Dynamics of asteroids and near-Earth objects from Gaia Astrometry
DDynamics of asteroids and near-Earth objects from Gaia Astrometry
D. Bancelin a , D. Hestroffer a , W. Thuillot a a IMCCE, Paris Observatory, CNRS, UPMC77, Av. Denfert-Rochereau 75014 Paris France
Abstract
Gaia is an astrometric mission that will be launched in spring 2013. There are many scientific outcomes from this mission andas far as our Solar System is concerned, the satellite will be able to map thousands of main belt asteroids (MBAs) and near-Earthobjects (NEOs) down to magnitude ≤
20. The high precision astrometry (0 . − Keywords:
Gaia, Asteroids, Near-Earth Objects, Astrometry, Dynamics
1. Introduction
Science of asteroids and comets, from near-Earth objects(NEOs) to trans-Neptunian objects (TNOs), and small bodiesof the Solar System at large is fundamental to understand theformation and evolution of the Solar System starting from theproto-Sun and the planetary embryos. Having little geologicalevolution and being atmosphere free, their pristine charactermakes them good tracers of the constitution of the primordialSolar System. Being numerous and spread over a wide range ofheliocentric distances they act also as good constraints for plan-etary formation scenario and the Solar System dynamical evo-lution at large. Last, knowledge of the process within our SolarSystem is useful if not mandatory to understand formations andevolution of other planetary system than our own Solar System.While some objects can be considered as small world on theirown, such as targets of space probes, the vast majority will beconsidered through general groups and classes. Some asteroidsare planet crossers or evolving in the vicinity of Earth’s orbit.Among the latter, a small fraction of potentially hazardous as-teroids (PHAs) can show particuliar threat of collision with theEarth while others have no incidence at all. Near-Earth ob-jects are also of interest to understand the physics process asnon-gravitational forces (in particular the Yarkovsky effect) andfundamental physics with local tests of General Relativity.
2. Gaia detection and observations of asteroids
Gaia will observe a large number of asteroids, however withsome specificity and limits. The limiting magnitude is mod-est when compared to present and future ground-based surveys aimed at making a census of small bodies . On another handGaia will enable observations with a single instrument of theentire celestial sphere and also at low solar elongation, makinga difference between space-based observations – such as As-teroidFinder (Mottola et al., 2010) and NEOSSat (Hildebrandet al., 2004)– and typical ground-based observations and sur-veys. As seen in Mignard et al. (2007), the Gaia satellite willhave a peculiar scanning law enabling a full coverage of theentire sky over 6 months, which coverage is repeated over the5 years mission providing stellar parallaxes and proper motions.Besides, only objects detected and confirmed in the front CCDsforming the sky mapper will be subsequently observed throughthe main astrometric field-of-view. This ensures that no cosmicrays are treated as scientific sources and enables to download toground only small windows around a scientific source and notall the pixels of the large CCD mosaic. Nevertheless the detec-tion algorithm is so that extended sources, when too wide, arenot detected by the on-board algorithm. As shown in Fig. 1,there is no clear detection limit, solar system objects in the sizerange 0.7-0.9 arcsec will not be systematically detected, whileobjects larger than 0.9 arcsec will not be observed.The sequence of observation of any object hence depends onthis scanning law, the on-board detection, and the limiting mag-nitude. Starting with the astorb database (Bowell et al., 1994)of orbital elements, one can compute dates of rendez-vous ofasteroids crossing the Gaia FOV with the CU4 Solar SystemSimulator. Simulations in the focal plane of images making useof the GIBIS tool (Luri and Babusiaux, 2011) will enable to setthe detection of large asteroids and planetary satellites. Mak-ing use of the GIBIS tool, Fig. 1 shows some detection limits The objectif reclaimed to the NASA by the US congress is to catalogue90% of NEOs larger than 140 m.
Preprint submitted to Planetary and Space Science October 18, 2018 a r X i v : . [ a s t r o - ph . E P ] A ug or binary objects and large asteroids. These are, in the case ofbinary systems, the detection in the SM CCD that are binned(2x2) and hence of lower resolution. In such case each compo-nent will be treated individually with an associated patch andwindowing for observation in the subsequent CCDs. While notdetected at the SM level, binary systems can still be observed inthe AF field, with higher, but basically one dimensional patchesresolution (personal communication). Concerning large aster-oids, it appears that even Ceres and some planetary satelliteswill be basically detected and observed. Figure 1: Detection limits, in the sky mapper, for binary objects (top) and largeasteroids (bottom). Top panel: the detection is given as a function of the separa-tion of the pair (irrespective of its position angle) and the magnitude differencebetween the secondary and the primary; the colour code indicates the magni-tude of the primary. The detection in the binned sky mapper CCDs stops at aseparation of less than approximately 0.3 arcsec (corresponding to ≈ . Statistics on observations of asteroids have been reported inMignard et al. (2007); Hestroffer et al. (2010a). On the aver-age there are 60 transits (or observations) per object over themission duration. Fast moving objects will not be observedcorrectly through the whole astrometric field of view becausethe windowing scheme is adapted to the relative motion of astar (personal communication). Objects like fast NEOs willhowever be observed in good conditions in the first and mid-dle CCDs (which has a larger associated window).
