Spin rate and spin axis orientation of LARES spectrally determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) is a powerful technique able to measure spin rate and spin axis orientation of the fully passive, geodetic satellites. This work presents results of the spin determination of LARES – a new satellite for testing General Relativity. 529 SLR passes measured between February 17 and June 9, 2012, were spectrally analyzed. Our results indicate that the initial spin frequency of LARES is f₀ = 86.906 mHz (RMS = 0.539 mHz). A new method for spin axis determination, developed for this analysis, gives orientation of the axis at RA = 12^h22^m48^s (RMS = 49^m), Dec = −70.4° (RMS = 5.2°) (J2000.0 celestial reference frame), and the clockwise (CW) spin direction. The half-life period of the satellite’s spin is 214.924 days and indicates fast slowing down of the spacecraft.     

Spectral filter for signal identification in the kHz SLR measurements of the fast spinning satellite Ajisai

The high repetition rate satellite laser ranging (SLR) measurements to the fast spinning satellites contain a frequency signal caused by the rotational motion of the corner cube reflector (CCR) array. The spectral filter, developed here, is based on the Lomb algorithm, and is tested with the simulated and the observed high repetition rate SLR data of the geodetic satellite Ajisai (spin period ∼2 s). The filter allows for the noise elimination from the SLR data, and for identification of the returns from the single CCRs of the array – even for the low return rates. Applying the spectral filter to the simulated SLR data increases the S/N ratio by a factor 40–45% for all return rates. Filtering out the noise from the observed data strengthens the frequency signal by factor of ∼25 for the low return rates, which significantly helps to determine the spin phase of the satellite. The spectral filter is applied to the Graz SLR data and the spin rates of Ajisai are determined by two different methods: the frequency analysis and the phase determination of the spinning retroreflector array.The analysis of more than 8 years of the Graz SLR measurements indicates an exponential spin rate trend: f = 0.67034 exp(−0.0148542 Y) [Hz], RMS = 0.085 mHz, where Y is the year since launch. The highly accurate spin rate information demonstrates periodic changes related to the precession of the orbital plane of Ajisai, as it determines the amount of energy received by the satellite from the Sun. The rate of deceleration of Ajisai is not constant: the half life period of the satellite’s spin oscillates around 46.7 years with an amplitude of about 5 years.     

Estimation of the Love and Shida numbers: h2, l2 using SLR data for the low satellites

In this paper we present results for the global elastic parameters: Love number h₂ and Shida number l₂ derived from the analysis of Satellite Laser Ranging (SLR) data. SLR data for the two low satellites STELLA (H = 800 km) and STARLETTE (H = 810 km) observed during 2.5 years from January 3, 2005 until July 1, 2007 with 18 globally distributed ground stations were analyzed. The analysis was done separately for the two satellites. We do a sequential analysis and study the stability and convergence of the estimates as a function of length of the data set used.     

ETALON spin period determination from kHz SLR data

Using kHz Satellite LASER Ranging (SLR) data of the SLR station Graz only, we determined the spin periods of the two ETALON satellites – launched into high orbits of about 20,000 km – and their spin period increase during 3 years. The determined spin period values and spin period increase rates at 2004-01-01 are: T_ET1 = 63 s + 0.484 s/year, and T_ET2 = 65.5 s + 0.401 s/year.     

Determination of station positions and velocities from laser ranging observations to Ajisai,Starlette and Stella satellites

