Ecliptic Longitude Research Articles

Long-term Periodicities in North–south Asymmetry of Solar Activity and Alignments of the Giant Planets

The existence of ~12-year and ~51-year periodicities in the north-south asymmetry of solar activity is well known. However, the origin of these as well as the well-known relatively short periodicities in the north-south asymmetry is not yet clear. Here we have analyzed the combined daily data of sunspot groups reported in Greenwich Photoheliographic Results (GPR) and Debrecen Photoheligraphic Data (DPD) during the period 1874-2017 and the data of the orbital positions (ecliptic longitudes) of the giant planets in ten-day intervals during the period 1600-2099. Our analysis suggests that ~12-year and ~51-year periodicities in the north-south asymmetry of solar activity are the manifestations of the differences in the strengths of ~11-year and ~51-year periodicities of activity in the northern- and southern-hemispheres. During the period 1874-2017 the Morlet wavelet power spectra of the north-south asymmetry of sunspot-group area and the mean absolute difference of the orbital positions of the giant planets are found to be similar. Particularly, there is a suggestion that the ~12-year and ~51-year periodicities in the north-south asymmetry of sunspot-group area occurred during approximately the same times as the corresponding periodicities in the mean absolute difference of the orbital positions of the giant planets. Therefore, we suggest that there could be influence of some specific configurations of the giant planets in the origin of the ~12-year and ~50-year periodicities of the north-south asymmetry of solar activity.

On a New Analytic Theory of the Moon's Motion I: Orbital Angular Momentum

A new analytic theory of the Moon's motion is deduced from the Lagrangian of the Sun-Earth-Moon system expressed with relative velocities. In its first-order approximation, the first-degree terms of the ratio of distances from Earth to the Moon and to the Sun are taken. The calculated relative variation in the Moon's orbital angular momentum is resolved into components whose integrals yield the inclination of the orbital plane, the ecliptic longitude of the ascending node and the norm of the angular momentum as functions of the angle between the Moon and the ascending node.

Spin state evolution of asteroid (367943) Duende during its 2013 earth flyby

On February 15, 2013 asteroid (367943) Duende, provisionally named 2012 DA14, experienced an extremely close earth encounter, passing within 27,700 km altitude. An observation campaign was made possible by one year's notice of the flyby. This campaign, discussed in detail in the companion paper by Moskovitz et al. (2019), yielded visible-wavelength photometry before and after closest approach. Post-flyby Goldstone Doppler-delay radar data were also obtained. These data indicated a roughly 40 m × 20 m object in non-principal axis rotation. Leveraging light curve frequency analysis from the Moskovitz et al. companion paper, dynamical and inertia constraints from the rough radar-derived elongations, and simulated photometry, only two post-flyby states were deemed viable. These were a long axis mode (LAM) with long axis convention periods Pϕ¯=6.36 h and Pψ = 8.73 h and a short axis mode (SAM) with Pϕ¯=8.71 h and Pψ = 23.7 h (each with nominal long-intermediate and long-short ellipsoid axis ratios of 1.7:1 and 2.3:1 respectively). The SAM solution was more consistent with the post-flyby photometry and radar data. Nevertheless, there were differences between the amplitude and phase of the post-flyby and best-fit simulated SAM light curves at some epochs. These discrepancies may be due to a non-ellipsoidal shape, non-uniform albedo, and/or incorrect spin state solution (attitude, inertias, tumbling periods, or rotation mode).Analysis of the sparse pre-flyby photometry by Moskovitz et al. yielded poor Fourier series solutions for all principal axis states and different peaks in the pre and post-flyby WindowCLEAN power spectra. This suggests the asteroid was tumbling before the encounter and that its spin state changed. Propagating the best-fitting LAM and SAM solutions backwards through the flyby with terrestrial tidal torques resulted in significant dispersion of the rotation states. The pre-flyby SAM states coincided with the notable Moskovitz et al. Fourier solution P1 = 8.37 h and P2 = 24.2 h. Overall, we propose Duende was tumbling before the 2013 flyby and that its spin state may have changed during the flyby. Furthermore, our analysis suggests Duende is currently in SAM with Pϕ¯=8.71 h and Pψ = 23.7 h with pole J2000 ecliptic longitude and obliquity of roughly 70° and 95° or 245° and 90° respectively. The spin state characterization approach outlined in this paper could be used for future analyses with inertia, dynamical, and observational constraints.