3. Dynamic of asteroids
Gaia will provide astrometry of asteroids and comets withunprecedented accuracy. Being a space-mission designed op-timally for doing astrometry it has some obvious advantages.Gaia will in particular enable both local astrometry from rel-ative positions and refined calibration, and global astrometry with absolute positions. Compared to classical ground-basedobservations, there are—among other—no limitation betweennorthern and southern hemisphere, no atmospheric refraction orturbulent effects, reduced zonal errors, and positions directly inthe Gaia sphere of reference and the optical ICRF. Such astrom-etry will yield improved orbital elements for almost all objectsobserved (see Fig. 2), together with detection of small effectsand determination of dynamical parameters. In particular, onewill be able to derive masses of asteroids (from close encounterand binary objects) and to perform local tests of general rela-tivity (GR). We do not consider here preliminary orbit determi-nation for newly detected objects that will be treated in Sect. 5,neither dynamics of planetary satellites that will not be treatedwithin DPAC with Gaia data alone.
Figure 2: Orbit improvement in semi-major axis and orbital plane orientation.The improvement is given as the precision on the correction to the state vectoror orbital elements from a linear least squares fit from Gaia observations alone.For a small percentage of objects the number of observations and/or their distri-bution will be too small to derive a complete orbit (rank deficiency in the linearleast squares inversion), but for the vast majority the astrometric precision ofthe order of 0.3–5 mas will enable orbit improvement by factor ≈ − The mass of an asteroid can be measured during a close en-counter from the trajectory’s deflection caused on a perturbedsmaller body (Hilton, 2002). The situation is improved and lesssubject to systematic errors when several perturbers per per-turber asteroid are involved. In the Gaia data processing schemea preselected list of perturber asteroids has been done based oncomputation of close encounters during the mission (Mouretet al., 2007). Simulation of a global inversion of the prob-lem involving 43 500 perturbed targets and 600 massive aster-oids (in 78 800 close approaches) has shown that 150 asteroids(i.e. ≈ Figure 3: Mass determination from close encounters. Cumulative distributionas a function of the relative precision reached (Mouret et al., 2007).
The refined orbits of asteroids will also provide valuable in-puts for local tests of General Relativity, basically derivationof the PPN parameter β (Will, 2010) from monitoring the pre-cession of perihelion of eccentric NEOs (i.e. large eccentricity e , small semi-major axis a ) together with the derivation of thesolar quadrupole J . Additionally all asteroids will contributeto a test of a possible time variation of the gravitational con-stant dG / dt and a possible residual rotation d W / dt betweenthe kinematic reference frame materialised by the QSO and thedynamical reference frame materialised by the motion of theasteroids. It has been shown in Hestroffer et al. (2010b) that—due to the good ( e , a ) plane coverage, good monitoring of bothperihelion ω , node Ω and inclination I , and the large number oftest particles involved—the parameters β and J will be derivedindividually to a precision of ≈ − and ≈ − , respectively.Such precision is similar to what is obtained from other tech-niques, yet independently and directly without assumptions onthe Sun interior or the Nordvedt parameter. Combination ofGaia astrometry of NEOs to radar data (Margot and Giorgini,2010) can in principle bring a higher time leverage for measur-ing this secular effect, this has to be investigated further.It is worth to mention that the Gaia data alone from direct ob-servation astrometry of Solar System objects can yield scientificoutputs as shown above, but it can also complement ground-based data over long time span. Last, the Gaia catalogue of starswill provide the astrometry of tomorrow including re-reductionor debiasing of ancient CCD observations, better prediction ofstellar occultation, and dense catalogue for small fields reduc- tion without severe zonal errors.
4. Observations of PHAs
During the 5 years mission, Gaia will continously scan thesky with a specific strategy as shown in Fig. 4: Objects willbe observed from two lines of sight separated with a constantbasic angle. Some constants already fixed determine thenominal scanning law of Gaia: The inertial spin rate (1 ◦ / min)that describes the rotation of the spacecraft around an axisperpendicular to those of the two fields of view, the solar-aspectangle (45 ◦ ) that is the angle between the Sun and the spacecraftspin axis, the precession period (63 .