The positions and velocities of the four Satellite Laser Ranging (SLR) stations: Yarragadee (7090), Greenbelt (7105), Graz (7839) and Herstmonceux (7840) from 5-year (2001–2005) SLR data of low orbiting satellites (LEO): Ajisai, Starlette and Stella were determined. The orbits of these satellites were computed from the data provided by 20 SLR stations. All orbital computations were performed by means of NASA Goddard’s GEODYN-II program. The geocentric coordinates were transformed to the topocentric North–South, East–West and Vertical components in reference to ITRF2005. The influence of the number of normal points per orbital arc and the empirical acceleration coefficients on the quality of station coordinates was studied. To get standard deviation of the coordinates determination lower than 1 cm, the number of the normal points per site had to be greater than 50. The computed positions and velocities were compared to those derived from LAGEOS-1/LAGEOS-2 data. Three parameters were used for this comparison: station coordinates stability, differences from ITRF2005 positions and velocities. The stability of coordinates of LEO satellites is significantly worse (17.8 mm) than those of LAGEOS (7.6 mm), the better results are for Ajisai (15.4 mm) than for Starlette/Stella (20.4 mm). The difference in positions between the computed values and ITRF2005 were little bit worse for Starlette/Stella (6.6 mm) than for LAGEOS (4.6 mm), the results for Ajisai were five times worse (29.7 mm) probably due to center of mass correction of this satellite. The station velocities with some exceptions were on the same level (≈1 mm/year) for all satellites. The results presented in this work show that results from Starlette/Stella are better than those from Ajisai for station coordinates determination. We can applied the data from LEO satellites, especially Starlette and Stella for determination of the SLR station coordinates but with two times lower accuracy than when using LAGEOS data.     

10 Years of LAGEOS-1 and 15 years of LAGEOS-2 spin period determination from SLR data

Satellite Laser Ranging (SLR) stations measure distance to the satellites equipped with Corner Cube Reflectors (CCRs). These range measurements contain information about spin parameters of the spacecraft. In this paper we present results of spin period determination of two passive satellites from SLR data only: 10 years of LAGEOS-1 (10426 values), and 15 years of LAGEOS-2 (15580 values). The measurements have been made by standard 10 Hz SLR systems and the first 2 kHz SLR system from Graz (Austria). The obtained data allowed calculation of the initial spin period of the satellites: 0.61 s for LAGEOS-1 and 0.906 s for LAGEOS-2. Long time series of the spin period values show that the satellite’s slowing down rate is not constant but is oscillating with a period of 846 days for LAGEOS-1 and 578 days for LAGEOS-2. The results presented here definitely prove that the SLR is a very efficient technique able to measure spin period of the geodetic satellites.     

Contribution of satellite laser ranging to combined gravity field models

In the framework of satellite-only gravity field modeling, satellite laser ranging (SLR) data is typically exploited to recover long-wavelength features. This contribution provides a detailed discussion of the SLR component of GOCO02S, the latest release of combined models within the GOCO series. Over a period of five years (January 2006 to December 2010), observations to LAGEOS-1, LAGEOS-2, Ajisai, Stella, and Starlette were analyzed. We conducted a series of closed-loop simulations and found that estimating monthly sets of spherical harmonic coefficients beyond degree five leads to exceedingly ill-posed normal equation systems. Therefore, we adopted degree five as the spectral resolution for real data analysis. We compared our monthly coefficient estimates of degree two with SLR and Gravity Recovery and Climate Experiment (GRACE) time series provided by the Center for Space Research (CSR) at Austin, Texas. Significant deviations in C₂₀ were noted between SLR and GRACE; the agreement is better for the non-zonal coefficients. Fitting sinusoids together with a linear trend to our C₂₀ time series yielded a rate of (−1.75 ± 0.6) × 10⁻¹¹/yr; this drift is equivalent to a geoid change from pole to equator of 0.35 ± 0.12 mm/yr or an apparent Greenland mass loss of 178.5 ± 61.2 km³/yr. The mean of all monthly solutions, averaged over the five-year period, served as input for the satellite-only model GOCO02S. The contribution of SLR to the combined gravity field model is highest for C₂₀, and hence is essential for the determination of the Earth’s oblateness.     

22 Years of AJISAI spin period determination from standard SLR and kHz SLR data

Satellite Laser Ranging (SLR) is a powerful and efficient technique to measure spin parameters of satellites equipped with corner cube reflectors. We obtained spin period determination of the satellite AJISAI from SLR data only: 17246 pass-by-pass estimates from standard 1–15 Hz SLR data (14/Aug/1986–30/Dec/2008) and 1444 pass-by-pass estimates (9/Oct/2003–30/Dec/2008) from data of the first 2 kHz SLR system from Graz, Austria. A continuous history of the slowing down of AJISAI spin is derived from frequency analysis, and corrected for the apparent effects. The apparent corrections, elaborated here, allowed very accurate determination of AJISAI initial spin period: 1.4855 ± 0.0007 [s]. The paper identifies also non-gravitational effects as a source of the periodical changes in the rate of slowing down of the satellite.     

