Determination of relative position between two stations using the translocation technique in satellite doppler tracking

The main errors in satellite Doppler positioning are ephemeris errors and refraction errors. For different stations observing the same satellite pass, these errors are correlated. By taking advantage of the correlation, we can increase the positioning accuracy. We have applied this “translocation” technique /5,6/ to 14 passes on 1980 August 23–24 observed at Beijing and Shanghai. Our result on the relative coordinates between these two stations has an internal accuracy of ± 2m, and our result on the baseline length differs from the geodetic result by 1.5m.     

Ionospheric scale height from the refraction of satellite signals

Accurate observations of the elevation angle of arrival of 20 MHz signals from the polar orbiting satellite Beacon-B for a 20 month period have provided transmission ionograms which may be reduced to give H_p, the scale height at the peak of the ionosphere. Noon seasonal averages of H_p are 1.35 (in winter) to 1.55 (in summer) times greater than the scale height obtained from bottom-side ionograms. A comparison of scale height at the peak with routine measurements of total content and peak electron density indicates that the O⁺/H⁺ transition level is above 1000 km during the day but comes down to about 630 km on winter nights. A predawn peak in the overall scale height (∝ total content/peak density) is caused by a lowering of the layer to a region of increased recombination and is magnified in winter by low O⁺/H⁺ transition levels. After sunrise in winter and equinoxes the overall scale height is less than the scale height at the peak, implying an outwards flux of ionisation which lasts for about three hours. The summer evening increase in ƒ₀F2 requires both a cooling and a raising of the layer for its occurrence.     

A method to determine regional lunar gravity fields from earth-based satellite tracking data

A method to determine regional gravity fields of the Moon from Earth-based Doppler and range satellite tracking data residuals of a low Moon-orbiting satellite has been developed and thoroughly tested in a controlled simulation environment. A short-arc approach, where one arc consists of the time it takes the satellite to cross the grid of interest on the lunar surface, is used in order to filter out most long-wavelength signal that can still be present in the residuals. Simulation results where the data are contaminated with either typical systematic or stochastic noise show that recovery of the local gravity field down to the level of several mGal is possible. The inclusion of extremely low-altitude data also means that regularisation in the sense of including a priori information in the form of a regularisation matrix is not necessary in order to obtain a good solution at high resolution.     

The secular acceleration of the Moon determined from lunar laser ranging data

Lunar Laser Ranging data covering the interval from August 1969 to December 1987 were used to determine the seculer acceleration in the mean longitude of the Moon (\.n). In our analysis, the DE200/LE200 planets and lunar ephemerides were adopted for calculating the theoretical distance between the observing station and reflector. The method of stepwise regression was used in the processing of the data and the value of –25.4 ± 0. 1/cy² was obtained by a weighted least squares fit.Our result is in good agreement with that derived by other authors using various methods. The uncertainty (\.n) estimated from LLR data would be decreasing rapidly with increasing the data span. The high precision obtained in this paper is mainly due to the longer span and higher measuring accuracy of data.     

Some results of investigating the stability of operation of the Ukrainian laser ranging stations

The stability of operation of the network of the Ukrainian laser ranging stations Simeiz, Katsyveli, Holosiiv-Kyiv, and L’viv is investigated by analyzing the Lageos-1 and Lageos-2 observations made over the period from January 5, 1989 through November 11, 2004. The coordinate determination stability is estimated for each station. Some factors which affect the network operation stability are pointed out.     

Spherical harmonic representation of the gravity field from dynamic satellite data

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:

$\text{(C}{}^1\text{, S}{}^1\text{) = (C}{}_{\mathrm{o}}\text{, S}{}_{\mathrm{o}}\text{) + Σ}{}_{\mathrm{i}}\text{= 1 (C}{}_{\mathrm{Ci}}\text{, S}{}_{\mathrm{Ci}}\text{) cos i ω + (C}{}_{\mathrm{Si}}\text{, S}{}_{\mathrm{Si}}\text{) sin i ω}$

. 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.     

Methods of calculating atmospheric densities from satellite orbit data

Formulae relating atmospheric density to the rate of change of period of a satellite have been obtained by various workers for two asymptotic cases: (i) eccentricity e small (< 0.3) and (ii) e large (> 0.012). These results arc reviewed, and in the overlapping region, 0.012 < e < 0.3, the formulae are shown to be in agreement to the various orders of magnitude considered.     

Study of Mars dynamics from lander tracking data analysis

After the touchdown of the two Viking landers on Mars, radio tracking measurements have been performed between them and Earth-based stations. With use of the first 9 months of data, we have improved the rotation rate and the mean orientation of the spin axis of Mars, referred to its mean orbit. For the first time, some nutations terms have also been estimated. Nevertheless the precise determination of the spin axis motion will require additional data collected during the extended mission. Our solution includes also the lander locations and the relativistic parameter .Paper presented at the European Workshop on Planetary Sciences, Organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Improvement of the numerical lunar ephemeris with laser ranging data

Analysis of lunar laser ranging data is underway at several institutions. We describe here our efforts at improving the numerical ephemeris of Moon, based on over three years' span of data. Orbit generation and correction procedures are discussed briefly. Comparisons of the new ephemeris with observations and with a widely available ephemeris are illustrated. The standard deviation of the observation residuals is 7 m.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.     

