Statistical and Numerical Study of Asteroid Orbital Uncertainty

The knowledge of the orbit or the ephemeris uncertainty of asteroid presents a particular interest for various purposes. These quantities are for instance useful for recovering asteroids, for identifying lost asteroids or for planning stellar occultation campaigns. They are also needed to estimate the close approach of Near-Earth asteroids, and subsequent risk of collision. Ephemeris accuracy can also be used for instrument calibration purposes or for scientific applications. Asteroid databases provide information about the uncertainty of the orbits allowing the measure of the quality of an orbit. The aims of this paper is to analyse these different uncertainty parameters and to estimate the impact of the different measurements on the uncertainty of orbits. We particularly deal with two main databases ASTORB and MPCORB providing uncertainty parameters for asteroid orbits. Statistical methods are used in order to estimate orbital uncertainty and compare with parameters from databases. Simulations are also generated to deal with specific measurements such as future Gaia or present radar measurements. Relations between the uncertainty parameter and the characteristics of the asteroid (orbital arc, absolute magnitude, ...) are highlighted. Moreover, a review of the different measuments are compiled and the impact of these measures on the accuracy of the orbit is also estimated.Comment: 11 pages, 10 figures, accepted by A&

Dynamics of passing-stars-perturbed binary star systems

In this work, we investigate the dynamical effects of a sequence of close encounters over 200 Myr varying in the interval of 10000 -- 100000 au between a binary star system and passing stars with masses ranging from 0.1$M_{\odot}$ to 10$M_{\odot}$. We focus on binaries consisting of two Sun-like stars with various orbital separations $a_{\scriptscriptstyle 0}$ from 50 au to 200 au initially on circular-planar orbits. We treat the problem statistically since each sequence is cloned 1000 times. Our study shows that orbits of binaries initially at $a_{\scriptscriptstyle 0}$ = 50 au will slightly be perturbed by each close encounter and exhibit a small deviation in eccentricity (+0.03) and in periapsis distance (+1 and -2 au) around the mean value. However increasing $a_{\scriptscriptstyle 0}$ will drastically increase these variances: up to +0.45 in eccentricity and between +63 au and -106 au in periapsis, leading to a higher rate of disrupted binaries up to 50% after the sequence of close encounters. Even though the secondary star can remain bound to the primary, $\sim$20% of the final orbits will have inclinations greater than 10$^{\circ}$. As planetary formation already takes place when stars are still members of their birth cluster, we show that the variances in eccentricity and periapsis distance of Jupiter- and Saturn-like planets will inversely decrease with $a_{\scriptscriptstyle 0}$ after successive fly-bys. This leads to higher ejection rate at $a_{\scriptscriptstyle 0}$ = 50 au but to a higher extent for Saturn-likes (60%) as those planets' apoapsis distances cross the critical stability distance for such binary separation.Comment: Accepted for publication (MNRAS

Numerical integration of dynamical systems with Lie series

The original publication is available at www.springerlink.comInternational audienceThe integration of the equations of motion in gravitational dynamical systems--either in our Solar System or for extra-solar planetary systems--being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier and Dvorak, Astron Astrophys 132, 203 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie terms when other major forces are considered. As a matter of fact, previous studies have been done but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework of General Relativity and a simplified force for the Yarkovsky effect. A general iteration procedure is applied to derive the Lie series to any order and precision. We then give an application to the integration of the equation of motions for typical Near-Earth objects and planet Mercury

Near-Earth Asteroids Orbit Propagation with Gaia Observations

International audienceGaia is an astrometric mission that will be launched in 2013 and set on L2 point of Lagrange. It will observe a large number of Solar System Objects (SSO) down to magnitude 20. The Solar System Science goal is to map thousands of Main Belt Asteroids (MBAs), Near Earth Objects (NEOs) (including comets) and also planetary satellites with the principal purpose of orbital determination (better than 5 mas astrometric precision), determination of asteroid mass, spin properties and taxonomy. Besides, Gaia will be able to discover a few objects, in particular NEOs in the region down to the solar elongation 45° which are harder to detect with current ground-based surveys. But Gaia is not a follow-up mission and newly discovered objects can be lost if no ground-based recovery is processed. The purpose of this study is to quantify the impact of Gaia data for the known NEAs population and to show how to handle the problem of these discoveries when faint number of observations and thus very short arc is provided

