Determination of Mass of Jupiter and That of Some Minor Planets from Observations of Minor Planets Moving in 2:1 Commensurability with Jupiter

Abstract

Great number of observations of minor planets accumulated by now gives possibility to estimate once again the value of the Jupiter’ mass from perturbations of the minor planets being in 2:1 commensurability with Jupiter as proposed by Hill (1873). 9310 observations of 28 minor planets were used in general solution for orbital elements of minor planets and mass of Jupiter. The minor planet (944) Hidalgo was also included in the list of selected minor planets due to its close approaches to Jupiter (less than 1 au). In so doing the perturbations from 9 major planets and 5 asteroids in accordance with coordinates and masses from DE200/LE200 ephemeris were taken into account. The relativistic terms due to the Sun and Jupiter (Brumberg, 1999) were included in equations of motion. The observations were corrected for gravitational deflection of light and for phase effect by Lommel—Zeeliger law of scattering. The influence of weighting observations on accuracy of orbit parameters and Jupiter’ mass was estimated. The weights were assigned depending on residuals on different intervals (we considered observations since 1900). It turns out that best result is obtained in the case when the observations are considered with equal weights. The results are presented in Table I. The comparison of our results with those of other authors leads to conclusion that minor planets give value of Jupiter’ mass in good agreement with the results of its determination from tracking data.