Crater depths, often obtained from shadow measurements, have long been used for several purposes in planetary science. However, the usual method for obtaining depth from shadow length suffers from several drawbacks and limitations. Chappelow and Sharpton (2002) introduced a much improved shadow method, which has the advantages of giving some shape information (as well as depth), and is not limited to shadows that cross the crater bottom. However, it is not general, in that it only gives very approximate crater shape information, in terms of three special cases (parabolic, conical, or flat-floored). Here, I present a completely generalized method, valid for any conic section shaped crater, and give a proof of concept and demonstration of its use, using Linne crater as a test case. In the process, I find that Linne is neither parabolic nor conical, and that it contains approximately 20 m of bottom fill, which forms a flat floor. I also conclude that the long-used parabolic paradigm for the shapes of simple craters may need to be revised.

We report on the isotopic and microstructural properties of four presolar spinel grains identified in acid-resistant residues of the Murray CM2 and Orgueil (ORG) CI1 chondrites, and a mixture of the unequilibrated ordinary chondrites (UOC) QUE 97008 (L3.05), WSG 95300 (H3.3), and MET00452 (LL3.05) collected in Antarctica. All four grains have O-isotopic compositions indicating an origin in low-mass (~1.2 to 1.4 M_⊙) O-rich asymptotic giant branch (AGB) stars, although two of the grains have compositions indicating that non-standard mixing (cool-bottom processing) likely occurred in their parent stars. Three of the grains are single-crystal Mg-Al-rich spinels containing minor Fe and Cr; one is Mg deficient and one contains minor Ca. The fourth consists of an assemblage of three, Fe-Cr-rich crystalline grains with closely aligned crystallographic orientation but systematically varied cation composition. Each spinel grain within the assemblage also contains Ti-rich sub-grains (<100 nm) whose lattice structures are coherent with their host crystals. Oxygen isotope measurements of the Orgueil residue identified four additional particles all with similar elemental and isotope composition. These are the first known presolar Fe-Cr-rich spinels.
The isotopic and microstructural data indicate that the Al-Mg-rich and Fe-Cr-rich grains experienced different condensation and processing histories. The single-crystal, stoichiometric, nearly pure Mg-Al spinels are generally consistent with equilibrium condensation predictions, which constrain their condensation temperatures between 1161 K and 1221 K, assuming total gas pressures of 1×10^-6 and 1×10^-3 atm, respectively. Minor stacking disorder is observed in one of the Mg-Al spinels and is probably a result of slight perturbations to crystal growth during condensation in the circumstellar environment or by impact-induced sheer strain as a response to grain-grain collisions, which could have occurred in the circumstellar environment, the interstellar medium, or the solar nebula. The minor Ca in one of the Mg-Al spinels suggests back reaction with the circumstellar gas from which it formed. In comparison, the similarly oriented Fe-Cr-rich grains of the Orgueil assemblage and their homogeneous isotopic compositions are consistent with their condensation as a single circumstellar dust particle. However, the Fe-Cr-rich compositions (nearly chromite) are inconsistent with predictions for equilibrium condensation and suggest a complex cooling history that is not possible to precisely constrain.

Context. Binary asteroids are common in the solar system, including in the Kuiper belt. However, there seems to be a marked disparity between the binary populations in the classical part of the Kuiper belt and the part of the belt in the 3:2 resonance with Neptune – i.e., the region inhabited by the Plutinos. In particular, binary Plutinos are extremely rare.
Aims. We study the impact of the 3:2 resonance on the formation of Kuiper belt binaries, according to the Nice model, in order to explain such phenomenon.
Methods. Numerical simulations are performed within the 2 + 2 body approximation (Sun/Neptune + binary partners). The MEGNO chaos indicator is used to map out regular and chaotic regions of phase space. Residence times of test (binary) particles within the Hill sphere are compared inside and outside of the 3:2 resonance. The effect of increasing the heliocentric eccentricity of the centre of mass of the binary system is studied. This is done because mean-motion resonances between a planet and an asteroid usually have the effect of increasing the eccentricity of the asteroid.
Results. The stable zones in the MEGNO maps are mainly disrupted in the resonant, eccentric case: the number of binary asteroids created in this case is significantly lower than outside the 3:2 resonance.
Conclusions. In the 2 + 2 body approximation, the pumping of the eccentricity of the centre of mass of a potential binary destabilises the formation of binaries. This may be a factor in explaining the scarcity of binaries in the Plutino population.