Astron. Astrophys. 354, 725-731 (2000)

4. The mass of (121) Hermione

4.1. The encounter

The other encounter which was considered in this work is the close approach between (121) Hermione and (278) Paulina. During this approach, the minimal distance between both asteroids was 0.0017 AU (i.e. only about 250,000 km, less than the Earth-Moon distance), and the relative velocity of both asteroids was about 2.9 km/s. The mean diameter of (121) Hermione given by IRAS is 217 km, while the diameter of (278) Paulina is only 38 km. Another determination of the diameter of Hermione was made by Stamm (1988)from a star occultation, however the value obtained was imprecise ( 140 km). In consequence, the value given by IRAS was assumed.

The effect of the gravitational perturbation of Hermione on the orbit of Paulina was calculated the same way than between Psyche and Aurora. Hermione is a C-class asteroid and, as for Aurora, a mean density of 1.8 g/cm³ was assumed for this asteroid, which gave an estimated mass of about 5 10^-12 M. The corresponding maximal perturbation on the orbit of Paulina during the time interval covered by the observations of this asteroid is about 4" in right ascension and 2" in declination (Fig. 3). As it is described in the following, this perturbation enabled the determination of the mass of Hermione to be made.

Fig. 3. Effect of the gravitational perturbation of (121) Hermione on the orbit of (278) Paulina in right ascension, starting backward numerical integration at epoch JED 2450000.5 = 1995 October 10.0 TT and assuming a mass of 5 10-12 M for Hermione

4.2. Data

There are 144 observations of Paulina collected by the Minor Planet Center, and which are given with a precision better or equal than 0.1 sec of time in right ascension and 1" in declination. The residuals of these data, which cover the time interval from 1899 to 1998, are shown in Fig. 4.

Fig. 4. Residuals of observations of asteroid (278) Paulina with orbital elements taken in the Ephemerides of Minor Planets for 1995 and neglecting the perturbation of (121) Hermione; Bottom: same, taking into account the perturbation of Hermione with an assumed mass of 5 10-12 M

In this figure, the evolution of the accuracy of the observations with time is not evident. In consequence, the observations of Paulina were taken as a whole, instead of separating them in several groups, as made for (94) Aurora. The number of selected observations are detailed in Table 6.

Table 6. Characteristics of each group of observations of (278) Paulina; for explanations see Table 2

4.3. Results and discussion

Starting with a mass of Hermione equal to 5 10^-12 M, the corrections for this mass and for the six osculating elements of Paulina were calculated as described in Sect. 2.2. The new orbital elements of Paulina are given in Table 7, and the correlations coefficients of the parameters are given in Table 8.

Table 7. New orbital elements of (278) Paulina, and standard deviations, at epoch JED 2450000.5 = 1995 October 10.0 TT

Table 8. Correlation coefficients for initial position and velocity of (278) Paulina, and mass of (121) Hermione

The value obtained for the mass of Hermione is M. During the iterations, the value obtained always remained between 3.9 and 5.2 M, which indicates that the standard deviation obtained on the final result is quite consistent. This result is very close to the estimated mass of Hermione (Sect. 4.1), and gives for this asteroid a mean density of g/cm³. This value is in agreement to the mean density of C-class asteroids found by Standish et al. (1995) in the DE 403 ephemerides computations. It is also consistent with the fact that most of the asteroids of which mass has already been determined have a mean density of about 2 g/cm³ (Fig. 5).

Fig. 5. Mean density of each of the 16 asteroids for which mass determinations have already been made, sorted by class; references of the masses used: (in brackets is given the asteroid number) [1] Viateau & Rapaport (1998), [2 and 4] Standish et al. (1995), [10] Scholl et al. (1987), [11] Viateau & Rapaport (1997), [15] Hilton (1997), [16] this work, [20] Bange (1998), [24] Lopez Garcia et al. (1997), [45] Merline et al. (1999), [121] this work, [243] Belton et al. (1995), [253] Yeomans et al. (1997), [433] Yeomans et al. (1999), [704 and 804] Landgraf (1992)

© European Southern Observatory (ESO) 2000

Online publication: February 9, 2000
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