A&A 370, 311–319 (2001) Astronomy DOI: 10.1051/0004-6361:20010191 & c ESO 2001 Astrophysics Asteroid candidates for mass determination A. Gal´ad Astronomical Institute, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic Received 17 July 2000 / Accepted 31 January 2001 Abstract. The first 9511 numbered asteroids are studied in terms of their mutual closest approaches and encounter velocities during the period from November 6, 1967, to September 13, 2023. Several large asteroids (diameter 200 km and above) were (will be) encountered by smaller counterparts within a distance of 0.0200 AU. Thus, they are possible candidates for mass determination by the astrometrical method. Similarly, the search for effective perturbers is extended to even smaller asteroids for the much closer separation distance of 0.0020 AU and below. Only the simplified method for evaluation of observable effects on a perturbed body is used. Asteroid masses alone are not computed here. But a stronger criterion to reveal pairs for this purpose in comparison to some specially devoted papers should compensate for the difference and act as a reliable test. The best candidates for mass determination at present are asteroids (1), (2), (4), (10), (11), (24), (52) and (65). This list may be extended by at least (29) in the next 5 years and by many others in the next two decades. Several other strong perturbers from the last three decades are not included in the list, while there is still only a limited number of (or no) precise and reliable observations of perturbed asteroids before a close encounter. It seems that a perturbation by (10) is at least as effective as that by (2) and could be included in asteroid orbit determination in the future. Except for their bulk density determinations (knowing the size), the masses of perturbers could occasionally be used to improve the precision of the computed orbit for perturbed large-numbered and unnumbered asteroids as well. Key words. minor planets, asteroids – astrometry – ephemerides 1. Introduction cause deflection from the ephemeris position of their smaller counterparts. Knowledge of the encounter geome- Asteroid observations have a long history. Larger tele- try enables us to compute the masses (and densities, if the scopes, more sensitive detectors and different techniques size and shape is also evaluated) of new perturbers while were used to increase the number of known bodies. Due to the perturbed body residuals (observed minus computed observational effects large and close asteroids were discov- positions) should decrease. Precise astrometric positions ered at first. Most of the known asteroids orbit the Sun at of the perturbing and perturbed bodies are needed over adistanceof≈2–4 AU – in the main belt. several years before and after their close encounter. The The orbits of asteroids are usually computed by nu- observations from the period closer to the encounter are merical integration. This takes into account the pertur- helpful, as well. bations by the eight planets (Mercury to Neptune) and, The astrometrical method was used not only for the in addition, by the three largest minor planets (1) Ceres, mass determination of the three largest main-belt aster- (2) Pallas and (4) Vesta from the main belt of asteroids oids mentioned above. Many times it was used even for (Marsden 1995). The last three of these perturbers con- the smaller ones (see e.g. Hoffmann 1989; Kuzmanoski tain about half the mass of the belt. The Earth-Moon &Kneˇzevi´c 1994; Viateau 2000 and references therein). system may be considered as one body with the sum of 00 A deflection as small as 1 from the ephemeris posi- their masses or, in the case of Earth-approaching aster- tion of the perturbed body can be measured several (say oids, perturbations by both bodies are taken separatedly. ≈10–20) years after an encounter by optical telescopes It is known that the collisions of known objects are from the ground. Subarcsecond measurements by merid- extremely rare even in the main belt. Thus, it is ex- ian circles (Viateau & Rapaport 1997) and astrometric pected that sufficiently high accuracy of orbit solutions satellites like Hipparcos (Bange 1998) are the most precise for a long time period should be reached for numbered as- and valuable – they reduce the time needed for deflection teroids. However, from time to time interasteroidal close measurements. encounters occur. Then, some of the larger asteroids may Mass is an important physical characteristic. The rapid Send offprint requests to: A. Gal´ad, increase in new asteroid discoveries and the improvement e-mail: [email protected] (in precision) of poorly determined orbits in recent years Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20010191 312 A. Gal´ad: Asteroid candidates for mass determination challenge as to