Demonstrating the elliptical orbit of Mars using naked eye data

The discovery of Kepler's three laws of planetary motion served as a significant motivation to Newton to find the gravitational force law and explain why motion in an inverse square law force field produces orbits (or trajectories) that are conic sections. Kepler's discovery that Mars' orbit is an ellipse is one of the most significant in the history of astronomy. It relied on Tycho Brahe's observations, which were the most accurate data ever attained at that time. In this paper, we present an analysis of positional measurements carried out during two observing periods of ∼400 days centered on the 2016 and 2018 oppositions of Mars. Our observations were made with the naked eye and a simple cross staff. If we assume an elliptical orbit of Mars and simplify matters by adopting a circular orbit for the Earth, the data of the 2016 opposition indicate that the eccentricity of Mars' orbit is 0.093 ± 0.012. This is equal to the modern accepted value, but with a larger uncertainty. By adopting a more robust model that uses an ellipse for the Earth as well, we obtain a better fit, with an RMS residual of ±7.5 arc min for the ecliptic longitudes. The data of the 2018 opposition must be fit with an ellipse for Mars and the Earth.

Nautical Tables for Vasco da Gama, 1497–1500?

It is believed that Vasco da Gama carried nautical tables on his first voyage to the Indies, 1497–1499, that had especially been produced for the years 1497–1500 by Abraham Zacut, then Royal Astronomer in the service of the Portuguese court. Maritime history writers have suggested two manuscripts as surviving copies of these da Gama tables. One of them is a set of declination tables in the 1519 edition of Suma de Geographia by Martín Fernández de Enciso. Analysis of all available data shows that these tables are indeed good candidates, though their production from the 1505–1508 astronomical tables of Regiomontanus and of Stöffler and Pflaum would be about equally likely. The other candidate is a set of solar ecliptic longitudes, found in the Livro de Marinharia, attributed to André Pires. It is shown that with certainty these have been taken from 1505 to 1508 of Regiomontanus/Stöffler-Pflaum and therefore cannot have served da Gama on his first voyage.

The Characterization of Secondary Interstellar Neutral Oxygen beyond the Heliopause: A Detailed Analysis of the IBEX-Lo Oxygen Observations

Abstract In this study, we analyze the directional distribution of the secondary interstellar neutral (ISN) O population observed by the IBEX-Lo neutral atom camera on the Interstellar Boundary EXplorer (IBEX) via the comparison with simulated ISN O intensity maps produced by an analytical model. In the analytical model, we assume that there are primary and secondary ISN populations at the heliopause. We further assume that each population is represented by a Maxwellian velocity distribution function with its own flow parameters. For the viewing directions of IBEX-Lo, we compute the incoming atom speeds at the heliopause with a Keplerian equation of motion in the solar gravity field. Then, we calculate analytically the distribution function to obtain the ISN intensities at Earth’s orbit. We compare the simulated O intensity maps with the IBEX-Lo O sky map to determine the most likely flow parameters of the secondary ISN O population. Using this method, we find the most likely flow parameters of the secondary ISN O population: km s−1, , , and K. The results indicate that the secondary ISN O flow direction is deflected toward lower ecliptic longitude and higher negative ecliptic latitude from the ISN gas flow direction at the heliopause. The secondary ISN O flow direction is more deflected from the ISN gas flow direction than the secondary ISN He flow direction.

Загадка звёздного каталога Коперника (часть первая)

The Copernican catalog differs from the catalogs of previous epochs by transferring the reference point of ecliptic longitudes from the vernal equinox to the star γ Aries. This violation of the tradition which did not influence the catalogs of subsequent epochs, is regarded by N. I. Idelson as an anachronism, and in the opinion of E. P. Fedorov, this idea of Copernicus was ahead of time. Since the contradictions in the evaluation of Copernicus’ works are inherent in the literature of the 20th century, it is necessary to recall the pre-Copernican astronomy and refer to the text of his works. Our study consists of three parts (papers). The first one is devoted to the period from the studying the motion of heavenly bodies upon celestial sphere to passing to the World structure and the movements of the Solar system bodies. Copernicus’s heliocentric theory made invaluable contribution into the solution of this problem, impossible without determining the distances. The previous basis of astronomical observations was increased by 20 thousand times. A similar advance in the determination of distances by a mathematically exact method is hardly possible in the foreseeable future.

