Long-term Stable Equilibria for Synchronous Binary Asteroids

Synchronous binary asteroids may exist in a long-term stable equilibrium, where the opposing torques from mutual body tides and the binary YORP (BYORP) effect cancel. Interior of this equilibrium, mutual body tides are stronger than the BYORP effect and the mutual orbit semi-major axis expands to the equilibrium; outside of the equilibrium, the BYORP effect dominates the evolution and the system semi-major axis will contract to the equilibrium. If the observed population of small (0.1 - 10 km diameter) synchronous binaries are in static configurations that are no longer evolving, then this would be confirmed by a null result in the observational tests for the BYORP effect. The confirmed existence of this equilibrium combined with a shape model of the secondary of the system enables the direct study of asteroid geophysics through the tidal theory. The observed synchronous asteroid population cannot exist in this equilibrium if described by the canonical "monolithic" geophysical model. The "rubble pile" geophysical model proposed by \citet{Goldreich2009} is sufficient, however it predicts a tidal Love number directly proportional to the radius of the asteroid, while the best fit to the data predicts a tidal Love number inversely proportional to the radius. This deviation from the canonical and \citet{Goldreich2009} models motivates future study of asteroid geophysics. Ongoing BYORP detection campaigns will determine whether these systems are in an equilibrium, and future determination of secondary shapes will allow direct determination of asteroid geophysical parameters.Comment: 17 pages, 1 figur

Asteroid Systems: Binaries, Triples, and Pairs

In the past decade, the number of known binary near-Earth asteroids has more than quadrupled and the number of known large main belt asteroids with satellites has doubled. Half a dozen triple asteroids have been discovered, and the previously unrecognized populations of asteroid pairs and small main belt binaries have been identified. The current observational evidence confirms that small (<20 km) binaries form by rotational fission and establishes that the YORP effect powers the spin-up process. A unifying paradigm based on rotational fission and post-fission dynamics can explain the formation of small binaries, triples, and pairs. Large (>20 km) binaries with small satellites are most likely created during large collisions.Comment: 31 pages, 12 figures. Chapter in the book ASTEROIDS IV (in press

Thermal Infrared Observations of Asteroid (99942) Apophis with Herschel

The near-Earth asteroid (99942) Apophis is a potentially hazardous asteroid. We obtained far-infrared observations of this asteroid with the Herschel Space Observatory's PACS instrument at 70, 100, and 160 micron. These were taken at two epochs in January and March 2013 during a close Earth encounter. These first thermal measurements of Apophis were taken at similar phase angles before and after opposition. We performed a detailed thermophysical model analysis by using the spin and shape model recently derived from applying a 2-period Fourier series method to a large sample of well-calibrated photometric observations. We find that the tumbling asteroid Apophis has an elongated shape with a mean diameter of 375$^{+14}_{-10}$ m (of an equal volume sphere) and a geometric V-band albedo of 0.30$^{+0.05}_{-0.06}$. We find a thermal inertia in the range 250-800 Jm$^{-2}$s$^{-0.5}$K$^{-1}$ (best solution at 600 Jm$^{-2}$s$^{-0.5}$K$^{-1}$), which can be explained by a mixture of low conductivity fine regolith with larger rocks and boulders of high thermal inertia on the surface. The thermal inertia, and other similarities with (25143) Itokawa indicate that Apophis might also have a rubble-pile structure. If we combine the new size value with the assumption of an Itokawa-like density and porosity we estimate a mass between 4.4 and 6.2 10$^{10}$ kg which is more than 2-3 times larger than previous estimates. We expect that the newly derived properties will influence impact scenario studies and influence the long-term orbit predictions of Apophis.Comment: Accepted for publication in Astronomy & Astrophysics, 21 pages, 8 figures, 2 table

Photometry and Spin Rate Distribution of Small-Sized Main Belt Asteroids

Photometry results of 32 asteroids are reported from only seven observing nights on only seven fields, consisting of 34.11 cumulative hours of observations. The data were obtained with a wide-field CCD (40.5'x27.3') mounted on a small, 46-cm telescope at the Wise Observatory. The fields are located within 1.5 degrees from the ecliptic plane and include a region within the main asteroid belt. The observed fields show a projected density of ~23.7 asteroids per square degree to the limit of our observations. 13 of the lightcurves were successfully analyzed to derive the asteroids' spin periods. These range from 2.37 up to 20.2 hours with a median value of 3.7 hours. 11 of these objects have diameters in order of two km and less, a size range that until recently has not been photometrically studied. The results obtained during this short observing run emphasize the efficiency of wide-field CCD photometry of asteroids, which is necessary to improve spin statistics and understand spin evolution processes. We added our derived spin periods to data from the literature and compared the spin rate distributions of small main belt asteroids (5>D>0.15 km) with that of bigger asteroids and of similar-sized NEAs. We found that the small MBAs do not show the clear Maxwellian-shaped distribution as large asteroids do; rather they have a spin rate distribution similar to that of NEAs. This implies that non-Maxwellian spin rate distribution is controlled by the asteroids' sizes rather than their locations.Comment: 46 pages, 27 figures, 6 tables, accepted for publication in Icaru

