Spacecraft Doppler tracking with possible violations of LLI and LPI:upper bounds from one-way measurements on MEX

We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express(MEX) spacecraft to test possible violations of local Lorentz invariance(LLI) and local position invariance(LPI).These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China.These downlink signals were sent by MEX for telemetry at X-band.Because we are not able to decode the data in the form of telemetry and separate them from the carrier frequency,this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s~(-1).Even so,the residuals can still impose upper bounds on LLI and LPI at 10~(-1),which is consistent with the prediction based on our analysis of the detectability.Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work,one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.     

Spacecraft Doppler tracking with possible violations of LLI and LPI: a theoretical modeling

Currently two-way and three-way spacecraft Doppler tracking techniques are widely used and play important roles in control and navigation of deep space missions.Starting from a one-way Doppler model,we extend the theory to two-way and three-way Doppler models by making them include possible violations of the local Lorentz invariance(LLI) and the local position invariance(LPI) in order to test the Einstein equivalence principle,which is the cornerstone of general relativity and all other metric theories of gravity.After taking the finite speed of light into account,which is the so-called light time solution(LTS),we make these models depend on the time of reception of the signal only for practical convenience.We find that possible violations of LLI and LPI cannot affect two-way Doppler tracking under a linear approximation of LTS,although this approximation is sufficiently good for most cases in the solar system.We also show that,in three-way Doppler tracking,possible violations of LLI and LPI are only associated with two stations,which suggests that it is better to set the stations at places with significant differences in velocities and gravitational potentials to obtain a high level of sensitivity for the tests.     

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.     

Coronal velocity measurements with Ulysses: multi-link correlation studies during two superior conjunctions

A well-known method for studying the solar wind very close to the Sun (heliocentric distances: 4 to 40 solar radii) is by radio sounding between a spacecraft at superior conjunction and the Earth. The Ulysses Solar Corona Experiment was performed at the spacecraft's two solar conjunctions in summer 1991 and winter 1995, during which dual-frequency ranging and Doppler observations were conducted globally on a nearly continuous basis at the NASA Deep Space Network and other ground stations. The dual-frequency Doppler measurements were used to determine coronal plasma velocities by a cross-correlation analysis during those occasions when tracking data were recorded simultaneously at two well-separated ground stations. A filtering technique was developed to suppress noise and enhance the 2-station correlations, a procedure particularly effective at small solar offsets. From the electron content measurements during the two solar conjunctions it was found that regions of higher electron density tend to occur when the two-station correlations yield slower outward flow velocities.     

Results of IPS Observations in the Period Near Solar Activity Minimum

IPS observations with the Big Scanning Array of Lebedev Physical Institute (BSA LPI) radio telescope at the frequency 111 MHz have been monitored since 2006. All the sources, about several hundred daily, with a scintillating flux greater than 0.2 Jy are recorded for 24 hours in the 16 beams of the radio telescope covering a sky strip of 8^° declination width. We present some results of IPS observations for the recent period of low solar activity considering a statistical ensemble of scintillating radio sources. The dependences of the averaged over ensemble scintillation index on heliocentric distance are considerably weaker than the dependence expected for a spherically symmetric geometry. The difference is especially pronounced in the year 2008 during the very deep solar activity minimum period. These features are explained by the influence of the heliospheric current sheet that is seen as a strong concentration of turbulent solar wind plasma aligned with the solar equatorial plane. A local maximum of the scintillation index is found in the anti-solar direction. Future prospects of IPS observations using BSA LPI are briefly discussed.     

Insight-building models for lunar range and range rate

The analysis of range or Doppler data between sites on the Earth and Moon requires an accurate computation of the lunar orbit and detailed models of the orientation of the Earth and Moon. Models constructed to understand range and range rate can lack detail, but if they include the largest lunar orbit variations, tracking stations on a rotating Earth, and lunar sites on a synchronously rotating Moon, then they will display the largest effects for orbit elements, Earth orientation, tracking station locations, and lunar site coordinates. The range and range rate are expanded into periodic series. To understand accurate solutions, the largest periodic terms that are sensitive to various solution parameters indicate the sensitivity of data to solution parameters and the time spans needed for their determination. Conclusions include: cylindrical coordinates work well for sites on the rapidly rotating Earth, but Cartesian coordinates are more natural for the synchronously rotating Moon since the series for the three coordinate projections are distinct. For range and range rate data, daily, semimonthly, monthly, and longer periods are present. For Doppler data, the daily periods may be stronger and more useful than the long periods, particularly for terms associated with the terrestrial tracking station. Doppler data do not determine the lander coordinate toward the Earth well. Observational strategies for range and Doppler data are not identical. For all data types, one wishes a variety of hour angles, lunar declinations, times of month, and longer periods. A long span of high-quality range data can improve the lunar orbit, orientation of the Earth’s equator, and physical librations. The locations of new lunar sites or new tracking stations can be determined from shorter spans of data.     