Near-Earth Asteroids Astrometry with Gaia and Beyond

4 p.International audienceGaia is an astrometric mission that will be launched in 2012 and will observe a large number of Solar System Objects down to magnitude 20. The Solar System Science goal is to map thousand of Main Belt Asteroids (MBAs), Near Earth Objects (NEOs) (including comets) and also planetary satellites with the principal purpose of orbital determination (better than 5 mas astrometric precision), determination of asteroid mass, spin properties and taxonomy. Besides, Gaia will be able to discover a few objects, in particular NEOs in the region down the solar elongation (45°) which are harder to detect with current ground-based surveys

Orbit of potentially hazardous asteroids using Gaia and ground-based observations

International audiencePotentially Hazardous Asteroids (PHAs) are Near Earth Asteroids characterized by a Minimum Orbital Intersection Distance (MOID) with Earth less to 0,05 A.U and an absolute magnitude H<22. Those objects have sometimes a so significant close approach with Earth that they can be put on a chaotic orbit. This kind of orbit is very sensitive for exemple to the initial conditions, to the planetary theory used (for instance JPL's model versus IMCCE's model) or even to the numerical integrator used (Lie Series, Bulirsch-Stoer or Radau). New observations (optical, radar, flyby or satellite mission) can improve those orbits and reduce the uncertainties on the Keplerian elements

Dynamics of asteroids and near-Earth objects from Gaia astrometry

The original publication is available at www.sciencedirect.com/science/journal/00320633International audienceGaia is an astrometric mission that will be launched in spring 2013. There are many scientific outcomes from this mission and as far as our Solar System is concerned, the satellite will be able to map thousands of main belt asteroids (MBAs) and near-Earth objects (NEOs) down to magnitude ≤20. The high precision astrometry (0.3-5 mas of accuracy) will allow orbital improvement, mass determination, and a better accuracy in the prediction and ephemerides of potentially hazardous asteroids (PHAs).We give in this paper some simulation tests to analyse the impact of Gaia data on known asteroids's orbit, and their value for the analysis of NEOs through the example of asteroid (99942) Apophis. We then present the need for a follow-up network for newly discovered asteroids by Gaia, insisting on the synergy of ground and space data for the orbital improvement

Statistical analysis on the uncertainty of asteroid ephemerides

International audienceThe large number of asteroids allows a statistical analysis especially for their orbital uncertainty. It presents a particular interest for Near-Earth asteroids in order to estimate their close approach from Earth and eventually their risk of collision. Using ASTORB and MPCORB databases, we analyse the different uncertainty parameters (CEU, U) and highlight relations between the uncertainty parameter and the characteristics of the asteroid (orbital arc, absolute magnitude, ...)

Asteroid data mining and precoveries in the Gaia area

Program available at: http://www.imcce.fr/hosted_sites/naroo/program.htmlInternational audienceAsteroids are components of a very large family of the Solar System. We denote more than 590 000 such objects at the present date. As soon as there is a discovery of an asteroid, a preliminary orbit can be calculated and the improvement of this orbit can be performed thanks to new observations to be done starting from their discovery. But ancient observations can also be retrieved in the past. The data mining allows us to find these old observations in archives. We present general considerations on the asteroid orbital precision in this article and the very important impact of the future Gaia catalogue. We show the expected consequences for the study of Near-Earth Asteroids, in particular for 99942 Apophis

Asteroid (99942) Apophis: new predictions of Earth encounters for this potentially hazardous asteroid

Reproduced with permission. Copyright ESO.International audienceContext. The potentially hazardous asteroid (99942) Apophis, previously designated 2004 MN4, is emblematic of the study of asteroids that could impact the Earth in the near future. Orbit monitoring and error propagation analysis are mandatory to predict the probability of an impact and, furthermore, its possible mitigation. Several aspects for this prediction have to be investigated, in particular the orbit adjustment and prediction updates when new astrometric data are available. Aims: We analyze Apophis orbit and provide impact predictions based on new observational data, including several orbit propagations. Methods: New astrometric data of Apophis have been acquired at the Pic du Midi one-meter telescope (T1m) during March 2011. Indeed, this asteroid was again visible from ground-based stations after a period of several years of unfavorable conjunction with the Sun. We present here the original astrometric data and reduction, and the new orbit obtained from the adjustment to all data available at Minor Planet Center (until March 2011). Results: We present a new sketch of keyholes and impacts for the next century. Additionally, we discuss observational errors, astrometric reduction, orbit adjustment, and adequacy of the dynamical model used. Based on observations made at Pic du Midi station and data from IAU-MPC