In today’s gravity research there exists a number of gravitational theories which predict the existence of various corrections to the classical gravitational potential. In this paper using the different potentials that exist in the literature and with the help of Gauss’ planetary equations we examine the time rate of change of the Tisserand parameter as a function of the time rate of change of the three orbital elements involved. We find that the Tisserand parameter remains constant over a full orbital revolution in all the different potential resulting from the various theories. This fortifies and generalises the use of Tisserand parameter not only in case of Newtonian dynamics but also in more extended theories of gravity, thus ensuring its validity in determining the identity of a returning comet. Furthermore, we find that the parameter remains unchanged even in the case where a gravitational potential derived from a D-dimensional gravitational force, in the case where D = 4. Next quantization of orbits calculation is performed and the constancy of the Tisserand parameter is also recovered. Finally, assuming fractal orbits we obtain an expression for the fractal dimension of three well known Jupiter family comets in terms of their orbital elements and the constancy of the Tisserand parameter is also recovered.
Mechanisms for core formation in differentiated bodies in the early solar system are poorly constrained. At temperatures below those required to extensively melt planetesimals, core formation could have proceeded via percolation of metallic liquids. Although there is some geochemical data to support such ‘low-temperature’ segregation, experimental studies and simulations suggest that percolation-driven segregation might have only contributed to core formation in a proportion of fully-differentiated bodies. Here, the effects low-temperature core-formation on elemental compositions of planetesimal cores and mantles are explored. Immiscibility of Fe-rich and FeS-rich liquids will occur in all core-formation models, including those involving large fraction silicate melting. Light element content of cores (Si, O, C, P, S) depends on conditions under which Fe-rich and FeS-rich liquids segregated, especially pressure and oxygen fugacity. The S contents of FeS-rich liquids significantly exceed eutectic compositions in Fe–Ni–S systems and cannot be reconciled with S-contents of parent bodies to magmatic iron meteorites. Furthermore, there is limited data on trace element partitioning between FeS-rich and Fe-rich phases, and solid/melt partitioning models cannot be readily applied to FeS-rich liquids. Interaction of metallic liquids with minor phases stable up to low fraction silicate melting could provide a means for determining the extent of silicate melting prior to initiation of core-formation. However, element partitioning in most core-formation models remains poorly constrained, and it is likely that conditions under which segregation of metallic liquid occurred, especially oxygen fugacity and pressure, had as significant a control on planetesimal composition as segregation mechanisms and extent of silicate melting.
This work presents a new method for estimating the population index of meteor showers using the entire distribution of meteors, thus avoiding the arbitrary choice of a threshold magnitude. This method was used to estimate the monthly population indices of 9771 sporadic meteors observed by the Brazilian Meteor Observation Network (BRAMON) between 2014 Aug. and 2021 Feb. The magnitude threshold was derived from the parameters of a Tsallis’q-exponential distribution proposed by Betzler Borges (2015) and fitted to the observed distribution of apparent magnitudes. Population indices show temporal variation between May and September relative to the average monthly index ( 3.63± 0.01 ). The primary sources between May and September have a λ _⊙ solar longitude associated with helion and antihelion sources. A secondary source has a time-varying solar longitudes and a larger number of meteors than the helion source between July and November. The secondary source has solar longitudes probably related to sporadic meteors in the north toroid. The helion and antihelion sources have average λ _⊙ = 352 and 215 degrees and radii of 8 and 4 degrees, respectively.
