Gravitational Effects of Minor Planets and Their Mass Determination

Abstract

There are two groups of methods for asteroid mass determination: astrophysical and dynamical. In dynamical methods, the mass of an asteroid is estimated from its perturbation of the motion of some other body. In our work, we tried to find out whether it was possible to determine the correction of perturbing mass separately from the corrections of the six osculating elements of the perturbed asteroid. As a consequence, we introduce a modified method of asteroid mass determination. The procedure for the mass determination is based on a calculation of the perturbed orbit using observations that cover the preor post-encounter part of the orbit. The preand post-encounter parts of the perturbed orbit are linked by some chosen value for the mass of a perturbing body. The procedure is an iterative one. The resulting mass of the perturbing asteroid is found to provide the minimum O C residuals in the rms sense. We calculated the masses of the eight largest asteroids independently for all found perturbed asteroids (62 bodies), using the standard and modified method. Some of these perturbed asteroids were never used before for this purpose (11 bodies). This thesis calculates the mass of (4) Vesta based on newly found encounters (A. Kovacevic, 2005, A&A, 430, 319), as well as the mass of (16) Psyche, which is the first successful attempt—based on a dynamical method—that leads to the conclusion that the composition of an asteroid is metallic (M. Kuzmanoski & A. Kovacevic, 2002, A&A, 395, L17). As can be seen from numerical tests, the modified method provides results that are in good agreement with the standard method and adopted values of the asteroid’s masses. This method can be used as a tool for asteroid mass determination. This work has been realized within the project “Dynamical Astronomy and Planetology” (No. 146004) supported by the Ministry of Science and Environmental Protection of the Republic of Serbia.