2010年上海天文台卫星激光测距观测报告

介绍了2010年上海天文台卫星激光测距的常规观测和白天千赫兹激光测距情况。在国际上首次对同步轨道卫星开展了千赫兹激光测距,作用距离达38800多千米,测距系统性能达到国际先进水平。利用2套独立的激光测距系统,开展了激光收发分离测距实验,为行星际异步应答式激光测距模拟试验提供了实测数据。最后概述了空间碎片目标激光测距进展情况。     

Tropospheric Delay from VLBI and GNSS Measurements

Using an updated version of the QUASAR software package developed at the Institute of Applied Astronomy of the Russian Academy of Sciences, we have processed the VLBI observations within the international CONT14 program (May 6–20, 2014), in which a global network of 17 stations was involved (a total of ~250 000 observations). The package update concerned the optimization of data structure and the refinement of stochastic models for the random variations in wet tropospheric delay and atomic clock difference. The main goal of this paper is to compare the VLBI determinations of the tropospheric delay with its independent determinations using global navigation satellite systems (GNSS). We show that both these determinations agree well between themselves only in the case of a global analysis of the VLBI observations, where the VLBI station coordinates are also refined, along with the tropospheric delay and the clock synchronization and Earth orientation parameters. If, alternatively, the station coordinates are insufficiently accurate and are not refined from VLBI observations, then it is appropriate not to determine the tropospheric delay from these observations, but to take it from the publicly accessible independent GNSS data. However, this requires that the VLBI and GNSS techniques operate simultaneously at a common observing site. We have established the shortcomings of the universally accepted method of stabilizing the global solution associated with the absence of a criterion for choosing reference stations and radio sources. Two ways of their elimination are proposed: (i) introducing a coordinated list of weight factors for the errors in the coordinates of such stations and sources into the stabilization algorithm and (ii) adopting a coordinated list of stations and sources the refinement of whose coordinates is not required at all for a certain time.     

Can variable meridional flows lead to false exoplanet detections?

The search for habitable exoplanets centers on planets with Earth-like conditions around late type stars. Radial velocity searches for these planets require precisions of 1 m/s and better. That is now being achieved. At these precisions stellar surface motions might lead to false detections. Of particular interest are variable meridional flows on stellar surfaces. I review the available observations of solar surface meridional flows using both Doppler shift and local helioseismology techniques. Interpretation in terms of Doppler shifts in integrated starlight leads to estimates of the likelihood of false detections. It is unlikely that these false detections occur in the habitability zones of exoplanets. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Venus Doppler winds at cloud tops observed with ESPaDOnS at CFHT

We present new wind measurements in Venus’ lower mesosphere from visible spectroscopy during the 2007 worldwide coordinated ground campaign in support of ESA's Venus Express mission. These observations consisted of high-resolution spectra of Fraunhofer lines in the entire visible range (0.37-1.05 μm) to measure the winds near 68 km using the Doppler shift of solar radiation scattered by clouds toward the observer's direction. The observations included various points of the dayside hemisphere at a phase angle of ∼109°. We took advantage of two symmetrical elongations in July and September 2007 at Canada-France-Hawaii's 3.6-m telescope. Kinematical fits to the Doppler winds provide a mean equatorial velocity of (104±10) m s⁻¹ for the zonal retrograde flow. This velocity agrees quite well with the mean value obtained by tracking the UV markings from several spacecraft.     

Values of the Atmospheric Density at 280 km Obtained from Spin Drag Data of COSMOS 54 Rocket

A set of atmospheric density values at a height of 280 km between MJD 39675—39702 is determined by using the spin drag data of COSMOS 54 rocket. For this purpose photometric observations from five tracking stations and data about the satellite and its orbital evolution were used. The density values determined firstly at the perigee height were reduced at a standard height of 280 km and then compared with density values determined by using orbital drag data of this rocket at the same height and in the same time interval. The agreement between the two sets of densities (determined by using two different methods) is satisfactory.     

