Paul A. Wiegert

Long term stability of planets in binary systems

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the systems center of mass, are examined. From the results, empirical expressions are developed for both (1) the largest orbit around each of the stars and (2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (104 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio μ and the binary eccentricity e, are determined for the range 0.0 ≤ e ≤ 0.7–0.8 and 0.1 ≤ μ ≤ 0.9 in both regions and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually interacting system of planets orbiting one star of a binary system is examined, though in less detail.

The trajectory, structure and origin of the Chelyabinsk asteroidal impactor

Earth is continuously colliding with fragments of asteroids and comets of various sizes. The largest encounter in historical times occurred over the Tunguska river in Siberia in 1908, producing an airburst of energy equivalent to 5–15 megatons of trinitrotoluene (1 kiloton of trinitrotoluene represents an energy of 4.185 × 1012 joules). Until recently, the next most energetic airburst events occurred over Indonesia in 2009 and near the Marshall Islands in 1994, both with energies of several tens of kilotons. Here we report an analysis of selected video records of the Chelyabinsk superbolide of 15 February 2013, with energy equivalent to 500 kilotons of trinitrotoluene, and details of its atmospheric passage. We found that its orbit was similar to the orbit of the two-kilometre-diameter asteroid 86039 (1999 NC43), to a degree of statistical significance sufficient to suggest that the two were once part of the same object. The bulk strength—the ability to resist breakage—of the Chelyabinsk asteroid, of about one megapascal, was similar to that of smaller meteoroids and corresponds to a heavily fractured single stone. The asteroid broke into small pieces between the altitudes of 45 and 30 kilometres, preventing more-serious damage on the ground. The total mass of surviving fragments larger than 100 grams was lower than expected.

Earth/'s Trojan asteroid

It was realized in 1772 that small bodies can stably share the same orbit as a planet if they remain near ‘triangular points’ 60° ahead of or behind it in the orbit. Such ‘Trojan asteroids’ have been found co-orbiting with Jupiter, Mars and Neptune. They have not hitherto been found associated with Earth, where the viewing geometry poses difficulties for their detection, although other kinds of co-orbital asteroid (horseshoe orbiters and quasi-satellites) have been observed. Here we report an archival search of infrared data for possible Earth Trojans, producing the candidate 2010 TK7. We subsequently made optical observations which established that 2010 TK7 is a Trojan companion of Earth, librating around the leading Lagrange triangular point, L4. Its orbit is stable over at least ten thousand years.

The stability of planets in the alpha centauri system

This paper investigates the long-term orbital stability of small bodies near the central binary of the Alpha Centauri system. Test particles on circular orbits are integrated in the field of this binary for 32 000 binary periods or approximately 2.5 Myr. In the region exterior to the binary, particles with semi-major axes less than roughly three times the binary’s semi-major axis ab are unstable. Inside the binary, particles are unstable if further than 0.2 ab from the primary, with stablility closer in a strong function of inclination: orbits inclined near 90 ◦ are unstable in as close as 0.01 ab from either star.

An asteroidal companion to the Earth

Near-Earth asteroids range in size from a few metres to more than 30 km: in addition to playing an important role in past and present impact rates on the Earth, they might one day be exploited as bases for space exploration or as mineral resources. Many near-Earth asteroids move on orbits crossing that of the Earth, but none has hitherto been identified as a dynamical companion to the Earth. Here we show that the orbit of asteroid 3753 (1986 TO), when viewed in the reference frame centred on the Sun but orbiting with the Earth, has a distinctive shape characteristic of ‘horseshoe’ orbits. Although horseshoe orbits are a well-known feature of the gravitational three-body problem, the only other examples of objects moving on such orbits are the saturnian satellites Janus and Epimetheus—and their behaviour is much less intricate than that of 3753. Moreover, the fact that 3753 exhibits such a dynamical relationship with the Earth shows that, although it is not a satellite of our planet per se, it is, apart from the Moon, the only known natural companion of the Earth.

The Orbital Evolution of Near-Earth Asteroid 3753

Asteroid 3753 (1986 TO) is in a 1:1 mean motion resonance with Earth, on a complex horseshoe-type orbit. Numerical experiments are performed to determine its medium-term stability and the means by which it may have entered its current orbit. Though 3753 moves primarily under the influence of the Sun and Earth, the giant planets (and Jupiter especially) play an important role by influencing, through torque-induced precession, the position of the asteroids nodes. Variations in the nodal distance strongly affect the interaction of 3753 with Earth and may change or destroy the horseshoe-like behavior currently seen. This precession of the nodes provides a mechanism for placing minor planets into, or removing them from, a variety of horseshoe-type orbits. The chaotic nature of this asteroids orbit makes predictions difficult on timescales longer than its Lyapunov time (~150 yr); therefore, ensembles of particles on orbits near that of 3753 are considered. The asteroid has a high probability of passing close to Venus and/or Mars on 104 yr timescales, pointing to a dynamical age much shorter than that of the solar system.