An essential requisite for the appearance and permanence of life on Earth is the onset of a continuous “cycling” of some key atoms and molecules. Cycling of elements probably also occurs on other objects and is driven by biological or a-biological processing. Here we investigate the cycling of some species in the icy Galilean satellites that are exposed to the intense fluxes of energetic particles coming from the Jupiter magnetosphere. Among the most studied effects of particle bombardment, there is the production of molecules not originally present in the sample. These newly synthesized species are irradiated as well and in some circumstances can re-form the original species, giving rise to a “cycle”. Here we discuss the cycling of some atoms (C, N, O, S) incorporated in molecules observed on the surface of the icy Galilean satellites. The results indicate that cycling of carbon atoms starts with solid elemental carbon. Irradiated in the presence of water ice, carbon dioxide is produced and forms carbonic acid and other organics whose irradiation re-produces carbon dioxide and solid carbon. The effect on nitrogen atoms is limited to a continuous cycle among nitrogen oxides (e.g. NO 2 produces NO, and N 2 O). Oxygen is mostly incorporated in water ice. When irradiated, the large majority of the water molecular fragments recombine to re-form water molecules. The sulfur cycle occurs among SO 2 (that cannot be produced by ion irradiation only), sulfuric acid and elemental sulfur. The results are discussed in view of their relevance to the expected space observations of the JWST telescope (NASA, ESA, CSA) and the JUICE (ESA) spacecraft.
The interior of a crater should have a lower mean areal density of smaller impact craters than nearby plains have, because the impacts are spread out over a larger surface area, and because the crater’s wall partially shields its interior. Inside a crater shaped like a spherical bowl (a spherical cap turned upside-down), smaller primary impact craters should be spread uniformly, but secondary craters have a more complicated distribution, usually concentrated near the center. These results may help to distinguish between populations of primary and secondary craters, and should be of interest for interpreting counts of craters within craters.
Photometric correction is a necessary step in planetary image pre-processing since the images of planetary surfaces are acquired by orbiting spacecraft at various observational geometries. In this study, visible (748 nm) and near-infrared (948 nm) bands of Hyper Spectral Imager (HySI) onboard Chandrayaan-1 have been used to derive a preliminary photometric correction for lunar data. The purpose of the proposed photometric correction for HySI is to convert observations taken at solar incidence (i), sensor emission (e), and the solar phase angles (α) to a fixed geometry by applying i = α = 30° and e = 0° to each image. The Lommel–Seeliger function was used to model the lunar limb darkening effect, while topography data from the merged Digital Elevation Model of Lunar Reconnaissance Orbiter—Lunar Orbiter Laser Altimeter (LRO-LOLA) and SELENE Terrain Camera (TC) was used to correct local topographic effects. Data from Moon Mineralogy Mapper (M3), SELENE Multiband Imager (MI) and Clementine Ultraviolet and Visible Camera (UV/VIS) were also used to compare radiance, reflectance and phase functions derived from HySI. Our analysis reveals that HySI is darker than M3 primarily due to low surface radiance conditions observed by HySI. The derived phase functions for the two HySI bands indicate a good correlation between the derived reflectance and phase angle as well as with the phase functions derived for the empirically corrected M3 data. This approach led to the derivation of a photometric correction for maria regions. Finally, it is expected that the proposed correction would be applicable to all HySI images covering the lunar mare region.
This is the fourth data paper publishing lightcurve survey work of 52 Near Earth Asteroids (NEAs) using 10 telescopes available to the EURONEAR network between 2017 and 2020. Forty six targets were not observed before our runs (88% of the sample) but some of these were targeted during the same oppositions mainly by Brian Warner. We propose new periods for 20 targets (38% of the sample), confirming published data for 20 targets, while our results for 8 targets do not match published data. We secured periods for 15 targets (29% of the sample), candidate periods for 23 objects (44%), tentative periods for 11 asteroids (21%), and have derived basic information about 3 targets (6% of the sample). We calculated the lower limit of the ellipsoid shape ratios a/b for 46 NEAs (including 13 PHAs). We confirmed or suggested 4 binary objects, recommending two of them for follow-up during future dedicated campaigns.