Gravity field of Mars from Mariner 9 tracking data

Further reduction of Doppler tracking data from Mariner 9 confirms our earlier conclusion that the gravity field of Mars is considerably rougher than the fields of either the Earth or the Moon. The largest positive gravity anomaly uncovered is in the Tharsis region which is also topographically high and geologically unusual. The best determined coefficients of the harmonic expansion of the gravitational potential are: J₂ = (1.96 ± 10.01) × 10^?3 ; C₂₂ = ?(5.1 ± 0.2) × 10^?5; and S₂₂ = (3.4 ± 0.2) × 10^?5. The other coefficients have not been well determined on an individual basis, but the ensemble yields a useful model for the gravity field for all longitudes in the vicinity of 23° South latitude which corresponds to the periapse position for the orbiter.The value obtained for the inverse mass of Mars (3 098 720 ± 70 M⊙^?1) is in good agreement with prior determinations from Mariner flyby trajectories. The direction found for the rotational pole of Mars, referred to the mean equinox and equator of 1950.0, is characterized by α = 317°.3 ± 0°.2, δ = 52°.7 ± 0°.2. This result is in excellent agreement with Sinclair's recent value, determined from earth-based observations of Mars' satellites, but differs by about 0°.5 from the previously accepted value. Other important physical constants that have either been refined or confirmed by the Mariner 9 data include: (i) the dynamical flattening, f = (5.24 ± 0.02) × 10^?3; (ii) the maximum principal moment of inertia, C = (0.375 ± 0.006) MR²; and (iii) the period of precession of Mars' pole, P ? (1.73 ± 0.03) × 10⁵ yr, corresponding to a rate of 7.4 sec of arc per yr.     

Estimation of the dissociation energy of CO+ from spectroscopic data

The potential energy curves for theX ² Σ⁺ andB ² Σ⁺ states of CO⁺ have been constructed by the Rydberg-Klein-Rees (RKR) method as modified by van der Sliceet al. The dissociation energy is estimated to be 7.70±0.19 eV by the method of curve fitting using the five parameter Hulburt-Hirschfelder’s function. The estimated value is in good agreement with the value (7.839 eV) given by Misraet al. Carefull observation of the results reveals that accurateD ₀ value for CO⁺ is 8.33 eV     

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.     

17 years of ranging from the Helwan SLR station

The satellites laser ranging from Helwan SLR station during the last 20 years are discussed. The internal calibration method used at the Helwan SLR station is explained. The root mean square value of the calibrations carried out during the period from 1991 to 2008 is computed. To clarify the difference in the accuracy of the measurements, the results of the analysis of the data taken for all the satellites after the upgrading (2000) are given and compared with those of the satellites observed before the upgrading (1996). The total number of passes of the satellite observed during the period from 1991 to 2008 is presented and the results are compared with the other SLR stations.     

Solutions and periodicity of satellite relative motion under even zonal harmonics perturbations

Finding relative satellite orbits that guarantee long-term bounded relative motion is important for cluster flight, wherein a group of satellites remain within bounded distances while applying very few formationkeeping maneuvers. However, most existing astrodynamical approaches utilize mean orbital elements for detecting bounded relative orbits, and therefore cannot guarantee long-term boundedness under realistic gravitational models. The main purpose of the present paper is to develop analytical methods for designing long-term bounded relative orbits under high-order gravitational perturbations. The key underlying observation is that in the presence of arbitrarily high-order even zonal harmonics perturbations, the dynamics are superintegrable for equatorial orbits. When only J ₂ is considered, the current paper offers a closed-form solution for the relative motion in the equatorial plane using elliptic integrals. Moreover, necessary and sufficient periodicity conditions for the relative motion are determined. The proposed methodology for the J ₂-perturbed relative motion is then extended to non-equatorial orbits and to the case of any high-order even zonal harmonics (J _2n , n ≥ 1). Numerical simulations show how the suggested methodology can be implemented for designing bounded relative quasiperiodic orbits in the presence of the complete zonal part of the gravitational potential.     

Method of unit vectors for the determination of preliminary orbit with single-arc and single-station ranging data

We present a method of unit vectors of calculating preliminary orbit with single-station and single-arc ranging data, assuming known orbital plane parameters i and Ω. Practical calculations show that this method is effective. This method is particularly valuable in cases where the angle data are either unavailable or obviously less accurate than the ranging data.     

Simultaneous solution for the masses of the principal planets from analysis of optical,radar, and radio tracking data

The Jet Propulsion Laboratory has developed a set of computer programs known as the Solar System Data Processing System (SSDPS) which is employed in improving the ephemerides of the major planets and for improving the values of several associated astronomical constants. A group of solutions for the masses of the major planets, together with the AU and radii of Mercury, Venus, and Mars, is presented. These solutions based upon optical, radar, and spacecraft radio tracking data are preliminary. The relative power of radar and radio tracking data vis-à-vis purely optical data in a solution is shown. The problems which could arise by adopting solutions based upon a single data type are demonstrated.Presented at IAU Colloquium No. 9, the IAU System of Astronomical Constants' Heidelberg, Germany, August 12–14, 1970.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Processing and compression of noise-dominated data: application to the cosmic microwave background data on board the Planck satellite

We address the problem of encoding and compressing data dominated by noise. Information is decomposed into 'reference' sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download-rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates,     can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck , this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps.     

Solar protons in the Earth’s magnetosphere from riometric and satellite data during magnetic storms in October 2003

The fluxes and penetration boundaries of solar energetic particles on the CORONAS-F satellite during October 2003 superstorms are compared with the riometric absorption measurements on a worldwide network of riometers. The dynamics of the polar cap boundaries is investigated at various phases of magnetic storms. The dependence of absorption on time of the day and on solar proton spectrum is calculated at various phases of a solar energetic particle event.