| 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 $200 \mathrm{km}$ and above) were (will be) encountered by smaller counterparts within a distance of $0.0200 \mathrm{AU}$. 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 $0.0020 \mathrm{AU}$ 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.
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