The Moon’s physical librations and determination of their free modes

The Lunar Laser Ranging experiment has been active since 1969 when Apollo astronauts placed the first retroreflector on the Moon. The data accuracy of a few centimeters over recent decades, joined to a new numerically integrated ephemeris, DE421, encourages a new analysis of the lunar physical librations of that ephemeris, and especially the detection of three modes of free physical librations (longitude, latitude, and wobble modes). This analysis was performed by iterating a frequency analysis and linear least-squares fit of the wide spectrum of DE421 lunar physical librations. From this analysis we identified and estimated about 130–140 terms in the angular series of latitude librations and polar coordinates, and 89 terms in the longitude angle. In this determination, we found the non-negligible amplitudes of the three modes of free physical libration. The determined amplitudes reach 1.296′′ in longitude (after correction of two close forcing terms), 0.032′′ in latitude and 8.183′′ × 3.306′′ for the wobble, with the respective periods of 1056.13 days, 8822.88 days (referred to the moving node), and 27257.27 days. The presence of such terms despite damping suggests the existence of some source of stimulation acting in geologically recent times.     

Harmonic development of tide-generating potential of terrestrial planets

The aim of this study is to obtain high-accurate harmonic developments of the tide-generating potential (TGP) of Mercury, Venus and Mars. The planets’ TGP values have been first calculated on the base of DE/LE-406 numerical planetary/lunar ephemerides over a long period of time and then processed by a new spectral analysis method. According to this method the development is directly made to Poisson series where both amplitudes and arguments of the series’ terms are high-degree polynomials of time. A new harmonic development of Mars TGP is made over the time period 1900 AD–2100 AD and includes 767 second-order Poisson series’ terms of minimum amplitude equal to 10⁻⁷ m² s⁻². Analogous series composing both Mercury and Venus TGP harmonic models are built over the time period 1000 AD–3000 AD and include 1,061 and 693 terms, respectively. A modification of the standard HW95 format for representation of the terrestrial planets’ TGP is proposed. The number of terms in the planets’ TGP models transformed to the modified HW95 format is 650 for Mercury, 422 for Venus, and 480 for Mars. The quality of the new developments of the terrestrial planets’ TGP is better than that of the similar developments obtained earlier.

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Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.      

Compressed planetary and lunar ephemerides

A package of FORTRAN software has been developed which provides planetary and lunar positions, with respect to the solar system barycenter, for all times in the interval 1801–2049; positions agree to 1 milliarcsecond with those generated by Jet Propulsion Laboratory Development Ephemeris 200 (DE200). The system consists of approximately 800 kilobytes of ephemeris files and 40 kilobytes of programs, totalling 5% of the storage required by DE200. After removal of reference orbits, segments of DE200 positions were fitted by finite Chebyshev series of degree 40. The Chebyshev coefficients were rounded to integer multiples of a suitable unit and packed to form the ephemeris files.     

Radio synthesis imaging of anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R⊙, the major axis scattering angle is ∼ 0.7" atλ= 6 cm and it varies with heliocentric distance asR ^-1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized toλ = 20 cm, has a value 20 ± 7 at 5R⊙and varies with heliocentric distance asR ^-3. Comparison with earlier resu lts suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scale sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are l k m at 2R⊙ and 4 km at 13R⊙. These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Russian lunar ephemeris EPM-ERA 2012

The paper describes the lunar ephemeris EPM-ERA 2012. It is a part of the Ephemerides of Planets and the Moon (EPM) developed at the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences (RAS). In order to construct EPM-ERA 2012, 17580 lunar laser ranging (LLR) observations for 1970–2012 have been processed including 21 observations from the Lunokhod 1 reflector found by the Lunar Reconnaissance Orbiter (LRO) at the end of 2010. EPM-ERA 2012 is compared with American ephemerides DE403, DE405, DE421 ephemeris, and the French ephemeris INPOP10. The possibility of the use of the ephemeris EPM-ERA 2012 to address contemporary problems of ephemeris astronomy is considered.     

Principal algorithms for the control of Kourovka Observatory SBG camera

We report the algorithms used in the software of the upgraded SBG camera. Fast-moving satellites are observed in the “rotated” coordinate system where one of the axes points towards the pole of the object’s orbit. The ephemeris for this coordinate system is computed based on the ephemeris for the equatorial coordinate system using special transition matrices. The parameters of the matrices are the coordinates of the orbital pole, which are found by averaging the vector products of the radius vectors of the consecutive positions of the satellite. The position angle of the image is computed as the difference between the hour angles of the orbital and celestial poles in the coordinate system, the pole of which coincides with the optical center of the frame. The speed of object tracking is computed via quadratic interpolation of the ephemeris in the “rotated” coordinate system.     

