The Relativistic Factor in the Orbital Dynamics of Point Masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations

"TNOs are Cool": A survey of the trans-Neptunian region: XIV. Size/albedo characterization of the Haumea family observed with Herschel and Spitzer

Context. A group of trans-Neptunian objects (TNOs) are dynamically related to the dwarf planet 136108 Haumea. Ten of them show strong indications of water ice on their surfaces, are assumed to have resulted from a collision, and are accepted as the only known TNO collisional family. Nineteen other dynamically similar objects lack water ice absorptions and are hypothesized to be dynamical interlopers. Aims. We have made observations to determine sizes and geometric albedos of six of the accepted Haumea family members and one dynamical interloper. Ten other dynamical interlopers have been measured by previous works. We compare the individual and statistical properties of the family members and interlopers, examining the size and albedo distributions of both groups. We also examine implications for the total mass of the family and their ejection velocities. Methods. We use far-infrared space-based telescopes to observe the target TNOs near their thermal peak and combine these data with optical magnitudes to derive sizes and albedos using radiometric techniques. Using measured and inferred sizes together with ejection velocities, we determine the power-law slope of ejection velocity as a function of effective diameter. Results. The detected Haumea family members have a diversity of geometric albedos 0.3-0.8, which are higher than geometric albedos of dynamically similar objects without water ice. The median geometric albedo for accepted family members is pV = 0.48-0.18 +0.28, compared to 0.08-0.05 +0.07 for the dynamical interlopers. In the size range D = 175-300 km, the slope of the cumulative size distribution is q = 3.2-0.4 +0.7 for accepted family members, steeper than the q = 2.0 ± 0.6 slope for the dynamical interlopers with D < 500 km. The total mass of Haumea's moons and family members is 2.4% of Haumea's mass. The ejection velocities required to emplace them on their current orbits show a dependence on diameter, with a power-law slope of 0.21-0.50. © ESO 2018.Part of this work was supported by the German DLR project number 50 OR 1108. T.M., C.K., P.S., and R.D. acknowledge that the research leading to these results has received funding from the European Union's Horizon 2020 Research and Innovation Programme, under Grant Agreement no 687378. A.P. acknowledges the grant LP2012-31 of the Hungarian Academy of Sciences. N.P. acknowledges funding by the Portuguese FCT - Foundation for Science and Technology (ref: SFRH/BGCT/113686/2015). CITEUC is funded by Portuguese National Funds through FCT - Foundation for Science and Technology (project: UID/Multi/00611/2013) and FEDER - European Regional Development Fund through COMPETE 2020 - Operational Programme Competitiveness and Internationalisation (project: POCI-01-0145-FEDER-006922). C.K. has been supported by the K-125015 and GINOP-2.3.2-15-2016-00003 grants of the National Research, Development and Innovation Office (NKFIH, Hungary)

Impact cratering experiments in brittle targets with variable thickness: implications for deep pit craters on Mars

High-resolution images reveal that numerous pit craters exist on the surface of Mars. For some pit craters, the depth-to-diameter ratios are much greater than for ordinary craters. Such deep pit craters are generally considered to be the results of material drainage into a subsurface void space, which might be formed by a lava tube, dike injection, extensional fracturing, and dilational normal faulting. Morphological studies indicate that the formation of a pit crater might be triggered by the impact event, and followed by collapse of the ceiling. To test this hypothesis, we carried out laboratory experiments of impact cratering into brittle targets with variable roof thickness. In particular, the effect of the target thickness on the crater formation is studied to understand the penetration process by an impact. For this purpose, we produced mortar targets with roof thickness of 1–6 cm, and a bulk density of 1550 kg/m3 by using a mixture of cement, water and sand (0.2 mm) in the ratio of 1:1:10, by weight. The compressive strength of the resulting targets is 3.2±0.9 MPa. A spherical nylon projectile (diameter 7 mm) is shot perpendicularly into the target surface at the nominal velocity of 1.2 km/s, using a two-stage light-gas gun. Craters are formed on the opposite side of the impact even when no target penetration occurs. Penetration of the target is achieved when craters on the opposite sides of the target connect with each other. In this case, the cross section of crater somehow attains a flat hourglass-like shape. We also find that the crater diameter on the opposite side is larger than that on the impact side, and more fragments are ejected from the crater on the opposite side than from the crater on the impact side. This result gives a qualitative explanation for the observation that the Martian deep pit craters lack a raised rim and have the ejecta deposit on their floor instead

The Delivery of Water During Terrestrial Planet Formation

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. We review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, and the delivery efficiency is very low, such that it may be difficult to deliver even a single Earth ocean of water this way. The most promising route for water delivery is the accretion of material from beyond the snow line, similar to carbonaceous chondrites, that is scattered into the terrestrial planet region as the planets are growing. Two main scenarios are discussed in detail. First is the classical scenario in which the giant planets begin roughly in their final locations and the disk of planetesimals and embryos in the terrestrial planet region extends all the way into the outer asteroid belt region. Second is the Grand Tack scenario, where early inward and outward migration of the giant planets implants material from beyond the snow line into the asteroid belt and terrestrial planet region, where it can be accreted by the growing planets. Sufficient water is delivered to the terrestrial planets in both scenarios. While the Grand Tack scenario provides a better fit to most constraints, namely the small mass of Mars, planets may form too fast in the nominal case discussed here. This discrepancy may be reduced as a wider range of initial conditions is explored. Finally, we discuss several more recent models that may have important implications for water delivery to the terrestrial planets