Dynamic Limits on Planar Libration-Orbit Coupling Around an Oblate Primary

This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion or when the satellite will circulate with respect to the primary. We find the existence of stable equilibrium points about which the satellite can librate, and explore both the linearized and non-linear dynamics around these points. Absolute bounds are placed on the phase space of the libration-orbit coupling through the use of zero-velocity curves that exist in the system. These zero-velocity curves are used to derive a sufficient condition for when the satellite's libration is bound to less than 90 degrees. When this condition is not satisfied so that circulation of the satellite is possible, the initial conditions at zero libration angle are determined which lead to circulation of the satellite. Exact analytical conditions for circulation and the maximum libration angle are derived for the case of a small satellite in orbits of any eccentricity.Comment: Submitted to Celestial Mechanics and Dynamical Astronom

A Gravitational Tractor for Towing Asteroids

We present a concept for a spacecraft that can controllably alter the trajectory of an Earth threatening asteroid using gravity as a towline. The spacecraft hovers near the asteroid with thrusters angled outward so the exhaust does not impinge on the surface. This deflection method is insensitive to the structure, surface properties, and rotation state of the asteroid.Comment: 4 pages, 1 figure - to be published in Natur

Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields : A first approach

This article provides a method for nding initial conditions for perturbed frozen orbits around inhomogeneous fast rotating asteroids. These orbits can be used as reference trajectories in missions that require close inspection of any rigid body. The generalized perturbative procedure followed exploits the analytical methods of relegation of the argument of node and Delaunay normalisation to arbitrary order. These analytical methods are extremely powerful but highly computational. The gravitational potential of the heterogeneous body is rstly stated, in polar-nodal coordinates, which takes into account the coecients of the spherical harmonics up to an arbitrary order. Through the relegation of the argument of node and the Delaunay normalization, a series of canonical transformations of coordinates is found, which reduces the Hamiltonian describing the system to a integrable, two degrees of freedom Hamiltonian plus a truncated reminder of higher order. Setting eccentricity, argument of pericenter and inclination of the orbit of the truncated system to be constant, initial conditions are found, which evolve into frozen orbits for the truncated system. Using the same initial conditions yields perturbed frozen orbits for the full system, whose perturbation decreases with the consideration of arbitrary homologic equations in the relegation and normalization procedures. Such procedure can be automated for the first homologic equation up to the consideration of any arbitrary number of spherical harmonics coefficients. The project has been developed in collaboration with the European Space Agency (ESA)

The tumbling rotational state of 1I/‘Oumuamua

The discovery of 1I/2017 U1 (1I/‘Oumuamua) has provided the first glimpse of a planetesimal born in another planetary system. This interloper exhibits a variable colour within a range that is broadly consistent with local small bodies, such as the P- and D-type asteroids, Jupiter Trojans and dynamically excited Kuiper belt objects. 1I/‘Oumuamua appears unusually elongated in shape, with an axial ratio exceeding 5:1. Rotation period estimates are inconsistent and varied, with reported values between 6.9 and 8.3 h. Here, we analyse all the available optical photometry data reported to date. No single rotation period can explain the exhibited brightness variations. Rather, 1I/‘Oumuamua appears to be in an excited rotational state undergoing non-principal axis rotation, or tumbling. A satisfactory solution has apparent lightcurve frequencies of 0.135 and 0.126 h−1 and implies a longest-to-shortest axis ratio of ≳5:1, although the available data are insufficient to uniquely constrain the true frequencies and shape. Assuming a body that responds to non-principal axis rotation in a similar manner to Solar System asteroids and comets, the timescale to damp 1I/‘Oumuamua’s tumbling is at least one billion years. 1I/‘Oumuamua was probably set tumbling within its parent planetary system and will remain tumbling well after it has left ours

Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA

Space missions and ground-based observations have shown that some asteroids are loose collections of rubble rather than solid bodies. The physical behaviour of such ‘rubble-pile’ asteroids has been traditionally described using only gravitational and frictional forces within a granular material. Cohesive forces in the form of small van der Waals forces between constituent grains have recently been predicted to be important for small rubble piles (ten kilometres across or less), and could potentially explain fast rotation rates in the small-asteroid population. The strongest evidence so far has come from an analysis of the rotational breakup of the main-belt comet P/2013 R3, although that was indirect and poorly constrained by observations. Here we report that the kilometre-sized asteroid (29075) 1950 DA is a rubble pile that is rotating faster than is allowed by gravity and friction. We find that cohesive forces are required to prevent surface mass shedding and structural failure, and that the strengths of the forces are comparable to, though somewhat less than, the forces found between the grains of lunar regolith

The Main Belt Comets and ice in the Solar System

We review the evidence for buried ice in the asteroid belt; specifically the questions around the so-called Main Belt Comets (MBCs). We summarise the evidence for water throughout the Solar System, and describe the various methods for detecting it, including remote sensing from ultraviolet to radio wavelengths. We review progress in the first decade of study of MBCs, including observations, modelling of ice survival, and discussion on their origins. We then look at which methods will likely be most effective for further progress, including the key challenge of direct detection of (escaping) water in these bodies

The dynamic geophysical environment of (101955) Bennu based on OSIRIS-REx measurements

The top-shaped morphology characteristic of asteroid (101955) Bennu, often found among fast-spinning asteroids and binary asteroid primaries, may have contributed substantially to binary asteroid formation. Yet a detailed geophysical analysis of this morphology for a fast-spinning asteroid has not been possible prior to the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) mission. Combining the measured Bennu mass and shape obtained during the Preliminary Survey phase of the OSIRIS-REx mission, we find a notable transition in Bennu’s surface slopes within its rotational Roche lobe, defined as the region where material is energetically trapped to the surface. As the intersection of the rotational Roche lobe with Bennu’s surface has been most recently migrating towards its equator (given Bennu’s increasing spin rate), we infer that Bennu’s surface slopes have been changing across its surface within the last million years. We also find evidence for substantial density heterogeneity within this body, suggesting that its interior is a mixture of voids and boulders. The presence of such heterogeneity and Bennu’s top shape are consistent with spin-induced failure at some point in its past, although the manner of its failure cannot yet be determined. Future measurements by the OSIRIS-REx spacecraft will provide insight into and may resolve questions regarding the formation and evolution of Bennu’s top-shape morphology and its link to the formation of binary asteroids

Evidence for widespread hydrated minerals on asteroid (101955) Bennu

Early spectral data from the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) mission reveal evidence for abundant hydrated minerals on the surface of near-Earth asteroid (101955) Bennu in the form of a near-infrared absorption near 2.7 µm and thermal infrared spectral features that are most similar to those of aqueously altered CM-type carbonaceous chondrites. We observe these spectral features across the surface of Bennu, and there is no evidence of substantial rotational variability at the spatial scales of tens to hundreds of metres observed to date. In the visible and near-infrared (0.4 to 2.4 µm) Bennu’s spectrum appears featureless and with a blue (negative) slope, confirming previous ground-based observations. Bennu may represent a class of objects that could have brought volatiles and organic chemistry to Earth