The Orbital Elements of Venus in Medieval Islamic Astronomy: Interaction Between Traditions and the Accuracy of Observations

The orbital elements of each planet are the eccentricity and the direction of the apsidal line of its orbit defined by the ecliptic longitude of either of its apses, i.e., the two points on its orbit where the planet is either furthest from or closest to the Earth, which are called the planet’s apogee and perigee. In the geocentric view of the solar system, the eccentricity of Venus is a bit less than half of the solar one, and its apogee is located behind that of the Sun. Ptolemy correctly found that the apogee of Venus is behind that of the Sun, but determined the eccentricity of Venus to be exactly half the solar one. In the Indian Midnight System of Āryabhaṭa (b. ad 476), the eccentricity of Venus is assumed to be half the solar one, and also the longitudes of their apogees are assumed to be the same. This hypothesis became prevalent in early medieval Middle Eastern astronomy (ad 800–1000), where its adoption resulted in large errors of more than 10° in the values for the longitude of the apogee of Venus adopted by Yaḥyā b. Abī Manṣūr (d. ad 830), al-Battānī (d. ad 929), and Ibn Yūnus (d. ad 1007). In Western Islamic astronomy, it was used in combination with Ibn al-Zarqālluh’s (d. ad 1100) solar model with variable eccentricity, which only by coincidence resulted in accurate values for the eccentricity of Venus. In late Islamic Middle Eastern astronomy (from ad 1000 onwards), Āryabhaṭa’s hypothesis gradually lost its dominance. Ibn al-A‘lam (d. ad 985) seems to have been the first Islamic astronomer who rejected it. Late Eastern Islamic astronomers from the middle of the thirteenth century onwards arrived at the correct understanding that the eccentricity of Venus should be somewhat less than half of the solar one. Its most accurate medieval value was measured in the Samarqand observatory in the fifteenth century. Also, the values for the longitude of the apogee of Venus show a significant improvement in late Middle Eastern Islamic works, reaching an accuracy better than a degree in Khāzinī’s Mu‘tabar zīj, Ibn al-Fahhād’s ‘Alā’ī zīj, the Īlkhānī zīj, and Ulugh Beg’s Sulṭānī zīj.

Predicted Yield of Transits of Known Radial Velocity Exoplanets from the TESS Primary and Extended Missions

Radial velocity (RV) surveys have detected hundreds of exoplanets through their gravitational interactions with their host stars. Some will be transiting, but most lack sufficient follow-up observations to confidently detect (or rule out) transits. We use published stellar, orbital, and planetary parameters to estimate the transit probabilities for nearly all exoplanets that have been discovered via the RV method. From these probabilities, we predict that of the known RV exoplanets should transit their host stars. This prediction is more than double the amount of RV exoplanets that are currently known to transit. The Transiting Exoplanet Survey Satellite (TESS) presents a valuable opportunity to explore the transiting nature of many of the known RV exoplanet systems. Based on the anticipated pointing of TESS during its two-year primary mission, we identify the known RV exoplanets that it will observe and predict that of them will have transits detected by TESS. However, we only expect the discovery of transits for ∼3 of these exoplanets to be novel (i.e., not previously known). We predict that the TESS photometry will yield dispositive null results for the transits of ∼125 RV exoplanets. This will represent a substantial increase in the effort to refine ephemerides of known RV exoplanets. We demonstrate that these results are robust to changes in the ecliptic longitudes of future TESS observing sectors. Finally, we consider how several potential TESS extended mission scenarios affect the number of transiting RV exoplanets we expect TESS to observe.

Model-free Maps of Interstellar Neutral Hydrogen Measured with IBEX between 2009 and 2018

Abstract The Interstellar Boundary Explorer (IBEX) is a NASA satellite in Earth orbit, dedicated to observing interstellar neutral (ISN) atoms entering the heliosphere and energetic neutral atoms from the heliosheath from 11 eV to 6 keV. This work presents comprehensive maps of ISN hydrogen observed with IBEX at energies between 11 and 41 eV, covering almost an entire solar cycle from 2009 to 2018. ISN hydrogen measurements can provide information on the interstellar medium and on the heliosphere that modifies the incoming ISN flow. Whereas hydrogen is the dominant species in the unperturbed interstellar medium, most ISN hydrogen atoms crossing into the heliosphere do not reach the inner solar system: some are filtered out around the heliopause, while others are held off by solar radiation pressure or may be ionized as they approach the Sun. This paper presents and evaluates several approaches for generating model-free maps of ISN hydrogen from IBEX measurements. We discuss the basic implications of our results for ISN hydrogen inflow and outline the remaining discrepancies between observations and model predictions. Our maps show, during weak solar activity from 2009 to 2011, a clear signal of ISN hydrogen for ecliptic longitudes between 240° and 310°, roughly one month after the signal of ISN helium has peaked. When the solar activity approached its maximum around 2014, the ISN hydrogen signal weakened and dropped below the detection threshold because of increasing solar radiation pressure and ionization. The ISN hydrogen signal then reappeared in 2017.