Spin parameters of High Earth Orbiting satellites Etalon-1 and Etalon-2 determined from kHz Satellite Laser Ranging data

The high repetition rate Satellite Laser Ranging (SLR) system developed in Graz, Austria, measures ranges to the High Earth Orbiting satellites Etalon-1 and Etalon-2 with the millimeter accuracy. The 2 kHz repetition rate of the laser and the relatively high return rates allow to use the SLR data to calculate the spin parameters of the Etalon satellites. The analysis of the 10 years (October 2003–September 2013) of the SLR data gives trends of the spin axes orientation (J2000 Inertial Reference Frame):     

Estimation of the elastic Earth parameters (h2, l2) using SLR data

We present results for the global elastic parameters h₂ and l₂ derived from the analysis of Satellite Laser Ranging (SLR) data. SLR data for the two satellites LAGEOS 1 and LAGEOS 2 observed during 2.5 years from January 3, 2005 until July 1, 2007 with 18 globally distributed ground stations were analysed using different approaches. The analysis was done separately for the two satellites and approaches to estimate the two elastic parameters independently and together were performed. We do a sequential analysis and study the stability of the estimates as a function of length of the data set used. The adjusted final values for h₂ equal to 0.6151 ± 0.0008 and 0.6152 ± 0.0008, and those for l₂ equal to 0.0886 ± 0.0003 and 0.0881 ± 0.0003 for LAGEOS 1 and LAGEOS 2 tracking data are compared to other independently derived estimates. These parameters and their errors achieve stability at about the 24 and 27 month time interval for h₂ and l₂, respectively.     

Spin axis orientation of Ajisai determined from Graz 2 kHz SLR data

The Graz 2 kHz Satellite Laser Ranging (SLR) measurements allow determination of the spin axis orientation of the geodetic satellite Ajisai. The high repetition rate of the laser makes it possible to determine the epoch time when the laser is pointing directly between two corner cube reflector (CCR) rings of the satellite. Identification of many such events during a few (up to 3) consecutive passes allows to state the satellite orientation in the celestial coordinate system. Six years of 2 kHz SLR data (October 2003–October 2009) delivered 331 orientation values which clearly show precession of the axis along a cone centered at 14^h56^m2.8^s in right ascension and 88.512° in declination (J2000.0 celestial reference frame) and with an half-aperture angle θ of 1.405°. The spin axis precesses with a period of 117 days, which is equal to the period of the right ascension of the ascending node of Ajisai’s orbit. We present a model of the axis precession which allows prediction of the satellite orientation – necessary for the envisaged laser time transfer via Ajisai mirrors.     

Optical response of nanosatellite BLITS measured by the Graz 2 kHz SLR system

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The optical response of BLITS has been measured by the Graz 2 kHz SLR station and compared with the response of the classical retroreflector arrays (RRA) of the Low Earth Orbiting satellites such as ERS-2 and Stella. This work demonstrates that the optical response of BLITS is flat and featureless, comparable with the signature of a point-source or a flat target, and suggests that this innovative design will deliver a higher normal point (NP) accuracy (2.55 mm) than any other SLR target currently in orbit. The high reflectivity of the glassy BLITS (about 60% of the return rate from the multi-reflector Stella) is found to be decreasing by about 30% per year, probably due to the solar irradiation. Detailed analysis of the reflective half-shell demonstrates that a high return rate of SLR measurements can be achieved regardless of the incident angle of the laser beam, thus making the spherical lens a perfect successor of the classical RRA panels mounted on active satellites such as CHAMP, GOCE and GRACE.     

