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.