(3200) Phaethon: Bulk density from Yarkovsky drift detection

Context. The recent close approach of the near-Earth asteroid (3200) Phaethon offered a rare opportunity to obtain high-quality observational data of various types. Aims. We used the newly obtained optical light curves to improve the spin and shape model of Phaethon and to determine its surface physical properties derived by thermophysical modeling. We also used the available astrometric observations of Phaethon, including those obtained by the Arecibo radar and the Gaia spacecraft, to constrain the secular drift of the orbital semimajor axis. This constraint allowed us to estimate the bulk density by assuming that the drift is dominated by the Yarkovsky effect. Methods. We used the convex inversion model to derive the spin orientation and 3D shape model of Phaethon, and a detailed numerical approach for an accurate analysis of the Yarkovsky effect. Results. We obtained a unique solution for Phaethon’s pole orientation at (318 ° , − 47 ° ) ecliptic longitude and latitude (both with an uncertainty of 5°), and confirm the previously reported thermophysical properties (D = 5.1 ± 0.2 km, Γ = 600 ± 200J m−2 s−0.5 K−1). Phaethon has a top-like shape with possible north-south asymmetry. The characteristic size of the regolith grains is 1 − 2 cm. The orbit analysis reveals a secular drift of the semimajor axis of −(6.9 ± 1.9)×10−4 au Myr−1. With the derived volume-equivalent size of 5.1 km, the bulk density is 1.67 ± 0.47 g cm−3. If the size is slightly larger ∼5.7 − 5.8 km, as suggested by radar data, the bulk density would decrease to 1.48 ± 0.42 g cm−3. We further investigated the suggestion that Phaethon may be in a cluster with asteroids (155140) 2005 UD and (225416) 1999 YC that was formed by rotational fission of a critically spinning parent body. Conclusions. Phaethon’s bulk density is consistent with typical values for large (> 100 km) C-complex asteroids and supports its association with asteroid (2) Pallas, as first suggested by dynamical modeling. These findings render a cometary origin unlikely for Phaethon.

Evidence for a Circumsolar Dust Ring Near Mercury’s Orbit

Abstract To test a technique to be used on the white-light imager onboard the recently launched Parker Solar Probe mission, we performed a numerical differentiation of the brightness profiles along the photometric axis of the F-corona models that are derived from STEREO Ahead Sun Earth Connection Heliospheric Investigation observations recorded with the HI-1 instrument between 2007 December and 2014 March. We found a consistent pattern in the derivatives that can be observed from any S/C longitude between about 18° and 23° elongation with a maximum at about 21°. These findings indicate the presence of a circumsolar dust density enhancement that peaks at about 23° elongation. A straightforward integration of the excess signal in the derivative space indicates that the brightness increase over the background F-corona is on the order of 1.5%–2.5%, which implies an excess dust density of about 3%–5% at the center of the ring. This study has also revealed (1) a large-scale azimuthal modulation of the inner boundary of the pattern, which is in clear association with Mercury’s orbit; and (2) a localized modulation of the inner boundary that is attributable to the dust trail of Comet 2P/Encke, which occurs near ecliptic longitudes corresponding to the crossing of Encke’s and Mercury’s orbital paths. Moreover, evidence of dust near the S/C in two restricted ranges of ecliptic longitudes has also been revealed by this technique, which is attributable to the dust trails of (1) comet 73P/Schwassmann–Wachmann 3, and (2) 169P/NEAT.

Optical observations of NEA 3200 Phaethon (1983 TB) during the 2017 apparition

Context. The near-Earth asteroid 3200 Phaethon (1983 TB) is an attractive object not only from a scientific viewpoint but also because of JAXA’s DESTINY+ target. The rotational lightcurve and spin properties were investigated based on the data obtained in the ground-based observation campaign of Phaethon. Aims. We aim to refine the lightcurves and shape model of Phaethon using all available lightcurve datasets obtained via optical observation, as well as our time-series observation data from the 2017 apparition. Methods. Using eight 12-m telescopes and an optical imager, we acquired the optical lightcurves and derived the spin parameters of Phaethon. We applied the lightcurve inversion method and SAGE algorithm to deduce the convex and non-convex shape model and pole orientations. Results. We analysed the optical lightcurve of Phaethon and derived a synodic and a sidereal rotational periods of 3.6039 h, with an axis ratio of a∕b = 1.07. The ecliptic longitude (λp) and latitude (βp) of the pole orientation were determined as (308°, −52°) and (322°, −40°) via two independent methods. A non-convex model from the SAGE method, which exhibits a concavity feature, is also presented.