Some Results of the Educational Experiment APIS (Cervantes Mission on Board ISS)

Some results of the analysis of the pictures taken along the performance of the Análisis de Propiedades Inerciales de Sólidos, Analysis of the Inertia Properties of Solid Bodies (APIS) experiment carried out in the Cervantes mission on board ISS, are presented. APIS was an educational experiment devoted to take advantage of the unique conditions of absence of relative gravity forces of a space platform such as ISS, to show some of the characteristics of the free rotational motion of a solid body, which are impossible to carry out on earth. This field of experimental research has application to aerospace engineering science (e.g. attitude control of spacecrafts), to astrophysical sciences (e.g. state of rotation and tumbling motions of asteroids) and to engineering education. To avoid the effect of the ambient atmosphere loads on the motion, the test body is placed inside a sphere, which reduces the effect of the aerodynamic forces to just friction. The drastic reduction of the effect of the surrounding air during the short duration of the experimental sequences allows us to compare the actual motion with the known solutions for the solid body rotation in vacuum. In this paper, some selected, relevant sequences of the sphere enclosing a body with a nominal cylindrical inertia tensor, put into rotation by the astronaut, are shown; the main problems to extract the information concerning the characteristic parameters of the motion are outlined, and some of the results obtained concerning the motion of the test probe are included, which show what seems to be a curious and unexpected solution of the Euler equations for the solid body rotation in vacuum, without energy dissipation, when the angular momentum is almost perpendicular to the axisymmetry axis

Tidal disruption of NEAs - a case of P\v{r}\'ibram

This work studies the dynamical evolution of a possible meteor stream along the orbit of the P\v{r}\'{i}bram meteorite, which originated in the tidal disruption of the putative rubble-pile-like parent body during a close approach to the Earth. We assumed the disruption at the time when the ascending or descending node of the parent orbit was close to the Earth's orbit. In the last 5000 years, the P\v{r}\'{i}bram orbit has crossed the Earth orbit twice. It happened about 4200 years and 3300 years ago. In both cases, we modeled the release of particles from the simplified model of rotating asteroid, and traced their individual orbital evolution to the current date. It takes several hundred years to spread released meteoroids along the entire orbit of the parent body. Even today, the stream would be relatively narrow. Considering a model parent body with physical parameters of the asteroid Itokawa, the complete disintegration of the object produced 3.8$\times10^{11}$ meteoroid particles with diameter $\geq$ 1\,cm. The meteor activity observed from the Earth is revealed and justification of follow-up observation during suggested activity of the shower in the first two weeks of April is discussed. The Earth's tidal forces would disintegrate a fraction of NEA population into smaller objects. We evaluate the upper limit of mass of disintegrated asteroids within the mean NEA lifetime and the contribution of disrupted matter to the size distribution of the NEA.Comment: 8 pages, 10 figure

The strength and detectability of the YORP effect in near-Earth asteroids: a statistical approach

In addition to collisions and gravitational forces, it is now becoming widely acknowledged that photon recoil forces and torques from the asymmetric reflection and thermal re-radiation of sunlight are primary mechanisms that govern the rotational evolution of an asteroid. The Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect causes changes in the rotation rate and pole direction of an irregularly shaped asteroid. We present a simple Monte Carlo method to estimate the range of YORP rotational accelerations acting on a near-Earth asteroid (NEA) without knowledge of its detailed shape, and to estimate its detectability using light-curve observations. The method requires knowledge of an asteroid's orbital properties and size, and assumes that the future observational circumstances of an asteroid have already been thought through. It is verified by application to the observational circumstances of the seven YORP-investigated asteroids, and is then applied to 540 NEAs with NEOWISE and/or other diameter measurements, and to all NEAs using Minor Planet Center Orbit absolute magnitudes. The YORP detectability is found to be a strong function of the combined asteroid orbital and diameter properties, and is independent of the rotation period for NEAs that do not have very fast or slow rotation rates. The median and 1σ spread of YORP rotational acceleration expected to be acting on a particular NEA (dω/dt in rad yr−2) can be estimated from its semimajor axis (a in au), eccentricity (e) and diameter (D in km) by using |dω/dt|=1.20+1.66−0.86 ×10−2 (a2 √1−e2D2)−1 and/or by using |dω/dt|=1.00+3.07−0.81 ×10−2 (a2√1−e2D2)−1 if the diameter is instead estimated from the absolute magnitude by assuming a geometric albedo of 0.1. The length of a light-curve observational campaign required to achieve a 50 per cent probability of detecting the YORP effect in a particular NEA (TCAM_50 in yr) can be estimated by using TCAM_50=12.5(a2√1−e2D2)1/2 and/or by using TCAM_50 =13.7(a2√1−e2D2)1/2 for an absolute-magnitude-estimated diameter. To achieve a 95 per cent YORP-detection probability, these last two relations need to be multiplied by factors of ~3.4 and ~4.5, respectively. This method and approximate relations will be useful for astronomers who plan to look for YORP rotational acceleration in specific NEAs, and for all-sky surveys that may serendipitously observe NEA light curves