The paper examines instability of triangular equilibrium points of a test particle in the gravitational field of two primaries radiating with effective Poynting–Robertson (P–R) drag, enclosed by circumbinary disc. The equations of motion are derived and positions of triangular equilibrium points are located. It is seen that the locations are affected by the disc, radiation pressure and P–R drag of the primaries. In particular, for our numerical computations of the locations of the triangular equilibrium points and the linear stability analysis, we consider a low-mass pulsating star, IRAS 11472-0800 as the bigger primary, with a young white dwarf star; G29-38 as the smaller primary. We observe that the disc does not change the x-coordinates of the triangular points while their y-coordinates are been altered. However, radiation pressure, P–R drag and the mass parameter µ mainly contribute in shifting the location of the triangular points. As regards the stability analysis, these points are in general unstable under the combine effects of radiation, P–R drag and disc, in the entire range of the mass parameter due to complex roots with positive real parts. Further, in order to discern the effects of the parameters on the instability outcome, we broaden the range of the mass parameter to accommodate small values of the mass parameters. We observe that in the absence of radiation and the presence of disc, when the mass parameter is less than the critical mass, all the roots are pure imaginary and the triangular point is stable. However, when $$\mu = 0.038521$$ , the four roots are complex, but turn pure imaginary quantities when the disc is present. This proves that the disc is a stabilizing force while the radiation pressure and P–R drag induces instability around the triangular equilibrium points in the entire range of the mass parameter due to the presence of complex roots with positive real parts.
The Perseverance rover (Mars 2020) mission, the first step in NASA's Mars Sample Return (MSR) program, will select samples for caching based on their potential to improve understanding Mars' astrobiological, geological, geochemical, and climatic evolution. Geochronologic analyses will be among the key measurements planned for returned samples. Assessing a sample's shock history will be critical because shock metamorphism could influence apparent sample age. Shock effects in one Mars-relevant mineral class, plagioclase feldspar, have been well-documented using various spectroscopy techniques (thermal infrared reflectance, emission, and transmission spectroscopy, Raman, and luminescence). A subset of these data will be obtained with the SuperCam and SHERLOC (Scanning Habitable Environments with Raman & Luminescence for Organics & Chemicals) instruments onboard Perseverance to inform caching decisions for MSR. Here, we review shock indicators in plagioclase feldspar as revealed in Raman, luminescence, and IR spectroscopy lab data, with an emphasis on Raman spectroscopy. We consider how this information may inform caching decisions for selecting optimal samples for geochronology measurements. We then identify challenges and make recommendations for both in situ measurements performed with SuperCam and SHERLOC and for supporting lab studies to enhance the success of geochronologic analyses after return to Earth.
Neutral exospheres of large airless bodies consist of atoms or molecules on ballistic trajectories. An import example is the lunar water exosphere, thought to transport water to cold traps. In anticipation of future observational measurements, the theory of thermalized surface-bounded gravitationally-bound exospheres is further developed. The vertical density profile is calculated using thermodynamic averages of an ensemble of ballistic trajectories. When the launch velocities follow the Maxwell–Boltzmann Flux distribution, the classical density profile results. For many other probability distributions, including thermal desorption from a vertical wall, the density diverges logarithmically near the surface. Hence, an exosphere resulting from thermal desorption from a rough surface includes a ground-hugging population that appears to be colder than the surface. Another insight derived from the thermodynamic perspective is that cold traps can be interpreted in terms of the frostpoint of the water exosphere, if the long-term average of the pressure of the exosphere is considered. Ice in lunar caves is long-lasting only if the cave interior is below the cold trap temperature threshold.
Radar observations of the surface of Mercury had revealed areas with bright reflective properties in both polar regions of the planet. It was suggested that such areas contain depositions of volatile compounds, including water. In this paper, we investigated migration of water molecules to the permanently shaded areas, located in the impact crater in the polar regions of Mercury. To simulate the migration of water molecules in the exosphere of Mercury, we used the Monte Carlo method. To estimate the proportion of water molecules falling into cold traps in the polar regions of Mercury, we estimated the area of such regions. We found that the area of permanently shaded areas near the north pole of the planet reaches 23,300 km2, and in the area of the south pole—45,500 km2. Most of the water molecules (~ 92%) will be destroyed as a result of photolysis, and ~ 7.5% of them will be destroyed while they are on the planet's surface between hops. The fraction of water molecules that left the planet's exosphere as a result of reaching the escape velocity is only 0.3%. The fraction of water molecules trapped in permanently shaded areas in the polar regions of Mercury reaches 7.8% of the total number of particles participating in the simulation. Only 2.2% of them can be trapped in cold traps in the North Pole region and 5.6% in the South Pole region.
