be neglected, while the absolute error of the night electron density measurement is less than 4 × 108 m^?3, and the main effect of the satellite orbital error on the occultation leads to the lifting or falling of the ionospheric height. The result shows that the technical system of the Sino-Russian joint Mars ionosphere occultation exploration is advanced. It can be expected that the high accuracy electron density profile is obtained and the technical system can be applied to the exploration of the lunar ionospheric environment.