New data from observations of asteroid mutural perturbation events, observations of asteroid satellites, and spacecraft encounters have revolutionized our understanding of asteroid bulk density.

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Asteroid Density, Porosity, and Structure

Hubble Space Telescope images of asteroid 4 Vesta obtained during the favorable 1996 apparition show an impact crater 460 kilometers in diameter near the south pole. Color measurements within the 13-kilometer-deep crater are consistent with excavation deep into a high-calcium pyroxene-rich crust or olivine upper mantle. About 1 percent of Vesta was excavated by the crater formation event, a volume sufficient to account for the family of small Vesta-like asteroids that extends to dynamical source regions for meteorites. This crater may be the site of origin for the howardite, eucrite, and diogenite classes of basaltic achondrite meteorites.

https://science.sciencemag.org/content/sci/277/5331/1492.full.pdf

Impact excavation on Asteroid 4 Vesta: Hubble Space Telescope results

The research described in this publication was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. © 2014 California Institute of Technology. U.S. Government sponsorship acknowledged. abstract. — The planetary and lunar ephemerides DE430 and DE431 are generated by fitting numerically integrated orbits of the Moon and planets to observations. The present-day lunar orbit is known to submeter accuracy through fitting lunar laser ranging data with an updated lunar gravity field from the Gravity Recovery and Interior Laboratory (GRAIL) mission. The orbits of the inner planets are known to subkilometer accuracy through fitting radio tracking measurements of spacecraft in orbit about them. Very long baseline interferometry measurements of spacecraft at Mars allow the orientation of the ephemeris to be tied to the International Celestial Reference Frame with an accuracy of 0′′.0002. This orientation is the limiting error source for the orbits of the terrestrial planets, and corresponds to orbit uncertainties of a few hundred meters. The orbits of Jupiter and Saturn are determined to accuracies of tens of kilometers as a result of fitting spacecraft tracking data. The orbits of Uranus, Neptune, and Pluto are determined primarily from astrometric observations, for which measurement uncertainties due to the Earth’s atmosphere, combined with star catalog uncertainties, limit position accuracies to several thousand kilometers. DE430 and DE431 differ in their integrated time span and lunar dynamical modeling. The dynamical model for DE430 included a damping term between the Moon’s liquid core and solid mantle that gives the best fit to lunar laser ranging data but that is not suitable for backward integration of more than a few centuries. The ephemeris DE431 is similar to DE430 but was fit without the core/mantle damping term, so the lunar orbit is less accurate than in DE430 for times near the current epoch, but is more suitable for times more than a few centuries in the past. DE431 is a longer integration (covering years –13,200 to +17,191) than DE430 (covering years 1550 to 2650).

The Planetary and Lunar Ephemerides DE430 and DE431

[1] We modeled several thermal evolution scenarios for Ceres to explore the nature of large, wet protoplanets and to predict current-day evidence that might be found by close inspection, such as by the Dawn mission. The density for Ceres is near 2.1, suggesting a water content between 17% and 27% by mass. Short- and long-lived radioactive nuclide heating is considered. Even if only long-lived radionuclide heating is assumed, the water ice in Ceres melts quickly and a water mantle forms, but an approximately 10-km crust does not melt. The circulating warm water would alter the silicates. As heat is lost by conduction through the frozen crust, water begins to freeze out at the base of the crust. Solid-state convection begins and transports more heat as well as perhaps material dissolved or entrained in the water to or near the surface. Ceres' water layer eventually (but perhaps not entirely) freezes, forming a layered density structure with perhaps some liquid water remaining today. Our differentiated models are in agreement with the recently measured difference between the equatorial and polar radii. We find that Ceres' existence and evolution depend critically on it containing water at formation, and this depends strongly on the combination of when it accreted and the amount of 26Al present in the pre-Ceres ∼1-km-sized objects; slightly more 26Al or earlier accretion produces a dry Vesta-like object. Melting and freezing plus mineralization would lead to several dimensional changes over time, creating topographic features, zones of weakness, and perhaps disruptions in the crust.

https://hal.archives-ouvertes.fr/hal-00116029/document

Ceres: Evolution and current state

A Thermal Model for the Differentiation of Asteroid 4 Vesta, Based on Radiogenic Heating☆

A determination of the masses of Ceres, Pallas, and Vesta from their perturbations upon the orbit of Mars

It is shown that the problem of computing astronomical refraction for any value of the zenith angle may be reduced to a simple, nonsingular, numerical quadrature when the proper choice is made for the independent variable of integration. The angle between the radius vector and the light ray is such a choice. The implementation of the quadrature method is discussed in its general form and illustrated by means of an application to a piecewise polytropic atmosphere. The flexibility, simplicity, and computational efficiency of the method are evident.

https://iopscience.iop.org/article/10.1086/301325/pdf

Astronomical Refraction: Computational Method for All Zenith Angles

Galileo's observation of Neptune

The planetary and lunar ephemerides have their own inherent reference frame which is one of the key frames to he considered in the unification of the many present day frames, both celestial and terrestrial. The use of this frame requires an understanding of its own accuracies, both internal (i.e., relative) and external (e.g., w.r.t. the FK4 system or w.r.t. the dynamical equinox). Such accuracies are discussed in this paper. Also noted are the expected improvements in the future which will be obtained from newer data types.

E. Myles Standish

Papers

A determination of the masses of Ceres, Pallas, and Vesta from their perturbations upon the orbit of Mars

Astronomical Refraction: Computational Method for All Zenith Angles

Galileo's observation of Neptune

On the Reference Frame of the Planetary Ephemerides