Spin parameters of nanosatellite BLITS determined from Graz 2 kHz SLR data

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The 2 kHz SLR station Graz measures spin parameters of this satellite, providing information about the rotational dynamics of the body. The measurements obtained during the period from September 26, 2009 to November 24, 2010 show a significant change of the spin configuration. The spin axis was dynamically precessing since the launch and currently is sinus-like behaving between coordinates RA 120°…150°, Dec 30°…60° (J2000 inertial reference frame). The angle between the symmetry axis and the spin axis of BLITS is not constant, but is decreasing since the launch, while its spin period is rather stable with a mean value of 5.613 s (clockwise rotation). The satellite was dynamically changing its attitude during the first three months after deployment; after this time the spin parameters are relatively stable.     

First astrometric observations of space debris with the MéO telescope

The MéO (for Métrologie Optique) telescope is the Satellite and Lunar Laser Ranging (SLR) dedicated telescope of Observatoire de la Côte d’Azur (France) located at plateau de Calern. The telescope uses an altazimuth mount. The motorization of the mount has a capability of 6 deg/s allowing the follow up of Low Earth Orbits (LEO) satellites, as well as Medium Earth Orbits (MEO) and geostationary (GEO) satellites, and the Moon. The telescope has a primary mirror of 1.54 m. It uses a Nasmyth focus equipped with an EMCCD camera. The telescope field of view, defined by the equivalent focal length and the size of the camera, is currently 3.4 arcmin × 3.4 arcmin.     

Rotational constants of linear and/or bent Cn+1H and CnN(n = 1–6): A DFT study

The geometries, dipole moments, and rotational constants for the linear and/or bent cations, C_n+1H⁺ and C_nN⁺(n = 1–6), were studied by the B3LYP method with the modest basis sets. For C_nH⁺(n = odd; 3, 5, 7) and C_nN⁺(n = even; 2, 4, 6), the theoretical rotational constants (B_es) of closed-shell singlet C₃H⁺, C₅H⁺, C₇H⁺, CCN⁺, C₄N⁺, and C₆N⁺ were calculated to be about 11,244, 2420, 885.2, 11,970, 2439, and 880.8 MHz, respectively. By contrast, the triplets are stable than the corresponding singlets for C_nH⁺(n = odd; 2, 4, 6) and C_nN⁺(n = even; 3, 5) except CN⁺.     

Nusselt number for convection driven by tidal and radiogenic heating

The ‘traditional’ formulas giving the Nusselt number Nu as a function of Rayleigh number Ra cannot be used for low and moderate values of Ra. Moreover, the recent progress in 3D numerical modeling makes possible to determine the Nusselt number Nu as a function of Rayleigh number Ra for convection driven by radiogenic and tidal heating. We found that for low and moderate Ra: Nu(Ra) = ε(Ra+ξ)^λ where λ depends on rheology and boundary conditions, ε depends only on the mode of heating, and ξ = ε^−1/λ · Nu(Ra) makes possible to develop a parameterized theory of convection in medium size icy satellites. We also indicate some differences between convection driven by tidal and radiogenic heating and convection driven exclusively by radiogenic heating.     

Advanced architectures for real-time Delay-Doppler Map GNSS-reflectometers: The GPS reflectometer instrument for PAU (griPAU)

In recent years Global Navigation Satellite System’s signals Reflectometry (GNSS-R) has stood as a potential powerful remote sensing technique to derive scientifically relevant geophysical parameters such as ocean altimetry, sea state or soil moisture. This has brought out the need of designing and implementing appropriate receivers in order to track and process this kind of signals in real-time to avoid the storage of huge volumes of raw data. This paper presents the architecture and performance of the Global Positioning System (GPS) Reflectometer Instrument for PAU (griPAU), a real-time high resolution Delay-Doppler Map reflectometer, operating at the GPS L1 frequency with the C/A codes. The griPAU instrument computes 24 × 32 complex points DDMs with configurable resolution (Δf_Dmin = 20 Hz, Δτ_min = 0.05 chips) and selectable coherent (minimum = 1 ms, maximum = 100 ms for correlation loss Δρ < 90%) and incoherent integration times (minimum of one coherent integration period and maximum not limited but typically <1 s). A high sensitivity (DDM peak relative error = 0.9% and DDM volume relative error = 0.03% @ T_i = 1 s) and stability (Δρ/Δt = −1 s⁻¹) have been achieved by means of advanced digital design techniques.     