日本SELENE月球探测计划和卫星间多普勒跟踪的数学模型

日本月球探测计划（SELENE）定于2004年夏季利用HIIa火箭发射一组共3颗绕月人造卫星。他们是主卫星、跟踪中断卫星和空间VLBI电波源。其主要科学目标之一是利用对绕月卫星的多普勒跟踪数据精确测定月球重力场,研究月球的起源与演化。SELENE计划中实现这个科学目标的关键技术是引入中继卫星,目的在于当处于低轨道的主卫星飞行到月球背面地面观测站无法观测时,采用卫星间跟踪方法（SST）,建立地面站与主卫星之间的联系,以得到月球背面重力场的直接测量数据。介绍了几种典型的四程卫星间多普勒跟踪模式和相应的数学模型,并针对SELENE计划中采用的特殊四程多普勒跟踪模式建立了卫星相对观测站速度与跟踪信号多普勒频移之间的转换关系。提出了利用GEODYNⅡ定轨分析软件处理SELENE多普勒跟踪数据的流程。     

Martian gravity field model and its time variations from MGS and Odyssey data

We present results of several years of research and data processing aimed at modelling the Mars gravity field and its longest wavelength time variations. The new solution includes tracking data from Mars Global Surveyor (MGS) from 1998 to 2006 (end of mission) and from Mars Odyssey from 2002 to the spring of 2008; this is the longest analyzed data set from these two orbiter missions as compared to previous works. The new model has been obtained by a team working in Europe, independently from the works of groups at NASA Jet Propulsion Laboratory (JPL) and Goddard Space Flight Center (GSFC), also with totally independent software. Observations consist in two and three-way Doppler measurements (also one way for MGS), and range tracking data collected by the Deep Space Network and have been processed in 4 day arcs, taking into account all disturbing forces of gravitational and non-gravitational origins; for each arc the state vector, drag and solar pressure model multiplying factors, and angular momentum dump parameters are adjusted. The static field (MGGM08A) is represented in spherical harmonics up to degree and order 95 and is very close to previously published models (in terms of spectral components and also over specific features); correlations with the global Mars topography are established and apparent depths of compensation by degree are derived. Lumped zonal harmonics of degree two and three are solved for every 10 days, exhibiting variations in line with previous results (including authors’ ones); the work also shows the difficulty of finding clean signatures (annual and semi-annual) for the zonal coefficient of second degree. The k₂ Love number is also derived from the ensemble of data, as well as from subsets of them; values between 0.110 and 0.130 are found, which are consistent with the existence of a Martian fluid core of significant radius.     

The Zeeman broadening of high n solar recombination lines

The Zeeman broadening of high n lines is derived. While in areas of the quiet Sun with field strengths of 1 G the upper boundary of the observable frequency region of recombination lines is defined by electron impact broadening, in active regions with field strengths 25 G the Zeeman broadening will shift this boundary to higher frequencies. The frequency region most favourable for observations is derived and the corresponding Doppler, electron impact and Zeeman broadening are discussed. The strengths of the recombination lines obtained in earlier calculations is reduced when one considers besides the Doppler broadening the electron impact and Zeeman broadening also. The frequency region favourable for observations is compared with the atmospheric transparency of the microwave region; it is found that observations require at least high altitude stations or space-based platforms. Details of using the Zeeman broadening of high n recombination lines for mapping (coronal) magnetic fields are given.     

Mars: Hellas Planitia gravity analysis

Doppler radio tracking data from Viking Orbiter 1 has provided new detailed observations of gravity variations over Hellas Planitia. Line-of-sight Bouguer gravity definitely indicates that isostatic adjustment has occurred. Two theoretical models were tested to obtain fits to the gravity data. Results for a surface deficit model, and a model with a surface deficit and a mass excess at depth are displayed. The mass-at-depth model produced very marked improvement in the data fit as compared to the surface deficit model. The optimum depth for the mass excess is 130 km.     