12 days) which is theprecession of the spin axis around the Sun-Earth direction.Two other constants are still free parameters: the initial spinphase which has an influence on the observation’s dates and theinitial precession angle which has an influence on the numberof observations for a given target. Those parameters will befixed at the start of the nominal science operations. Theselatter are constrained by scientific outcome (e.g. possibilityof performing test of fundamental physics) together withoperational requirements (downlink to Earth windows).
Figure 4: Nominal scanning law of Gaia (Source: ESA). Six parameters deter-mine this scanning law: the basic-angle (angle between the two lines of sight),the inertial spin rate (angular speed of the spacecraft), the solar-aspect angle(angle between the Sun direction and the satellite spin axis), the precession pe-riod (rotation of the spacecraft around the Sun-Earth direction, the inertial spinphase and the initial precession angle.
Different sequences of observations of NEOs will be possi-ble according to the initial value of the initial precession an-gle. Figure 5 is an histogram showing the number of NEOs andPHAs that would be observed by the satellite (an object is con-sidered to be observed at the first detection). We can first seethat the number of NEOs that could be observed is weak com-pared to the population of knows NEOs ( ∼ ±
16 NEOs ob-served by Gaia and 585 ±
12 for PHAs. So we can just give themean value of objects that would be observed, regarding theirdynamical family as shown on Fig. 6.
Number of NEAs Number of PHAs
Initial Precession Angle ( ° ) Figure 5: Number of NEOs and PHAs that would be observed by Gaia withrespect to the initial precession angle. Only 30% of the NEOs population couldbe observed by Gaia. Amoung the most hazardous population, the PHAs, Gaiawould observe only 1 / To illustrate the impact of Gaia observations on PHAs orbit,we will consider here the case of the asteroid (99942) Apophis(previously designed 2004 MN ). This PHA was discovered inJune 2004 by R. Tucker, D. Thollen and F. Bernardi at the KittPeak observatory in Arizona. Since the first observations, it wasrevealed to be a threatening and hazardous asteroid in as muchas it reached the level four of Torino Scale for a possible impactwith the Earth in April 2029. Since, new observations ruled outevery possibility of collision for this date but this risk remains in2036. The 2029-threat is now just a 2029-close deep encounterwithin a distance of ∼ Figure 7: Number of Gaia observations for the asteroid Apophis with respectto the initial precession angle. Here, we have a great variation of the number ofobservations for a single object. Some sets can have more than 25 observationsas well as less than 10.
We can first analyse the improvement on the accuracy ofthe Keplerian elements due to the Gaia contribution. Table 1compares the standard deviation of Apophis’orbital elementswith ( σ O + G ) and without ( σ O ) Gaia observations. It is clear thatthe impact of those space data on Apophis’s orbit can be seenthrough the improvement of the semimajor axis value as theuncertainty is improved by a factor 1000. Table 1: Stantard deviations of Apophis’s keplerian elements without ( σ O ) andwith ( σ O + G ) Gaia observations. σ O σ O + G a [A.U.] 1 . × − . × − e 7 . × − . × − i [ ◦ ] 1 . × − . × − Ω [ ◦ ] 1 . × − . × − ω [ ◦ ] 1 . × − . × − M [ ◦ ] 7 . × − . × − The impact of Gaia data can also be analysed through theimprovement of the position uncertainty. From a linear prop-agation of the covariance matrix (provided by the least squaresolution), the uncertainty of the keplerian elements is propa-gated until the date of close approach in 2029. Fig. 8 shows the4omparison of the propagation of nominal orbits obtained fromthe fit of different sets of observations: • S (-): using all optical and radar data available; • S (-): using set S with additional Gaia data with 5 masaccuracy; • S (-): using set S with one additional future radar mea-surement in 2013 with 1 µ s accuracy (measurement of atiming echo); • S (-): using set S with one future optical observationdone in 2013 with 0 . • S (-): using set S and the case that Gaia would provideonly one observation with 5 mas accuracy. Figure 8: Evolution of the position uncertainty of asteroid Apophis consideringseveral different sets of observations. While the sets S , S and S lead to thesame level of accuracy, the set S using all Gaia data enable to decrease theposition uncertainty down to the kilometer level. This figure shows that the Gaia data enable to reduce theposition uncertainty knowledge down to the kilometer level(set S ) and it keeps this value until the close approach. Forcomparison, the effect of future accurate measurements (radarand optical) can be comparable to the impact of one futureGaia data.Other simulations can be done to compare the impact of fu-ture Gaia data with ground-based measurements by quantifyingthe position uncertainty at the date of close encounter. Gener-ally, the uncertainty region is represented in the b-plane or tar-get plane (Valsecchi