Quantifying the relationship between the measurement precision and specifications of a UV/visible sensor on a geostationary satellite

To investigate the feasibility of new satellite observations, including air quality (AQ) observations from geostationary (GEO) orbit, it is essential to link the measurement precision (ε) with sensor specifications in advance. The present study attempts to formulate the linkage between ε and specifications of a UV/visible sensor (signal-to-noise ratio (SNR), full width at half maximum (FWHM) of the slit function, and sampling ratio (SR)) on a GEO satellite. A sophisticated radiative transfer model (JACOSPAR) is used to calculate synthetic radiance spectra that would be measured by a UV/visible sensor observing the atmosphere over Tokyo (35.7°N, 139.7°E) from GEO orbit at 120°E longitude. The spectra, modified according to given sensor specifications, are analyzed by the differential optical absorption spectroscopy technique to estimate the ε for slant column densities of O₃ and NO₂. We find clear relationships: for example, the ε of the O₃ slant column density (molecules cm⁻²) and SNR at 330 nm are linked by the equation log(ε) = −1.06 · log(SNR) + 20.71 in the UV region, and the ε of the NO₂ slant column density and SNR at 450 nm are linked by log(ε) = −0.98 · log(SNR) + 18.00, at a FWHM = 0.6 nm (for the Gaussian slit function) and SR = 4. The relationships are mostly independent of other specifications (e.g., horizontal and temporal resolutions), as they affect ε primarily through SNR, providing constraints in determining the optimal SNR (and alternatively FWHM and SR) for similar UV/visible sensors dedicated for AQ studies.     

Compact frequency standard using atoms trapped on a chip

We present a compact atomic frequency standard based on the interrogation of magnetically trapped ⁸⁷Rb atoms. Two photons, in the microwave and radiofrequency domain excite the atomic transition. At a magnetic field of 3.23 G this transition from ∣F = 1, m_F = −1〉 to ∣F = 2, m_F = 1〉 is 1st order insensitive to magnetic field variations. Long Ramsey interrogation times can thus be achieved, leading to a projected stability in the low 10⁻¹³ at 1 s. This makes this device a viable alternative to LITE and HORACE as a good candidate for replacing or complementing the rubidium frequency standards and passive hydrogen masers already on board of the GPS, GLONASS, and GALILEO satellites. Here we present preliminary results. We use an atom chip to cool and trap the atoms. A coplanar waveguide is integrated to the chip to carry the Ramsey interrogation signal, making the physics package potentially as small as (5 cm)³. We describe the experimental apparatus and show preliminary Ramsey fringes of 1.25 Hz linewidth. We also show a preliminary frequency stability σ_y = 1.5 × 10⁻¹²τ^−1/2 for 10 < τ < 10³ s. This represents one order of magnitude improvement with respect to previous experiments.     

Studies of electron and ion temperatures at 500 km altitude during sunrise using Indian SROSS C2 satellite

Solar dependence of electron and ion temperatures (T_e and T_i) in the ionosphere is studied using RPA data onboard SROSS C2 at an altitude of ∼500 km and 77°E longitude during early morning hours (04:00–07:00 LT) for three solar activities: solar minimum, moderate and maximum during winter, summer and equinox months in 10°S–20°N geomagnetic latitude. In winter the morning overshoot phenomenon is observed around 06:00 LT (T_e enhances to ∼4000 K) during low-solar activity and to T_e ∼ 3800 K, during higher solar activity. In summer, it is observed around 05:30 LT, but the rate of T_e enhancement is higher during moderate solar activity (∼2700 K/hr) than the low-solar activity (∼1700 K/hr). During equinox, this phenomenon is delayed and is observed around 06:00 LT (∼4200 K) during all three activities.