Topocentric aberration of the moon

Aberrational displacement of the observed topocentric positions of the Moon differ from the aberrational effect in its apparent ephemeris geocentric coordinates. The differential aberrational corrections due to the mutual positions of the observer and the Moon, may account to 0 _. ^″ 3. The reduction method of astrometric observations of the Moon, which takes into account this effect, is proposed.     

Pluto's light curve in 1933-1934

The Pluto-Charon system has complex photometric variations on all time scales; due to rotational modulations of dark markings across the surface, the changing orientation of the system as viewed from Earth, occultations and eclipses between Pluto and Charon, as well as the sublimation and condensation of frosts on the surface. The earliest useable light curve for Pluto is from 1953 to 1955 when Pluto was 35 AU from the Sun. Earlier data on Pluto has the potential to reveal properties of the surface at a greater heliocentric distance with nearly identical illumination and viewing geometry. We are reporting on a new accurate photographic light curve of Pluto for 1933-1934 when the heliocentric distance was 40 AU. We used 43 B-band and V-band images of Pluto on 32 plates taken on 15 nights from 19 March 1933 to 10 March 1934. Most of these plates were taken with the Mount Wilson 60″ and 100″ telescopes, but 7 of the plates (now at the Harvard College Observatory) were taken with the 12″ and 16″ Metcalf doublets at Oak Ridge. The plates were measured with an iris diaphragm photometer, which has an average one-sigma photometric error on these plates of 0.08 mag as measured by the repeatability of constant comparison stars. The modern B and V magnitudes for the comparison stars were measured with the Lowell Observatory Hall 1.1-m telescope. The magnitudes in the plate's photographic system were converted to the Johnson B- and V-system after correction with color terms, even though they are small in size. We find that the average B-band mean opposition magnitude of Pluto in 1933-1934 was 15.73±0.01, and we see a roughly sinusoidal modulation on the rotational period (6.38 days) with a peak-to-peak amplitude of 0.11±0.03 mag. With this, we show that Pluto darkened by 5% from 1933-1934 to 1953-1955. This darkening from 1933-1934 to 1953-1955 cannot be due to changing viewing geometry (as both epochs had identical sub-Earth latitudes), so our observations must record a real albedo change over the southern hemisphere. The later darkening trend from 1954 to the 1980's has been explained by changing viewing geometry (as more of the darker northern hemisphere comes into view). Thus, we now have strong evidence for albedo changes on the surface of Pluto, and these are most easily explained by the systematic sublimation of frosts from the sunward pole that led to a drop in the mean surface albedo.     

Distribution of Impact Locations and Velocities of Earth Meteorites on the Moon

Following the analytical work of Armstrong et al. (Icarus 160:183–196, 2002), we detail an expanded N-body calculation of the direct transfer of terrestrial material to the Moon during a giant impact. By simulating 1.4 million particles over a range of launch velocities and ejecta angles, we have derived a map of the impact velocities, impact angles, and probable impact sites on the moon over the last 4 billion years. The maps indicate that the impacts with the highest vertical impact speeds are concentrated on the leading edge, with lower velocity/higher-angle impacts more numerous on the Moon’s trailing edge. While this enhanced simulation indicates the estimated globally averaged direct transfer fraction reported in Armstrong et al. (Icarus 160:183–196, 2002) is overestimated by a factor of 3–6, local concentrations can reach or exceed the previously published estimate. The most favorable location for large quantities of low velocity terrestrial material is 50 W, 85 S, with 8.4 times more impacts per square kilometer than the lunar surface average. This translates to 300–500 kg km⁻², compared to 200 kg km⁻² from the previous estimate. The maps also indicate a significant amount of material impacting elsewhere in the polar regions, especially near the South Pole-Aiken basin, a likely target for sample return in the near future. The magnitudes of the impact speeds cluster near 3 km/s, but there is a bimodal distribution in impact angles, leading to 43% of impacts with very low (<1 km/s) vertical impact speeds. This, combined with the enhanced surface density of meteorites in specific regions, increases the likelihood of weakly shocked terrestrial material being identified and recovered on the Moon.     

