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Determination of mass of Jupiter and that of some minor planets from observations of minor planets moving in 2:1 commensurability with Jupiter
Olga M. Ko chetova and Yulija A. Chernetenko
Institute of Applied Astronomy, St. Petersburg, Russia September 19, 2000 Keywords: Jupiter's mass, asteroid's masses, observations of minor planets

Great numb er of observations of minor planets accumulated by now gives p ossibility to estimate once again the value of the Jupiter' mass from p erturbations of the minor planets b eing in 2:1 commensurability with Jupiter as prop osed 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 p erturbations from 9 ma jor planets and 5 asteroids in accordance with co ordinates and masses from DE200/LE200 ephemeris were taken into account. The relativistic terms due to the Sun and Jupiter (Brumb erg, 1999) were included in equations of motion. The observations were corrected for gravitational deflection of light and for phase effect by Lommel­Zeeliger law of scattering. The influence of weighting observations on accuracy of orbit parameters and Jupiter' mass was estimated. The weights were assigned dep ending on residuals on different intervals (we considered observations since 1900). It turns out that b est 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 go o d agreement with the results of its determination from tracking data.

Table I. Values of the Jupiter' inverse mass Ob ject of study Pioneer&Voyager Martian landers Minor planets Sun-Jupiter mass ratio 1047.3486 ± 0.0008 1047.34830 0.00017 1047.3488 0.0006 Author Campbell et al., 1985 Pitjeva, 1997 This paper

c 2001 Kluwer Academic Publishers. Printed in the Netherlands.


2

O. M. Ko chetova and Yu. A. Chernetenko

In the second part of present work the masses of some minor planets have b een found from their gravitational p erturbations on a numb er of smaller planets. The corresp onding pairs of minor planets were chosen from those b eing in 2:1 commensurability with Jupiter. Sampling of the pairs was governed by criterion: minimal distance b etween planets is less or equal to 0.1 au. Usage of less stringent requirement than usually used 0.05 au is here warrantable as the approaches of planets are regularly rep eated due to commensurability 1:1 of their mean motions and mutual velo cities of the b o dies are rather small. Hoffmann (1989) p ointed out the fruitfull of that approach. Observations of all selected p erturb ed minor planets were used in general solution for their orbital elements, masses of p erturbing minor planets and mass of Jupiter. The obtained results are given in Table I I. One can add to the list of p erturb ed minor planets b eing in commensurability 1:1 the p erturb ed minor planets having o ccasional close approaches to p erturbing minor planets. Result 2) for Hygiea gives the example of such solution.
Table II. Results of mass determination of some asteroids Perturbing minor planet 10 Hygiea 1) 2) 31 Euphrosyne Mass (10 M
-11

S un

)

Perturbed minor planets 48,120,357,767 48,120,357,767,829,2619 212,319,381,643,667,1070,1107, 1298,1309,1373,2379,2439,2882, 2986,3011,3210 90,229,401,664,828,986,1003, 1154,1177,1254,2009,2164,2269, 5193,6106,6112,6203,6642,8590 92,401,489,491,595,635,1015, 1489,1571,1674,2197,2405,2582 526,979,1082,1261,1815 328,508,567,621,780,1678,2296, 2361,2394,2452,2894,4677,10920

Number of obs. 1118 1456 2205

5.0 ± 1.5 4.6 0.9 3.2 1.7

48 Doris

2.8

1.2

2800

52 Europa 65 Cybele 511 Davida

2.9 0.72 7.9

1.6 0.40 2.3

1803 865 1617

References
Brumberg, V. A. Trudy IPA RAN (in Russian), 4:199­224, 1999. Campbell, J. K. and S. P. Synnott. Astron. J., 90:364­372, 1985. Hill, G. W. Col lected Mathematical Works, I: 105, 1873. Hoffmann, M. Asteroids II, 228­239, 1989. Pitjeva, E. V. In Proceedings of IAU Col loquium 165, 251­256, 1997.