This article presents the results of an analysis of Tisserand's constant for 1389 long-period comets in relation to a hypothetical planet. A mechanism is proposed to apply Tisserand's criterion for a relatively trans-Neptunian planet with a notable inclination and orbit eccentricity. In particular, the algorithm considers the planet's heliocentric distance in the era of a clearly-defined transformational change in the cometary orbit. Thus, we carried out the corresponding calculations by simulating the planet motion plane. This study allows a comparative analysis of Tisserand constant values for proposed hypothetical planet parameters. The most notable result is for a planet at a proposed distance of 340 AU.
One meter class telescopes could bring important contributions in the acquisition of lightcurves of near earth asteroids (NEAs), based on which rotations and other physical properties could be derived or constrained. Part of a collaboration between IAC, ESA and the EURONEAR during the semester 2015A, the IAC80 and OGS telescopes at Teide Observatory in Tenerife were allocated for a photometric project during 64 nights spread in a few observing runs. The main funding for this long observing mission was raised by the student observer Radu Cornea from private sponsors based in his natal city of Sibiu, Romania, mentioned in the Acknowledgements. We observed 33 lightcurves of NEAs not published before, including 10 potentially hazardous asteroids (PHAs). Based on the quality of the Fourier period fits, we sorted the results in four groups which include 7 secured periods, 9 candidate periods, 10 tentative periods and 7 objects not solved. We resolved periods or suggested constraints for 13 NEAs having no other rotation knowledge (including 3 PHAs), confirming periods for other 6 targets published by other authors (mainly by Brian Warner). We suggested tumbling or binary nature for 6 targets (probing one of them) recommended for future dedicated campaigns. We derived ellipsoid shape ratios for 21 NEAs (including 4 PHAs) not known before.
The mechanical properties of Chelyabinsk LL5 chondrite (Chelyabinsk meteorite) were studied by uniaxial compression and diametral compression/indirect tension test. Twenty cylindrical samples, 10 for compression and 10 for tension, with the diameter 3.3 mm and 1.65 mm in height have been prepared for testing. It was shown that the strength of the tested samples under compression almost 45 times greater than it is at tension: 372 ± 10 MPa and 8.2 ± 0.7 MPa, respectively. Fracture behaviour under compression and tension was similar and can be characterised as brittle. The obtained compression strength of the Chelyabinsk meteorite lies close to the maximal values of strength for many other chondrites, whereas its tensile strength magnitude resides in the bottom quarter of the range of similar measurements. It may be caused by the small sizes of the investigated samples together with a large number of tiny cracks between the grains in the Chelyabinsk chondrite. Our estimations have shown that if one assumes that the initial shape of the Chelyabinsk fireball was spherical or ellipsoidal, then its fragmentation stress is close to the experimental tensile strength and much lower than the compression strength. Hence, a stress state equivalent to one appearing at the indirect tension test could occur in the Chelyabinsk fireball during its fall in the Earth atmosphere.