et al., 2003). This plane better representsthe state of an asteroid when approching the Earth. It passesthrough the Earth center and is perpendicular to the geocentricvelocity of the asteroid. Thus, it will have two geocentric coor-dinates ( ξ , ζ ). As a consequence, the projection of the ellipsoiduncertainty in this plane is just an ellipse centered on the nom-inal value of the geocentric coordinates ( ξ N , ζ N ) and with itssemimajor and semiminor axis respectively equal to the stan-dard deviations 3 σ ζ and 3 σ ξ calculated with a linear propaga-tion of the initial covariance matrix until 2029.Due to this close approach, the orbit of Apophis will be al-tered and both Apophis and the Earth are expected to be in the same position after some revolutions of Apophis aroundthe Sun and many years later. The most famous resonant re-turn occurs in 2036 where after 6 revolutions of Apophis and 7years later, both objects will meet again. As the 2029-post or-bit of Apophis is chaotic, some clones of Apophis (simulatingby Monte-Carlo the present orbital uncertainty) can lead to im-pact with the Earth at some resonant return and the pre-imagesof those impacts in the b-plane are called keyholes (Chodas andYeomans, 1999). The most famous keyhole is the 2036-keyholewith a size around 600 m. They can be primary keyholes if theyare spawned by one close approach and secondary if they arespawned by two consecutive close encounters. So, the risk canbe estimated by comparing the keyhole position with the sizeof the ellipse uncertainty in the b-plane. A better knowledge ofthe region uncertainty is necessary to prepare some deflectionmissions in case there is an important collision threat.The size of the region uncertainty, in the ( ξ , ζ ) plane, will de-pend on the kind of measurements available. Table 2 presentsthe size of the ellipse uncertainty using the different sets S i ofobservations as explained above. Even if Gaia would provideonly one observation, the gain in accuracy would be unprece-dented by comparison with the gain obtained with optical orradar data. While the impact of one Gaia data can be comparedto the effect of one radar measurement, one set of Gaia obser-vations can bring the uncertainties around the kilometer level. Table 2: Uncertainties ( σ ξ , σ ζ ) on the 2029 b-plane of Apophis consideringvarious sets S i of observations. S S S S S σ ξ (km) 10 0 . σ ζ (km) 240 1 . . .
5. Gaia-FUN-SSO network
During the mission, various unidentified objects will be ob-served by the satellite. Because of the scanning law, at theepoch of these discoveries, those objects will have at least twoobservations separated by approximately ∆ t ∼ . igure 9: 3 σ ellipse uncertainty on the 2029 b-plane of Apophis and positionof the center of primary ( (cid:63) ) and secondary keyholes leading to collision at as-cending node ( (cid:4) ) and descending node ( (cid:4) ). The dotted ellipse is computedusing set S and the filled one using set S . The coordinates are expressed in σ units. the discovery of new comets. In order to be ready to handlethose alerts, we first have to statistically quantify the numberof unknown NEOs that could be discovered by Gaia. In a firstapproach, using a synthetic population of NEOs (Bottke et al.,2002), we do expect a small number of alerts ( ∼ Figure 10: Number of known and synthetic NEOs that would be observed bythe satellite.
According to the previous considerations upon the inter-est of a ground-based follow-up network, we have set up aground-based network of observing sites labelled Gaia-FUN-SSO (standing for Gaia Follow-Up Network for Solar SystemObjects). This network included nineteen locations at the be-ginning of 2011 but several more stations are still expected inorder to have a large geographical coverage (candidate sites canget in touch with us at the address [email protected]). Thetelescope diameters of the network are spanning from 0.25 to 2.4 m; four telescopes have large field, which will be useful forrecoveries, and five are robotics ones, which will be precious forobservations on alert. Since the goal is mainly to perform as-trometric measurements, the standard specificities of telescopesare expected to be a field of view of at least 10 arcmin, pixel sizeat less than 1 arcsec, and limiting magnitude around 20. But,since we certainly need to search for new discovered objects inquite large field and larger field even with bigger pixel size willbe very useful.The role of this network will be to improve the orbit of someobjects and to enable Gaia to identify them during a furtherscan. This network is structured around a central node whichwill convert raw Gaia data into ephemerides useful for observa-tions and will collect the data. All the measurements performedby this network will be sent to the Minor Planet Center andwill thus allow the update of the database of auxiliary data usedin the Gaia system to perform the identification of SSO. A firstworkshop has been held in Paris in November 2010 and resultedin several discussions among the member of the network; pro-ceedings are accessible at the address: gaia-fun-sso.imcce.fr.
