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Register a new userFour Billion Year Stability of the Earth-Mars Belt
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Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the Earth-Mars belt from 1.08 au $< a <$ 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04-1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower `Earth-Mars belt covering $asim(1.09, 1.17)$ au, $e<0.04$, and $I<1^circ$ has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the $ u_3$, $ u_4$, and $ u_6$ secular resonances contribute to long-term instability in the outer (1.17-1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth-Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the $<200$ m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis, and use these to estimate that primordial asteroids with a diameter of 100 km or larger in the Earth-Mars belt would likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belts region at the end of the terrestrial planet formation.
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We have produced a multiannual climatology of airborne dust from Martian year 24 to 31 using multiple datasets of retrieved or estimated column optical depths. The datasets are based on observations of the Martian atmosphere from April 1999 to July 2013 made by different orbiting instruments: the Thermal Emission Spectrometer (TES) aboard Mars Global Surveyor, the Thermal Emission Imaging System (THEMIS) aboard Mars Odyssey, and the Mars Climate Sounder (MCS) aboard Mars Reconnaissance Orbiter (MRO). The procedure we have adopted consists of gridding the available retrievals of column dust optical depth (CDOD) from TES and THEMIS nadir observations, as well as the estimates of this quantity from MCS limb observations. Our gridding method calculates averages and uncertainties on a regularly spaced, but possibly incomplete, spatio-temporal grid, using an iterative procedure weighted in space, time, and retrieval uncertainty. In order to evaluate strengths and weaknesses of the resulting gridded maps, we validate them with independent observations of CDOD. We have statistically analyzed the irregularly gridded maps to provide an overview of the dust climatology on Mars over eight years, specifically in relation to its interseasonal and interannual variability. Finally, we have produced multiannual, regular daily maps of CDOD by spatially interpolating the irregularly gridded maps using a kriging method. These synoptic maps are used as dust scenarios in the Mars Climate Database version 5, and are useful in many modelling applications in addition to forming a basis for instrument intercomparisons. The derived dust maps for the eight available Martian years are publicly available and distributed with open access.
We discuss the current state of knowledge of terrestrial planet formation from the aspects of different planet formation models and isotopic data from 182Hf-182W, U-Pb, lithophile-siderophile elements, 48Ca/44Ca isotope samples from planetary building blocks, 36Ar/38Ar, 20Ne/22Ne, 36Ar/22Ne isotope ratios in Venus and Earths atmospheres, the expected solar 3He abundance in Earths deep mantle and Earths D/H sea water ratios that shed light on the accretion time of the early protoplanets. Accretion scenarios that can explain the different isotope ratios, including a Moon-forming event after ca. 50 Myr, support the theory that the bulk of Earths mass (>80%) most likely accreted within 10-30 Myr. From a combined analysis of the before mentioned isotopes, one finds that proto-Earth accreted 0.5-0.6 MEarth within the first ~4-5 Myr, the approximate lifetime of the protoplanetary disk. For Venus, the available atmospheric noble gas data are too uncertain for constraining the planets accretion scenario accurately. However, from the available Ar and Ne isotope measurements, one finds that proto-Venus could have grown to 0.85-1.0 MVenus before the disk dissipated. Classical terrestrial planet formation models have struggled to grow large planetary embryos quickly from the tiniest materials within the typical lifetime of protoplanetary disks. Pebble accretion could solve this long-standing time scale controversy. Pebble accretion and streaming instabilities produce large planetesimals that grow into Mars-sized and larger planetary embryos during this early accretion phase. The later stage of accretion can be explained well with the Grand-Tack, annulus or depleted disk models. The relative roles of pebble accretion and planetesimal accretion/giant impacts are poorly understood and should be investigated with N-body simulations that include pebbles and multiple protoplanets.