determine it for many objects. The first Neglecting the orbital eccentricity of the scattered aster- step is to provide a database of suitable close encounters. oid, they obtained Such searching was recently done by Hilton et al. (1996) in 6 Gm quite a large set of asteroids. They integrated 4583 orbits |∆n|' , (1) for57years.Thesubjectofthispaperistorecognize arv the best candidates from the main belt for asteroid mass where G is the universal constant of gravitation, m is the determination in a larger database. mass of the perturber, is the energy efficiency of the close approach (the fraction of the change in the heliocen- tric velocity, which occurs in the tangential direction), a is the semimajor axis of the perturbed asteroid, r is the 2. Data minimum separation distance, v is the encounter velocity. The asteroid orbital elements used in this paper were In fact, authors assumed that the mass of the perturbed taken from the CD Guide 7.0 (Gray 1998). In this software asteroid is much smaller than that of the perturber (they the orbital elements for various epochs are included due used the equation for mass determination of (1) Ceres). to the need of rapid drawing of asteroids in star charts More precisely, the sum of the masses should be written for any time in the recent past and near future. Only a instead. little programming is needed to convert them from a com- To find out possible candidates for mass determinaton, pressed form to a readable format. the mass of the perturber should be assessed from asteroid diameter D and the evaluated value of its bulk density ρ, The initial osculating elements for epoch October 14, as it is not known in advance. Three quantities (D, r and 1998 (JD 2451100.5) were based on observations and v) out of six that characterize ∆n may differ by several were taken from Bowell et al. (1994). All perturbations orders of magnitude (in different pairs). An auxiliary P mentioned above were taken into account. However, or- parameter can be defined by them so that P is a measure bital elements for the other epochs derived on the CD of ∆n. In this paper the search for possible candidates for are adjusted for planetary perturbations only. Asteroidal mass determination is focused on the search for largest perturbations were not included at all. The asteroid values of P . It is computed from the equation positions between adjacent epochs can be computed as a two-body problem at first approximation. Thus, it is D3 P = , (2) possible to study the whole sample of asteroids for mu- rv tual approaches without an additional numerical integra- tion. But we should bear in mind that the computations where D is the asteroid diameter in km (as the mass de- 3 of orbital elements excluding the perturbations by large pends on D ), r is the minimum separation distance in −1 asteroids is a source of inaccuracy in the estimation of the km, v is the encounter velocity in km s . It is possible to close encounter’s effect on these asteroids. The actual po- replace r with the impact parameter b and at the same sitions of asteroids may differ from their computed ones time v with the relative velocity of the scattered aster- far from the initial epoch. These can be checked by exam- oid at infinity v∞ (rv= bv∞). To be punctual, b and ining observations from the past. According to the CD’s v∞ are really computed here, but they are designated by manual this comparison was done for some asteroids, and the letters r and v, respectively. D is assessed from known the difference in position was less than 1 arcsec. albedos directly (Tedesco 1989), or indirectly through tax- onomic class (Tholen 1989). The latter usually determines By the release of the CD (October 1998) there were the narrow range of possible values for albedo. If neither 9511 numbered asteroids and thousands of multiopposi- albedo, nor taxonomic class data are available, only the tion and singleopposition unnumbered asteroids known. upper limit of the size is taken into account, with the In this paper only numbered asteroids were studied dur- albedo value set to 0.04. ing the period from November 6, 1967 (JD 2439800.5) to It must be noted that neither the P parameter nor ∆n September 13, 2023 (JD 2460200.5). In general, their or- are valid outside the sphere of action of the perturber. But bits are much better determined in comparison to multi- the computation of the P parameter is just an approxi- opposition unnumbered asteroids. Only (719) Albert was mation allowing comparisons between the encounters. lost at the time of the CD’s release. Increasing the num- ber of items (unnumbered asteroids) and choosing a longer The following steps were taken to gain and process the data in chronological order: time period would affect not only the time needed to pro- cess the data but also the reliability of data.