Near-Earth asteroids orbit propagation with Gaia observations
NNear-Earth asteroids orbit propagation with Gaia observations
D. Bancelin , D. Hestroffer , W. Thuillot
1. IMCCE/Paris observatory, 75014 Paris, France. [email protected],
Introduction
Gaia is an astrometric mission that will be launched in 2013 and set on L2 point of Lagrange. Itwill observe a large number of Solar System Objets (SSO) down to magnitude 20. The Solar Sys-tem Science goal is to map thousand of Main Belt Asteroids (MBAs), Near Earth Objects (NEOs)(including comets) and also planetary satellites with the principal purpuse of orbital determina-tion (better than 5 mas astrometric precision), determination of asteroid mass, spin properties andtaxonomy. Besides, Gaia will be able to discover a few objects, in particular NEOs in the regiondown 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-basedrecovery is processed. The purpose of this study is to quantify the impact of Gaia data for theknown NEAs population and to show how to handle the problem of these discoveries when faintnumber of observations and thus very short arc is provided.
1. The Gaia mission
During the 5-years mission, Gaia will continously scan the sky with a specific strategy: objectswill be observed from two lines of sight separated with a constant basic angle. The angle betweenthe Sun direction and the spin axis is set to 45 ◦ . The initial spin rate is 1”/min and the spin willprecess around the Sun-Earth direction with a mean period of 63 days. Because of this specificscanning law and its positionning, Gaia won’t be able to observe down to the solar elongation ∼ ◦ . But we do expect some observations and/or discovery of Atira asteroids (moving belowthe Earth orbit). Two other constants are still free parameters: the initial spin phase which hasan influence on the observation’s dates and the initial precession angle which has an influenceon the number of observations for a given target. Because of this specific scanning law, someasteroids can be well-observed – i.e. the Gaia observations cover at least one revolution period ofthe asteroids – and some others can be poorly-observed – i.e. the Gaia observations are faint andcover less than half the revolution period.
2. Astrometry for known NEAs
Among the NEAs that will be observed by Gaia, we do expect some observations of PotentiallyHazardous Asteroids (PHAs). Those asteroids can show particular threat of collision with theEarth in the future. To illustrate the impact of Gaia observations on PHAs orbit, we will considerhere the case of the asteroid (99942) Apophis (previously designed 2004 MN ). This asteroid willhave a deep close encounter with the Earth in April 2029 within ∼ a r X i v : . [ a s t r o - ph . E P ] A ug .1 Observations of asteroid (99942) Apophis
Because of the nominal scanning law of Gaia, and in particular the initial precession angle, thenumber of observations per object can be inhomogeneous. We can have more than 20 observationsas well as less than 10 observations. For our simulations, we chose a set with the longest arc length(with 12 Gaia observations) and with a 5 mas accuracy. This set covers half the orbit of Apophis(Fig. 1).
Figure 1:
Left: Gaia observations of Apophis versus time. The x-axis is expressed in terms ofthe number of years elapsed since the beginning of the mission. Right: spatial distribution of theobservations in the ecliptic frame and centered on the Sun ( • ).2.2 Orbital improvement
In the short term, one set of Gaia observations could substantially enhance the current accuracyof the keplerian orbital elements of Apophis (and in general for all the possible observed NEAs).Together with all the available ground-based observations (optical and radar), the Gaia observa-tions will enable to improve the 1 σ uncertainty of the semi-major by a factor 1000. Besides, thelong term uncertainty can be assessed using a linear propagation of the initial covariance matrix(provided by the least square solution). Comparing various sets of observations (Fig. 2) – eachset providing a nominal solution – one can see that one Gaia data (set S ) is enough to reducethe uncertainty to the same level as for the sets S (with an additional radar data) and S (with anadditional optical data). But, the impact of one set of Gaia data is incomparable as the uncertaintyis reduced to the kilometer level.