Investigation of Long-Period Oscillations of Sunspots with Ground-Based (Pulkovo) and SOHO/MDI Data

We applied special data-processing algorithms to the study of long-period oscillations of the magnetic-field strength and the line-of-sight velocity in sunspots. The oscillations were investigated with two independent groups of data. First, we used an eight-hour-long series of solar spectrograms, obtained with the solar telescope at the Pulkovo Observatory. We simultaneously measured Doppler shifts of six spectral lines, formed at different heights in the atmosphere. Second, we had a long time series of full-disk magnetograms (10 – 34 hour) from SOHO/MDI for the line-of-sight magnetic-field component. Both ground- and space-based observations revealed long-period modes of oscillations (40 – 45, 60 – 80, and 160 – 180 minutes) in the power spectrum of the sunspots and surrounding magnetic structures. With the SOHO/MDI data, one can study the longer periodicities. We obtained two new significant periods (> 3σ) in the power spectra of sunspots: around 250 and 480 minutes. The power of the oscillations in the lower frequencies is always higher than in the higher ones. The amplitude of the long-period magnetic-field modes shows magnitudes of about 200 – 250 G. The amplitude of the line-of-sight velocity periodicities is about 60 – 110 m s⁻¹. The absence of low-frequency oscillations in the telluric line proves their solar nature. Moreover, the absence of low-frequency oscillations of the line-of-sight velocity in the quiet photosphere (free of magnetic elements) proves their direct connection to magnetic structures. Long-period modes of oscillation observed in magnetic elements surrounding the sunspot are spread over the meso-granulation scales (10″ – 12″), while the sunspot itself oscillates as a whole. The amplitude of the long-period mode of the line-of-sight velocity in a sunspot decreases rapidly with height: these oscillations are clearly visible in the spectral lines originating at heights of approximately 200 km and fade away in lines originating at 500 km. We found a new interesting property: the low-frequency oscillations of a sunspot are strongly reduced when there is a steady temporal trend (strengthening or weakening) of the sunspot’s magnetic field. Another important result is that the frequency of long-period oscillations evidently depends on the sunspot’s magnetic-field strength.     

Approximation methods in celestial mechanics. Application to Pluto's motion

Various methods of approximation for the computation of planetary perturbations are investigated: Fourier, Fourier-Chebyschev and Legendre. Application is made to Pluto's motion. Based upon JPL's ephemeris DE200, Pluto's mean elements are provided and also a compact ephemeris covering 2 centuries.     

Comparison of joint and individual catalogs of radio source positions

Comparison is given of joint and individual catalogs of radio source positions created in preparation of ICRF2. Differences between catalogs are shown, and the “external” evaluation of their accuracy is carried out.     

Photographic observations of Saturn’s moons at the MAO NAS of Ukraine in 1961–1990

A catalog of 1385 astrometric positions of Saturn’s moons S2–S9 has been compiled with Tycho-2 as a reference frame from photographic observations obtained at the Main Astronomical Observatory, National Academy of Sciences of Ukraine, in 1961–1990. Astronegatives have been digitized with an Epson Expression 10000XL commercial scanner in 16-bit grayscale with a resolution of 1200 dpi. Reduction has been performed in the LINUX-MIDAS-ROMAFOT software supplemented with additional modules. The internal positional accuracy of the reduction is 0.09…0.23′′ for both coordinates and 0.27…0.37^m for the photographic magnitudes of the Tycho-2 catalog. The calculated topocentric positions of the moons are compared online with the IMCCE ephemeris data (DE405 + TASS1,7). Moon-minus-moon differential coordinates are found for most of the moons and compared with theoretical data (http://lnfm1.sai.msu.ru/neb/nss/nssephmr.htm).     

Detecting the errors in solar system ephemeris by pulsar timing

Pulsar timing uses planetary ephemerides to convert the measured pulse arrival time at an observatory to the arrival time at the Solar System barycenter(SSB). Since these planetary ephemerides cannot be perfect, a method of detecting the associated errors based on a pulsar timing array is developed. By using observations made by an array of 18 millisecond pulsars from the Parkes Pulsar Timing Array, we estimated the vector uncertainty from the Earth to the SSB of JPL DE421, which reflects the offset of the ephemeris origin with respect to the ideal SSB, in different piecewise intervals of pulsar timing data, and found consistent results. To investigate the stability and reliability of our method, we divided all the pulsars into two groups. Both groups yield largely consistent results, and the uncertainty of the Earth-SSB vector is several hundred meters, which is consistent with the accuracy of JPL DE421. As an improvement in the observational accuracy, pulsar timing will be helpful to improve the solar system ephemeris in the future.     

Long-Term Variations of Geomagnetic Rigidity Cutoffs

Using trajectory calculations of cosmic rays in the geomagnetic field, the changes of vertical cutoff rigidities in the past are discussed. The computations are done for selected positions at the Earth’s surface using the IGRF model data for 1900–2000. The contour maps of vertical cutoff rigidities using the set of ten Gauss coefficients for the period of years between 0 and 1600 are obtained. The trends in long-term variability of cutoffs at different positions on the Earth’s surface are described.     