We present a study on the relationship between the ratio of the depth of a crater to its diameter and the diameter for lunar craters both on the maria and on the highlands. We consider craters younger than 1.1 billion years in age, i.e. of Copernican period. The aim of this work is to improve our understanding of such relationships based on our new estimates of the craters’s depth and diameter. Previous studies considered similar relationships for much older craters (up to 3.2 billion years). We calculated the depths of craters with diameters from 10 to 100 km based on the altitude profiles derived from data obtained by the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter (LRO). The obtained ratios h/D of the depths h of the craters to their diameters D can differ by up to a factor of two for craters with almost the same values of diameters. The linear and power approximations (regressions) of the dependence of h/D on D were made for simple and complex Copernican craters selected from the data from Mazrouei et al. (Science 363:253–255, 2019) and Losiak et al. (Lunar Impact Crater Database, 2015). For the separation of highland craters into two groups based only on their dependences of h/D on D, at D < 18 km these are mostly simple craters, although some complex craters can have diameters D ≥ 16 km. Depths of mare craters with D ≤ 14 km are greater than 0.15D. Following Pike’s (Lunar Planet Sci XII:845–847, 1981) classification, we group mare craters of D < 15 km as simple craters. Mare craters with 15 < D < 18 km fit both approximation curves for simple and complex craters. Depths of mare craters with D > 18 km are in a better agreement with the approximation curve of h/D versus D for complex craters than for simple craters. At the same diameter, mare craters are deeper than highland craters at a diameter smaller than 30–40 km. For greater diameters, highland craters are deeper. The values of h/D for our approximation curves are mainly smaller than the values of the curve by Pike (in: Roddy, Pepin, Merrill (eds) Impact and explosion cratering: planetary and terrestrial implications, University of Arizona Press, Tucson, 1977) at D < 15 km. Only for mare craters at D < 11 km, our approximation curve is a little higher than the curve by Pike (1977). For our power approximations, the values of h/D obtained for complex craters are greater than those obtained by Pike (1981) at D > 53 km for highland craters, and at D < 80 km for mare craters.
The Martian surface is incised by numerous valley networks, which indicate the planet experienced sustained widespread flowing water in the past (e.g. Carr in Water on Mars, Oxford University Press, New York, 1996; Phil Trans R Soc A 370:2193–2212, 2012. https://doi.org/10.1098/rsta.2011.0500). Examining the distribution and geometries of these valley networks provides invaluable information about the Martian climate during the period of formation. The recent advancement in high resolution images has provided an opportunity to build upon past valley maps of Mars (Bahia et al. in LPSC 2018, 2018), however, the identification of these valley networks is extremely time-consuming. A citizen science project may aid in reducing this time-consuming process; this project conducts a valley mapping task with participants of varying expertise in valley mapping to determine whether a citizen science project of this kind should be worth pursuing. This was conducted in a region adjacent to Vogel Crater (36.1° S, 10.2° W). Repeated mapping of the area (a repeatability test) found that participants with low experience in valley mapping (22 a-level physics student’s representative of the public) were inconsistent when mapping valleys. Additionally, when comparing the results of participants within this group (a reproducibility test), the majority of reproduced valleys are false positives (i.e. incorrectly traced valleys). These results were consistent with those found for the medium experience group (45 2nd year geology undergraduates). The validated tracings of the low experience group improve upon the number and total length of valleys mapped by previous studies (Hynek et al. in J Geophys Res 115:1–14, 2010). To validate these valleys requires the input of an expert to remove false positives which is less time consuming than manually mapping the images; this may indicate that a citizen science project is worth pursuing. However, to effectively identify the maximum amount of valleys an expert is required.