The Stability of Quasi Satellites in the Outer Solar System

Quasi satellites are bodies in a particular configuration of a 1 : 1 mean motion resonance, one in which they librate about the longitude of their associated planet. We investigate numerically the stability of such orbits around the giant planets of our solar system. We find that test particles can remain on quasi-satellite orbits around Uranus and Neptune for times up to 109 yr in some cases, though only at low inclinations relative to their accompanying planet and over a restricted range of heliocentric eccentricities. These stable areas are well outside the traditional satellite region. Based on these results, we conclude that a primordial population of such objects may still exist in our solar system.

Searching for main-belt comets using the Canada-France-Hawaii Telescope Legacy Survey

Abstract The Canada–France–Hawaii Telescope Legacy Survey, specifically the Very Wide segment of data, is used to search for possible main-belt comets. In the first data set, 952 separate objects with asteroidal orbits within the main-belt are examined using a three-level technique. First, the full-width-half-maximum of each object is compared to stars of similar magnitude, to look for evidence of a coma. Second, the brightness profiles of each object are compared with three stars of the same magnitude, which are nearby on the image to ensure any extended profile is not due to imaging variations. Finally, the star profiles are subtracted from the asteroid profile and the residuals are compared with the background using an unpaired T-test. No objects in this survey show evidence of cometary activity. The second survey includes 11438 objects in the main-belt, which are examined visually. One object, an unknown comet, is found to show cometary activity. Its motion is consistent with being a main-belt asteroid, but the observed arc is too short for a definitive orbit calculation. No other body in this survey shows evidence of cometary activity. Upper limits of the number of weakly and strongly active main-belt comets are derived to be 630 ± 77 and 87 ± 28 , respectively. These limits are consistent with those expected from asteroid collisions. In addition, data extracted from the Canada–France–Hawaii Telescope image archive of main-belt Comet 176P/LINEAR is presented.

Will comet 209P/LINEAR generate the next meteor storm?

Previous studies have suggested that Comet 209P/LINEAR may produce strong meteor activity on Earth on 2014 May 24; however, exact timing and activity level is difficult to estimate due to the limited physical observations of the comet. Here we reanalyze the optical observations of 209P/LINEAR obtained during its 2009 apparition. We find that the comet is relatively depleted in dust production, with Afρ at 1 cm level within eight months around its perihelion. This feature suggested that this comet may be currently transitioning from typical comet to a dormant comet. Syndyne simulation shows that the optical cometary tail is dominated by larger particles with β � 0.003. Numerical simulations of the cometary dust trails confirm the arrival of particles on 2014 May 24 from some of the 1798–1979 trails. The nominal radiant is at RA 122 ◦ ± 1 ◦ , Dec 79 ◦ ± 1 ◦ (J2000) in the constellation of Camelopardalis. Given that the comet is found to be depleted in dust production, we concluded that a meteor storm (ZHR> 1000) may be unlikely. However, our simulation also shows that the size distribution of the arrived particles is skewed strongly to larger particles. Coupling with the result of syndyne simulation, we think that the event, if detectable, may be dominated by bright meteors. We encourage observers to monitor the expected meteor event as it will provide us with rare direct information on the dynamical history of 209P/LINEAR which is otherwise irretrievably lost.

An upper limit on gas production from 3200 Phaethon

Abstract Asteroid 3200 Phaethon resembles a comet in some ways, including a highly-eccentric orbit ( e ∼ 0.89 ) and a strong associated meteor shower (the Geminids). Yet this object has never been observed to exhibit any cometary activity, i.e., gas production. We observed 3200 Phaethon with the Caltech Submillimeter Observatory on two occasions, once while it was near its closest approach to Earth as it neared perihelion, and another while it was further from Earth post-perihelion. Observations of the J = 2 → 1 and J = 3 → 2 rotational transitions of 12CO, typically strong lines in comets and indicative of gas production, yielded no detection. Upper limits on the 12CO production of 1.8 × 10 28 and 7.6 × 10 28 molecules s −1 for Phaethon were determined on these two occasions.