Copernicus's Heliograph at Olsztyn: The 500th Anniversary of a Scientific Milestone

AbstractExactly 500 years ago, Nicolaus Copernicus drew a lattice of lines on a panel above the doorway to his rooms at Olsztyn Castle, then in the Bishopric of Warmia. Although its design has long been regarded as some kind of reflecting vertical sundial, the exact astronomical designation of the lines and related measuring techniques remained unknown. Surprisingly, Copernicus did not refer to his new observational methods in his principal work, De Revolutionibus. A data analysis of a 3D model of the panel has, at last, solved the mystery: Copernicus created a new type of measuring device—a heliograph with a nonlocal reference meridian—to precisely measure ecliptic longitudes of the Sun around the time of the equinoxes. The data, 3D model, and modeling results of our analysis are open access and available in the form of digital (Jupyter) notebooks.

Structure of the heliosheath from HSTOF energetic neutral atoms measurements

Context. From the year 1996 until now, High energy Suprathermal Time Of Flight sensor (HSTOF) on board Solar and Heliospheric Observatory (SOHO) has been measuring the heliospheric energetic neutral atoms (ENA) flux between ±17° from the ecliptic plane. At present it is the only ENA instrument with the energy range within that of Voyager LECP energetic ion measurements. The energetic ion density and thickness of the inner heliosheath along the Voyager 1 trajectory are now known, and the ENA flux in the HSTOF energy range coming from the Voyager 1 direction may be estimated. Aims. We use HSTOF ENA data and Voyager 1 energetic ion spectrum to compare the regions of the heliosheath observed by HSTOF and Voyager 1. Methods. We compared the HSTOF ENA flux data from the forward and flank sectors of the heliosphere observed in various time periods between the years 1996 and 2010 and calculated the predicted ENA flux from the Voyager 1 direction using the Voyager 1 LECP energetic ion spectrum and including the contributions of charge exchange with both neutral H and He atoms. Results. The ratio between the HSTOF ENA flux from the ecliptic longitude sector 210−300° (the LISM apex sector) for the period 1996−1997 to the estimated ENA flux from the Voyager 1 direction is ∼1.3, but decreases to ∼0.6 for the period 1996−2005 and ∼0.3 for 1998−2006. For the flank longitude sectors (120−210° and 300−30°), the ratio also tends to decrease with time from ∼0.6 for 1996−2005 to ∼0.2 for 2008−2010. We discuss implications of these results for the energetic ion distribution in the heliosheath and the structure of the heliosphere.

Characterization of the White-light Brightness of the F-corona between 5° and 24° Elongation

Abstract The white-light F-corona arises from light scattered by circumsolar dust. Using weekly models of the eastern side of the F-corona between 5° and 24° elongation, we analyzed the elongation and time dependence of the brightness of its photometric axis. The models were constructed from STEREO-A SECCHI/HI-1 images taken between 2007 December and 2014 March. We found that the brightness profiles can be approximated by power laws, with the coefficients of the models depending upon the observer’s ecliptic longitude. Their variation is not symmetric with respect to the orbital nodes of the dust plane, nor is the behavior similar in the two halves of the spacecraft orbit delimited by the line of nodes. The exponents range between −2.31 and −2.35, the former occurring when the observer is at the nodes. The asymmetry observed in the behavior of the proportionality constant is indicative of the projected center of the dust cloud being offset from the Sun’s center by ∼0.4 R ⊙. The coefficients exhibit a secular variation correlated with the location of the barycenter of the solar system. We also used the HI-1 frames obtained during STEREO-A calibration rolls to model the 360° F-corona. We found that (1) its flattening index ( f = R eq / R pol − 1 ) decreases from ∼0.66 to ∼0.46 with decreasing elongation and (2) the isophotes’ shape can be approximated by a series of superellipses, with the superellipse index n increasing (nonlinearly) with brightness ( ∼ 1.54 < n < ∼ 1.65 ). Cubic extrapolation of the results below 5° elongation points to a circular F-corona below 1° elongation.