The Photospheric Convection Spectrum

Spectra of the cellular photospheric flows are determined from observations acquired by the MDI instrument on the SOHO spacecraft. Spherical harmonic spectra are obtained from the full-disk observations. Fourier spectra are obtained from the high-resolution observations. The p-mode oscillation signal and instrumental artifacts are reduced by temporal filtering of the Doppler data. The resulting spectra give power (kinetic energy) per wave number for effective spherical harmonic degrees from 1 to over 3000. Significant power is found at all wavenumbers, including the small wavenumbers representative of giant cells. The time evolution of the spectral coefficients indicates that these small wavenumber components rotate at the solar rotation rate and thus represent a component of the photospheric cellular flows. The spectra show distinct peaks representing granules and supergranules but no distinct features at wavenumbers representative of mesogranules or giant cells. The observed cellular patterns and spectra are well represented by a model that includes two distinct modes – granules and supergranules.     

Numerical simulations of a Mars geodesy network experiment: Effect of orbiter angular momentum desaturation on Mars' rotation estimation

The scientific objectives of a geodetic experiment based on a network of landers, such as NEIGE (NEtlander Ionosphere and Geodesy Experiment) are to improve the current knowledge of Mars' interior and atmosphere dynamics. Such a network science experiment allows monitoring the motions of the Martian rotation axis with a precision of a few centimeters (or milli-arc-seconds (mas)) over annual and sub-annual periods. Thereto, besides radio tracking of a Mars orbiter from the Earth, radio Doppler shifts between this orbiter and several landers at the planet's surface will be performed. From the analysis of these radio Doppler data, it is possible to reconstruct the orbiter motion and Mars' orientation in space. The errors on the orbit determination (position and velocity of the orbiter) have an impact on the geodetic parameters determination from the Doppler shifts and must be removed from the signal in order to achieve a high enough accuracy. In this paper, we perform numerical simulations of the two Doppler signals involved in such an experiment to estimate the impact of the spacecraft angular momentum desaturations on the determination of Mars' orientation variations. The attitude control of the orbiter needs such desaturation maneuvers regularly repeated. They produce velocity variations that must be taken into account when determining the orbit. For our simulations, we use a priori models of the Martian rotation and introduce the spacecraft velocity variations induced by each desaturation event. By a least-squares adjustment of the simulated Doppler signals, we then estimate the orbiter velocity variations and the parameters of the Mars' rotation model. We show that these velocity variations are ill resolved when the spacecraft is not tracked, therefore requiring a near-continuous tracking from the Earth to accurately determine the orbit. In such conditions we show that only 15- of lander-orbiter tracking per week allows recovering Mars' orientation parameters with a precision of a few mas over a period of 1 Martian year.     

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.     

Orbit determination of satellite “Tance 1” with VLBI data

The satellite “Tance 1” of the “Double-Star Program” is the first truly scientific experimentation satellite of China. Its orbit is the farthest so far launched in China, with a geocentric apogee reaching 78 thousand kilometers. The tracking of “Tance 1” and of more distant space targets, such as the lunar exploration craft, can be realized with the VLBI technique of radio astronomy. In order to test and verify the role which the VLBI technique plays in the lunar exploration program of China, Shanghai Astronomical Observatory organized the only 3 tracking stations in China (located at Shanghai, Urumqi and Kunming), to carry out test tracking of “Tance 1,” and used the time delay data obtained to determine the orbit of “Tance 1” over a two-day period, so providing a preliminary assessment of the possibility of VLBI orbit determination. The fitting error of the orbit so obtained is about 5.5 m in the time delay and about 2 cm/s in the delay rate (this for checking only), much better than is provided by the preliminary orbit (used merely for ensuring tracking) in which the corresponding figures are around 2 km and 15 cm/s. Further, if the orbit is determined by using both the time delay and time delay rate data (with weights according to their internal accuracies), then the residuals are 5.5 m in the time delay and 2 cm/s in the delay rate. For an appreciation of the true accuracy of the VLBI orbit determination, we used simulation data (of the observed two-day VLBI data) and found the results depended greatly on the error in the dynamic model of the satellite which, however, is difficult to assess, while the formal residuals are of the order of 1 kin in the delay and of cm/s in the delay rate. The simulation computation also indicates that a joint determination using both VLBI and USB data will have an improved accuracy.     

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C_2,2, is well determined and correlates with the equatorial shape. The S_2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J₂, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C_2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (C_m/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.