Figure 11: Observing sites of the Gaia-FUN-SSO network in May 2011
6. Synergy ground/space data
When an alert occurs, we have to know where to look inthe celestial sphere and how much time we have in order torecover, from the Earth, an unidentified asteroid observedby Gaia. Knowing the threat of PHAs, we can not afford tolose them if no strategy is established. A way to deal withpotential alerts can be represented in Fig. 12: If an unidentifiedPHA is observed by Gaia, the satellite can send an alert tothe Earth within 24 hours. Then, a short preliminary arcorbit, compatible with the Gaia observations, can be computedusing the Statistical Ranging method (Virtanen et al., 2001;Muinonen, 2011). This method is based on estimating the gaia-centric distance using Monte-Carlo technique with at least twoobservations. It will provide the orbital elements compatiblewith the Gaia observations and propagate each orbit to a givendate. Then, from the ( α , δ ) distribution computed few daysafter its discovery, we can extract the maximum likelyhood ofthis distribution. We can then just center a telescope field ofview on this maximum likelyhood so that observers can be able6o know which part of the sky to scan and how much time theyhave until the asteroid is lost. Figure 12: Strategy of recovery from Earth for newly discovered PHAs. Gaiawill provide two observations before sending the coordinates to Earth within24 hours where a short preliminary arc orbit, compatible with the observations,can be computed using the Statistical Ranging method. (MC denotes Monte-Carlo Technique). Thus, an ( α , δ ) distribution can be computed few days afterthe discovery of the asteroid by Gaia. As an example, we considered an hypophetical PHA, Ge-ographos, that would be discovered by Gaia. Figure 13 showsthe ( α , δ ) distribution on the sky plane ( ◦ ) until 10 days after thediscovery of Geographos. Each window is centered on the max-imum likelyhood ( • ) and the size of the window is the size of a24 ×
24 arcmin telescope field of view. So, the asteroid can stillbe recovered until 7 days after its discovery because the truevalue ( (cid:78) ), computed from the real initial state of Geographos,lies in this window for this given field of view. . . Prediction 4 days after the discovery of the hypophetical Geographos ra[h] de c [ ° ] Distribution (ra,dec)Expected valueMaximum likelyhood . . Prediction 7 days after the discovery of the hypophetical Geographos ra[h] de c [ ° ] . . Prediction 10 days after the discovery of the hypophetical Geographos ra[h] de c [ ° ] Figure 13: Prediction on the sky plane of a hypothetical Geographos discoveredby Gaia, until 10 days after its discovery by Gaia.
Finally, when the asteroid is recovered from Earth, it willbe followed, at least, during one night. Thus, optical data can be done and can be combined with the space data in order toimprove the ( α , δ ) prediction in the sky plane. We consideredfour observations made during that night with a 0 . α , δ )prediction as the size of the distribution is well-reduced (lightcircles), compared to the distribution obtained only with Gaiadata (black circles). . . . . Prediction 7 days after the discovery of the hypothetical Geographos ra(h) de c ( ° ) Distribution (ra,dec) gaia only Distribution (ra,dec) gaia+opticalexpected value
Figure 14: Distribution ( α , δ ) considering additional ground-based data, twodays after the discovery of the hypothetical Geographos by Gaia.
7. Conclusion
We have given a broad overview of results and actions con-nected to the astrometry of asteroids and NEOs with Gaia.This includes the orbit improvement, mass determination, testof GR. This paper also presented the usefulness of Gaia datathanks to an unprecedented data accuracy reached. Orbit ofNEOs and PHAs could really be improved, even if the num-ber of observations provided by the satellite is faint. This im-provement can be shown through the improvement of orbital el-ements, position uncertainty and even for close-approach statis-tics.Even if Gaia won’t be a big NEOs discoverer and is not afollow-up mission, a strategy has to be settled in order to beable to recover newly discovered PHAs from Earth. Statisticaltools can enable observers to know where to focus on the celes-tial sphere with only two Gaia data. Besides, the parallax effect,with addionnal ground-based data, will allow a better follow-upfrom Earth.
Acknowledgements:
The authors wish to thank J. Blanchot andM. Sylvestre – master trainees at IMCCE – for her work onGIBIS detection, C. Ordenovic and F. Mignard (OCA) for pro-viding the CU4 Solar System Simulator, and all the colleaguesfrom Gaia DPAC CU4/SSO and REMAT groups at large forfruitful discussions.7 eferences