Acoustic Events in the Solar Atmosphere from <Emphasis Type="Italic">Hinode</Emphasis>/SOT NFI Observations

We investigate the properties of acoustic events (AEs), defined as spatially concentrated and short duration energy flux, in the quiet Sun, using observations of a 2D field of view (FOV) with high spatial and temporal resolution provided by the Solar Optical Telescope (SOT) onboard Hinode. Line profiles of Fe i 557.6 nm were recorded by the Narrow-band Filter Imager (NFI) on a 82″×82″ FOV during 75 min with a time step of 28.75 s and 0.08″ pixel size. Vertical velocities were computed at three atmospheric levels (80, 130, and 180 km) using the bisector technique, allowing the determination of energy flux to be made in the range 3 – 10 mHz using two complementary methods (Hilbert transform and Fourier power spectrum). Horizontal velocities were computed using local correlation tracking (LCT) of continuum intensities providing divergences. We found that the net energy flux is upward. In the range 3 – 10 mHz, a full FOV space and time averaged flux of 2700 W m⁻² (lower layer 80 – 130 km) and 2000 W m⁻² (upper layer 130 – 180 km) is concentrated in less than 1 % of the solar surface in the form of narrow (0.3″) AE. Their total duration (including rise and decay) is of the order of 10³ s. Inside each AE, the mean flux is 1.6×10⁵ W m⁻² (lower layer) and 1.2×10⁵ W m⁻² (upper). Each event carries an average energy (flux integrated over space and time) of 2.5×10¹⁹ J (lower layer) to 1.9×10¹⁹ J (upper). More than 10⁶ events could exist permanently on the Sun, with a birth and decay rate of 3500 s⁻¹. Most events occur in intergranular lanes, downward velocity regions, and areas of converging motions.     

March 1, 2005 Daylight Fireball Over Galicia (NW of Spain) and Minho (N. Portugal)

A daylight bolide was observed over Galicia (NW Spain) and Minho (N. Portugal) on March 1, 2005 at 15 h10 min ± 3 min UTC. We interviewed 23 eyewitnesses of the event in order to obtain the azimuth, altitude, and slope of the fireball’s trajectory. Reports suggest an atmospheric ending height below 20 km, indicating that meteorite survival was likely. From the reconstructed trajectory and the fireball’s duration, we obtained the approximate heliocentric orbits for the meteoroid. Assuming an entry velocity higher than 20 km s⁻¹ which is consistent with its estimated duration, the meteoroid originated in the asteroid belt.     

Spectral observations of the novalike star TT Ari. II

Results from a spectral study of one of the brightest cataclysmic variables, the star TT Ari, are presented. They are generally in good agreement with previous observations, but there are some differences. The luminosity of the star, as well as the equivalent widths of emission lines, reveal variations that are probably periodic in character. Emission from the star in the CIV 5801Å and 5812 Å lines is observed for the first time. The observed variations in the symmetry of the broad absorption Balmer series (beginning with Hβ) may be a consequence of the appearance of a P Cyg line profile. The Hα line manifests a P Cyg profile consisting of two components corresponding to 600 and 1900 km/s. The average of the ratio EWHα/EWHβ indicates that the formation of these lines may be explained, at least partially, in terms of a simple photoionization-recombination model. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 445–460 (August 2008).     

Microwave observations of compact radio sources during solar eclipses on RT-22

Based on the observations of solar eclipses performed on the RT-22 radio telescope at CrAO in the wavelength range 2.0–3.5 cm, we consider the fine spatial structure of the microwave emission from the quiet Sun. We have established that the positions of compact radio sources with a typical size of about 7″.0 and coronal bright points coincide. The mean radio flux exceeds the level of the quiet Sun by 0.28 sfu. The brightness temperatures increase with wavelength and lie within the range 0.3–2.7 MK. Evidence for a nonthermal nature of the emission from compact radio sources has been obtained.     

A new distribution function for relativistic counterstreaming plasmas

The particle distribution function that describes two interpenetrating plasma streams is re-investigated. It is shown how, based on the Maxwell–Boltzmann–Jüttner distribution function, which has been derived almost a century ago, a counterstreaming distribution function can be derived that uses velocity space. Such is necessary for various analytical calculations and numerical simulations that are reliant on velocity coordinates rather than momentum space. The application to the electrostatic two-stream instability illustrates the differences caused by the use of the relativistic distribution function.