We have statistically analyzed a set of 115 low frequency (Deca-Hectometer wavelengths range) type II and type III bursts associated with major Solar Energetic Particle (SEP: Ep > 10 MeV) events and their solar causes such as solar flares and coronal mass ejections (CMEs) observed from 1997 to 2014. We classified them into two sets of events based on the duration of the associated solar flares:75 impulsive flares (duration < 60 min) and 40 gradual flares (duration > 60 min).On an average, the peak flux (integrated flux) of impulsive flares × 2.9 (0.32 J m−2) is stronger than that of gradual flares M6.8 (0.24 J m−2). We found that impulsive flare-associated CMEs are highly decelerated with larger initial acceleration and they achieved their peak speed at lower heights (− 27.66 m s−2 and 14.23 Ro) than the gradual flare-associated CMEs (6.26 m s−2 and 15.30 Ro), even though both sets of events have similar sky-plane speed (space speed) within LASCO field of view. The impulsive flare-associated SEP events (Rt = 989.23 min: 2.86 days) are short lived and they quickly reach their peak intensity (shorter rise time) when compared with gradual flares associated events (Rt = 1275.45 min: 3.34 days). We found a good correlation between the logarithmic peak intensity of all SEPs and properties of CMEs (space speed: cc = 0.52, SEcc = 0.083), and solar flares (log integrated flux: cc = 0.44, SEcc = 0.083). This particular result gives no clear cut distinction between flare-related and CME-related SEP events for this set of major SEP events. We derived the peak intensity, integrated intensity, duration and slope of these bursts from the radio dynamic spectra observed by Wind/WAVES. Most of the properties (peak intensity, integrated intensity and starting frequency) of DH type II bursts associated with impulsive and gradual flare events are found to be similar in magnitudes. Interestingly, we found that impulsive flare-associated DH type III bursts are longer, stronger and faster (31.30 min, 6.43 sfu and 22.49 MHz h−1) than the gradual flare- associated DH type III bursts (25.08 min, 5.85 sfu and 17.84 MHz h−1). In addition, we also found a significant correlation between the properties of SEPs and key parameters of DH type III bursts. This result shows a closer association of peak intensity of the SEPs with the properties of DH type III radio bursts than with the properties DH type II radio bursts, atleast for this set of 115 major SEP events.
Major advancements in surface wave testing over the past 2 decades have led researchers to revisit and re-analyze archived seismic records, particularly those involving measurements on the Moon. The goal of such recent efforts with lunar seismic measurements has been to gain further insights into lunar geology. We examined the active seismic data from the Apollo 16 mission for their surface wave information using a multichannel approach. The inversion of Rayleigh surface waves provided a subsurface estimate for the uppermost 8 m of the lunar subsurface with the shear wave velocities varying from 40 to 50 m/s at the surface to velocities in the range of 95–145 m/s with an average of 120 m/s at a depth of about 7 m. Generally, the results from this inversion demonstrated good agreement with previous studies. Also, we carried out numerical modeling of wave propagation in a highly-heterogeneous domain to examine the effects of such anomalous features on the acquired seismograms. Results confirmed that a sharp-contrast bi-material domain can indeed produce significant coda wave as reflected on the lunar seismic traces.
One of the challenges of planetary science is the age determination of geological units on the surface of the different planetary bodies in the solar system. This serves to establish a chronology of the geological events occurring on these different bodies, hence to understand their formation and evolution processes. An approach for dating planetary surfaces relies on the analysis of the impact crater densities with size. Approaches have been proposed to automatically detect impact craters in order to facilitate the dating process. They rely on color values from images or elevation values from Digital Elevation Models (DEM). In this article, we propose a new approach for crater detection, more specifically using their rims. The craters can be characterized by a round shape that can be used as a feature. The developed method is based on an analysis of the DEM geometry, represented as a 3D mesh, followed by curvature analysis. The classification process is done with one layer perceptron. The validation of the method is performed on DEMs of Mars, acquired by a laser altimeter aboard NASA’s Mars Global Surveyor spacecraft and combined with a database of manually identified craters. The results show that the proposed approach significantly reduces the number of false negatives compared to others based on topographic information only.
Noble gas and nitrogen isotopic compositions of Karimati ordinary (L5) chondrite are presented. Aliquots of the meteorite were studied in two noble gas mass spectrometers. Its cosmic ray exposure (CRE) history, trapped noble gases and nitrogen isotopic systematic are examined. The compositions of Ne and Kr in this meteorite indicate presence of mixture of solar wind and Q trapped components. In addition to the primordial components, radiogenic 129Xe (from the decay of short-lived radioactive 129I) is observed in the two aliquots (129Xe/132Xe ranges between 1.054 and 1.311). The U/Th-4He and K-40Ar ages are discordant. U/Th-4He ages are younger than the K-40Ar ages, indicating loss of helium. The trapped N component is isotopically light analogous to Q gas/solar wind. The cosmic-ray exposure ages of the two aliquots are 16.1 ± 2.7 Ma and 16.6 ± 2.0 Ma based on the cosmogenic 21Nec and 38Arc concentrations.
