Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...287.1014t&link_type=abstract
Astronomy and Astrophysics 287, 1014-1020 (1994)
Astronomy and Astrophysics
Astrophysics
Astrometry, Planets And Satellites: Mars, Jupiter
Scientific paper
In the field of the astrolabe (power=175), the image of a planet is, generally speaking, a disk. While Uranus is starlike, Mars and Jupiter have an apparent diameter. In these last cases, the position of the object (its geometric center) has to be determined from an image affected by the phase on one side according to the relative position of the Sun, the Earth and the planet. A limb correction must be applied for the difference between the center and the photocenter. The last one depends on the distribution of light in intensity, the reflecting characteristics of the surface and one can assume that a certain factor k could represent its character. Models can be established to represent as accurately as possible the planetary surface, being employed for the determination of the phase correction to be taken into account for the use of observations to establish ephemerides. In the case of JPL ephemerides, the phase correction was taken into account (Standish 1990) under the form of an empirical term whose amplitude is 0.4" for Mars, 1.0" for Jupiter and 0.8" for Saturne. For a given phase angle i and a given value of k, the position of the photocenter P is obtained by a barycentric calculation. According to the symmetrical figure, the photocenter - on the photometric equator - has an abscissa d given by Eq. (1). Mathematical models of the ground reflectivity of Mars surface have been tested. Table 1 gives their geometric characteristics, their advantages and disadvantages. A statistical study of the incorrected results in right ascension versus the phase angle (or date from the opposition) allows us to calculate the coefficients a and b in equation {DELTA}α=a.N+b ({DELTA}α in arcseconds and N in days). This equation constitutes a first approximation representation of the "phase effect" with {DELTA}α=(-0.020+/-0.004)N+0 (Mars) and {DELTA}α=(-0.018+/-0.005)N+0 (Jupiter) for each planet. The phase corrections previously proposed are not sufficient. On the other hand we must consider that any "good" reflection model corresponds to a=0. A phase correction d=0.5Rsin(i/2) corresponds to such an assumption as it can be seen from Figs. 2 and 3. Furthermore, the photocenter must correspond to the reflecting point F when a better representation is obtained. The new model (MT4) is characterized by a reflected intensity represented by Eq. (3) where s and t angles correspond to the position of M(x,y) related to S and T (Fig. 1). The first factor (cos s) represents the Lambert law and the second one (cos t) corresponds to a limb darkening effect. Table 2 gives d as a function of k and i, which represents the position of the photocenter for each given model, with k being equal to 0, 1, 2, 3 or 4, respectively. When calculating the integrals J and J' for intermediate values of k, the difference between d(k,i) and 0.5 R sin (i/2) is obtained under the form of a polynomial of degree three for i (Table 3), allowing to determine a real good value for k. Doing so, it is seen that, when k has the value 0.66 and 0.86, the {DELTA}α residuals are accurately represented for Mars and Jupiter, respectively. The new phase correction is then deduced having the form d=R/2sin(i/2). Isophotes (IConst) are represented in Figs. 4 and 5 and compared with a photograph of Mars obtained in 1952.
Chollet Fernand
Toulmonde M.
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