3. Astrometry for newly discovered asteroids
When NEAs are discovered, a strategy of recovery can be undertaken. At the epoch of the discov-ery, Gaia will provide at most two observations separated by approximately ∆ t ∼
015 2020 2025
Time [years] P o s i t i on un c e r t a i n t y [ k m ] −−−−− S1: optical + radar onlyS2: Set S1+ Gaia data [5 mas]S3: Set S1 + 1 radar data [1µs]S4: Set S1 + 1 optical data [0.1 arcsec]S5: Set S1 + 1 Gaia data [5 mas] Figure 2:
Position uncertainty propagation considering various sets of observations. While S , S ,S reduce the uncertainty to the same level, S (using a set of Gaia data) decreases the uncertaintyto the kilometer level.3.1 Near-Earth asteroids alerts
We presently know more than 9000 NEAs and only ∼ ≤ a (AU) H mag
Synthetic populationKnown population
Figure 3:
Representation of the known ( × ) and synthetic (+) populations possibly observed bythe satellite Gaia during the mission.In order to identify and quantify the number of alerts per year after the beginning of the mission,we removed all the synthetic NEAs for which the semi-major axis a and absolute magnitude H lie between the minimum and maximum values of (a,H) defining the known NEAs populationobserved (see Fig. 3). The results are presented in Fig. 4 and show a mean of 4 or 5 alerts perweek during the first 4-years after the start of the mission. Total Number
Year after start of mission
Number of alert per yearKnown populationSynthetic populationAlerts expected
Figure 4:
Number of alerts ( (cid:4) ) compared with the number of observed synthetic NEAs ( (cid:4) ) andknown NEAs ( (cid:4) ), per year after the beginning of the mission.3.2
Strategy of recovery
When an alert occurs, a preliminary short arc orbit can be computed with the two ( α , δ ) Gaiaobservations using the Statistical Ranging method [5]. Thus, a distribution ( α , δ ) can be assesseduntil a certain number of days after the discovery. Because the distribution can be quite large, weused statistical tools to extract the maximum likelyhood (ML) of the distribution. Compared tothe theoretical position of the object (given by the orbital elements from astorb database), we canestimate the minimum field of view (FOV) required to recover this object. As shown in Fig. 5,some asteroids will need typical FOV < 25 ×
25 arcmin (case of asteroid Cuno) until 10 days aftertheir discovery, while some others (case of asteroids Apophis and Phaethon) require a FOV ofhundreds of square degrees after their recovery. This behaviour can be explained by their relativedistance to the Earth – Geographos and Cuno are relatively far from the Earth ( > < l l l l l l l l l l Day after discovery M i n i m u m F O V [ a r c m i n ² ] l Toutatis [~0.55 AU at To]Geographos [~1.1 AU at To ]Cuno [~2.5 AU at To] l l l l ll l l l l
Day after discovery M i n i m u m F O V [ a r c m i n ² ] l Apophis [0.21 AU at To]Phaethon [0.45 AU at To]
Figure 5:
Variation of the minimum FOV required for the recovery process versus time. Leftpanel: for the asteroids Toutatis, Geographos and Cuno. Right panel: for the asteroids Apophisand Phaethon. this method uses Monte Carlo technique on the ( α , δ ) observations and on the topocentric distances inally, when the object is recovered by the Gaia-FUN-SSO, complementary ground-based mea-surements will enable to improve the orbital elements and the quality of the orbit. This processwill enable to optimize the short-term pipeline and the organisation of the network in as much as,the orbital improvement will enable to use telescopes with smaller FOV and keep the larger onesfor asteroids requiring large FOV during the recovery process. Conclusion
Even if Gaia will not be a big NEAs discoverer, there is a need of the science community to supportthe Gaia mission in order to be ready for this opportunity of discovering new NEAs. Among them,there could be some threatening potentially hazardous asteroids and we can not afford to lose themis no Gaia-FUN-SSO is well organized
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