LRO/LAMP study of the interstellar medium via the HeI 58.4 nm resonance line

Context.Recent measurements by IBEX and detailed modeling have changed our understanding of the flow of the interstellar medium through the solar system. In particular, a time dependence of the direction of the interstellar medium flow has been proposed, and a new population of helium atoms, called the “warm breeze”, has been discovered.Aims.We aim to constrain the structure of the interstellar medium close to the downwind focusing cone using the sensitive LAMP FUV/EUV imaging spectrograph onboard the Lunar Reconnaissance Orbiter.Methods.We measured the brightness of the emission line from interstellar helium atoms resonantly scattering solar photons at 58.4 nm (HeI) and compare it to our “modified cold model” of interstellar HeI sky brightness as a function of ecliptic latitude and longitude. Additionally, we compared LAMP observations to a model with time-dependent inflow direction and a model of the brightness of the “warm breeze”, to see if they can be distinguished by LAMP.Results.We find that the LAMP observations agree within error bars to our “modified cold model”, which in turn is consistent with the latest interstellar helium flow parameters found with IBEX. Our model can therefore be applied to other UV spectroscopic observations of the interstellar helium. However, LAMP observations cannot distinguish between our model and a model with a different inflow direction, since the latter has negligible effect on the 2D brightness of the interstellar HeI emission line. For the same reason, LAMP could not detect the effect of the “warm breeze”. We note a discrepancy between solar irradiances measured by TIMED/SEE and those measured by SDO/EVE. We recommend using values from SDO/EVE. Finally, we derive a value of LAMP sensitivity at the EUV wavelength (58.4 nm) of 0.485 ± 0.014 Hz/Rayleigh.Conclusions.These measurements pave the way to observations of the interstellar wind from lunar orbit.

The decomposition of temporal variations of pulsar dispersion measures

Pulsar dispersion measure (DM) accounts for the total electron content between a pulsar and us. High-precision observations for projects of pulsar timing arrays show temporal DM variations of millisecond pulsars. The aim of this paper is to decompose the DM variations of 30 millisecond pulsars by using Hilbert-Huang Transform (HHT) method, so that we can determine the general DM trends from interstellar clouds and the annual DM variation curves from solar wind, interplanetary medium and/or ionosphere. We find that the decomposed annual variation curves of 22 pulsars exhibit quasi-sinusoidal, one component and double components features of different origins. The amplitudes and phases of the curve peaks are related to ecliptic latitude and longitude of pulsars, respectively.

A revised shape model of asteroid (216) Kleopatra

We used three different sets of Arecibo delay-Doppler radar images and five well-covered occultations to generate a revised three-dimensional shape model of asteroid (216) Kleopatra with a spatial resolution of ∼10 km. We find Kleopatra to be a bi-lobate contact binary of overall dimensions 276 × 94 × 78 km ± 15% and equivalent diameter Deq = 122 ± 30 km; our uncertainties are upper and lower bounds. Separated binary models are ruled out by multi-chord occultations. Our model is 27% longer than the “dog-bone” model originally published by Ostro et al. (2000) but is similar to their model in the minor and intermediate axes extents. Our model's dimensions are also consistent with more recent ones based on lightcurves, adaptive-optics, and interferometric imaging. We confirm a rotational period of P = 5.385280 h ± 0.000001 h and a rotation pole at ecliptic longitude and latitude (λ, β) = (74°, + 20°) ± 5°. Over its southern hemisphere (the one most frequently observed on Earth), Kleopatra's radar albedo is 0.43 ± 0.10, consistent with a high near-surface bulk density and, by inference, the high metal content expected for M-class asteroids. However, the radar albedo for equatorial observations is considerably lower and more typical of a dominantly silicate composition. This observation could readily be explained by a relatively thin (1–2 m) silicate mantle over equatorial latitudes. Kleopatra's surface is relatively smooth with a mean slope of 12° at the ∼10 km baseline scale. Analysis of its geopotential surface suggests loose material will preferentially migrate to the neck, and this is supported by our radar observations.

Long-term variations in solar activity and planetary configurations

AbstractWe have analyzed the data on yearly mean international sunspot number (RZ) during the period 1610 – 2015 and orbital positions (ecliptic longitudes) of the giant planets in each 10-day interval during the period 1600 – 2099. We determined mean absolute difference ($\overline{\psi _D}$) of the orbital positions of the giant planets in each interval. We find that there exits a good correlation between cycle amplitude (RM, i.e. the maximum value of RZ) and the value of $\overline{\psi _D}$ at cycle maximum, suggesting that on longer time scales low/high solar activity associated with less/large spread in orbital positions of the giant planets (i.e. with a low/high value of $\overline{\psi _D}$).