Composition of terrestrial planets records planetary accretion, core-mantle and crust-mantle differentiation, and surface processes. Here we compare the compositional models of Earth and Mars to reveal their characteristics and formation processes. Earth and Mars are equally enriched in refractory elements (1.9 $times$ CI), although Earth is more volatile-depleted and less oxidized than Mars. Their chemical compositions were established by nebular fractionation, with negligible contributions from post-accretionary losses of moderately volatile elements. The degree of planetary volatile element depletion might correlate with the abundances of chondrules in the accreted materials, planetary size, and their accretion timescale, which provides insights into composition and origin of Mercury, Venus, the Moon-forming giant impactor, and the proto-Earth. During its formation before and after the nebular disks lifetime, the Earth likely accreted more chondrules and less matrix-like materials than Mars and chondritic asteroids, establishing its marked volatile depletion. A giant impact of an oxidized, differentiated Mars-like (i.e., composition and mass) body into a volatile-depleted, reduced proto-Earth produced a Moon-forming debris ring with mostly a proto-Earths mantle composition. Chalcophile and some siderophile elements in the silicate Earth added by the Mars-like impactor were extracted into the core by a sulfide melt. In contrast, the composition of Mars indicates its rapid accretion of lesser amounts of chondrules under nearly uniform oxidizing conditions. Mars rapid cooling and early loss of its dynamo likely led to the absence of plate tectonics and surface water, and the present-day low surface heat flux. These similarities and differences between the Earth and Mars made the former habitable and the other inhospitable to uninhabitable.
The only discovery of Earth Trojan 2010 TK$_7$ and the subsequent launch of OSIRIS-REx motive us to investigate the stability around the triangular Lagrange points $L_4$ and $L_5$ of the Earth. In this paper we present detailed dynamical maps on the $(a_0,i_0)$ plane with the spectral number (SN) indicating the stability. Two main stability regions, separated by a chaotic region arising from the $ u_3$ and $ u_4$ secular resonances, are found at low ($i_0leq 15^circ$) and moderate ($24^circleq {i_0}leq 37^circ$) inclinations respectively. The most stable orbits reside below $i_0=10^circ$ and they can survive the age of the Solar System. The nodal secular resonance $ u_{13}$ could vary the inclinations from $0^circ$ to $sim 10^circ$ according to their initial values while $ u_{14}$ could pump up the inclinations to $sim 20^circ$ and upwards. The fine structures in the dynamical maps are related to higher-degree secular resonances, of which different types dominate different areas. The dynamical behaviour of the tadpole and horseshoe orbits, reflected in their secular precession, show great differences in the frequency space. The secular resonances involving the tadpole orbits are more sensitive to the frequency drift of the inner planets, thus the instabilities could sweep across the phase space, leading to the clearance of tadpole orbits. We are more likely to find terrestrial companions on horseshoe orbits. The Yarkovsky effect could destabilize Earth Trojans in varying degrees. We numerically obtain the formula describing the stabilities affected by the Yarkovsky effect and find the asymmetry between the prograde and retrograde rotating Earth Trojans. The existence of small primordial Earth Trojans that avoid being detected but survive the Yarkovsky effect for 4.5,Gyr is substantially ruled out.
This study constrains the lower bound of the scattering phase function of Martian water ice clouds (WICs) through the implementation of a new observation aboard the Mars Science Laboratory (MSL). The Phase Function Sky Survey (PFSS) was a multiple pointing all-sky observation taken with the navigation cameras (Navcam) aboard MSL. The PFSS was executed 35 times during the Aphelion Cloud Belt (ACB) season of Mars Year 34 over a solar longitude range of L_s=61.4{deg}-156.5{deg}. Twenty observations occurred in the morning hours between 06:00 and 09:30 LTST, and 15 runs occurred in the evening hours between 14:30 and 18:00 LTST, with an operationally required 2.5 hour gap on either side of local noon due the sun being located near zenith. The resultant WIC phase function was derived over an observed scattering angle range of 18.3{deg} to 152.61{deg}, normalized, and compared with 9 modeled phase functions: seven ice crystal habits and two Martian WIC phase functions currently being implemented in models. Through statistical chi-squared probability tests, the five most probable ice crystal geometries observed in the ACB WICs were aggregates, hexagonal solid columns, hollow columns, plates, and bullet rosettes with p-values greater than or equal to 0.60, 0.57,0.56,0.56, and 0.55, respectively. Droxtals and spheres had p-values of 0.35, and 0.2, making them less probable components of Martian WICs, but still statistically possible ones. Having a better understanding of the ice crystal habit and phase function of Martian water ice clouds directly benefits Martian climate models which currently assume spherical and cylindrical particles.
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