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results from the other two methods. Because of this situation, Rabe and Francis in 1966 undertook a reinvestigation of the Eros motion by means of IBM 7094 integrations using the value 1/met c = 328 912, which is consistent with the astronomical unit adopted by the IAU in 1964, extending the comparison with observations through the period 1926-65. It became evident then that the true value of met & was indeed close to 1/328 912 (Rabe and Francis, 1967a), and it was found that a conceptual error had led to erroneous mass coefficients in the original 1926-45 observation equations. The erroneous nature of these coefficients was discovered independently also by Schubart and Zech (1967) when they tried to reconcile the dynamical value of the astronomical unit with the radar measures, after Schubart had first found that the observations of 1221 Amor seemed to call for an Earth+Moon mass fairly consistent with the radar results for the astronomical unit. Rabe's corrected 1926-45 determination (Rabe, 1967) produced for 1/meet the result 328 863+29 (mean errors are quoted from here on) from a 13-unknowns solution, whereas from the extended 1926-65 arc Rabe and Francis (1967b) obtained the comparable result 328890+16. The gain in accuracy corresponds roughly to the longer arc involved. The most disappointing finding was that the masses of Mars, Venus, and Mercury are very poorly determined from the Eros solutions, contrary to earlier predictions and expectations. This fact has been confirmed even by the as yet most comprehensive and rigorous study of the Eros motion, namely that by Lieske (1968), for which all the 1893-1966 observations have been reduced to the uniform reference system of the FK4. Lieske's result 1/meet = 328.915+4 almost approaches in its small formal error those from radar determinations and space probes, which now point to a true value near 328 900+1. While the dynamical and radar determinations of the astronomical unit have thus been reconciled, in close agreement with the IAU value 8"794.05 for the solar parallax, a full explanation of the still discordant trigonometric result 8"790+0"001 has not been given as yet. It appears that the motion of Eros will remain of some value for determinations of merc even in the future, especially if it should be possible to secure precise radar observations of its distance during close approaches. As to Amor, Schubart (1969) has noted the fact that the lack of observations outside of the perihelion approaches significantly reduces the accuracy of the results for met c. The motion of 1566 Icarus, on the other hand, from which Lieske and Null (1969) obtained a good determination of the mass of Mercury, will probably remain important for this purpose, at least until space probes make close approaches to this planet. In general, though, it looks as if the future use of asteroids for determinations of the masses of the inner planets will have a strong competition from space probes, as well as from comprehensive adjustments of the (rigorously integrated) orbits and masses of these planets on the basis of combined radar and optical observations of their own motions. As to the latter approach, the relevant investigation by Ash, Shapiro, and Smith (1967), based on a still relatively short time interval, already reveals the high accuracy obtainable in this way not only for the planetary masses involved, but even for the Moon/Earth mass ratio u. As to space probes, the even greater accuracy with which they seem to be able to determine planetary masses is apparent in the result from Mariner 2 for Venus, as quoted by Clemence (1966), and in the one from Mariner 4 for Mars, as obtained by Null (1967). For most of the asteroids, though, Jupiter is the principal disturbing planet, and many investigators have recently taken up the proposal made in 1873 by Hill (1907) to improve Jupiter's mass on the basis of the particularly large perturbations experienced by certain minor planets in consequence of their closeness to the 2/1 commensurability with respect to Jupiter's mean motion. A recent determination by Klepczynski (1969), for instance, combines the four separate mass corrections obtained from the motions of 10 Hygiea, 24 Themis, 31 Euphrosyne, and 52 Europa into the result 1/m 2 - 1047.360+0.004, with a mean error much smaller than the one appearing in Bec's (1969) determination from Jupiter's ninth satellite: 1/m . = 1047.386+0.041. On the other hand, an even more recent determination from the disturbed motion of the Hilda group planet 334 Chicago (which approaches Jupiter to within 1.1 AU) by Scholl (1971) gave the result 1/m 2 = 1047.325+0.010. The minor planet results by Klepczynski and Scholl differ by 3.5 times the larger mean error, and there are other relevant determinations from individual asteroids with formal errors much smaller than the actual differences between some of the results. Nevertheless, it appears that the combination of numerous results from asteroids should eventually give us a Jupiter mass more precise than one can get from satellites. Because space missions may soon be used also for more accurate determinations of the mass of Jupiter, the major planet whose mass can now be most usefully determined by means of minor planet observations is Saturn. Such a determination, using 944 Hidalgo, has been made by Marsden (1970), who suggests that it would be worthwhile to verify his result (1/3498.5) by means of several minor planets with aphelion distances greater than 4 AU. Corrections to the orbital elements of the Earth-Moon barycenter and to the constants defining the equatorial reference system have been included in some comprehensive solutions, especially in those using Eros, sometimes simply to prevent other unknowns from unduly absorbing some of their effects. In this connection, Lieske (1970) found that corrections to the adopted precession in longitude and to Newcomb's rate of change of the obliquity of the ecliptic are not well determined from the Eros data. As to systematic programs using asteroids, the papers by Brouwer (1935), Clemence (1948), Schmeidler (1958), and Petri (1958) may be consulted. First results from meridian observations of the first four numbered planets have been obtained and discussed by Jackson (1968). He finds that the results are considerably less accurate than predicted by Clemence (1948). This is because of the clustering of the observations around opposition and also the less-than-anticipated precision of the individual measures. It is still concluded, however, that meaningful corrections to the coordinate system can indeed be obtained from the observations of all four planets during a planned program, if an effort is made to secure observations as close to quadrature as possible. This last requirement is necessary for a satisfactory separation of the corrections to the minor planet orbit from those to the orbit of the Earth. For photographic asteroid observations, the program initiated by Brouwer (1935) has, to a limited extent, been completed by Pierce (1971). Aside from orbital corrections for the 15 minor planets involved, Pierce determines local corrections, Ao and A6, for 54 small areas of the Yale Catalogue zones, and for 60 such areas in the Boss General Catalogue. These catalog corrections are the principal objective of this paper; only rough estimates of the equinox and equator corrections are given, as arithmetic means of all the individual area corrections, and no attempt is made to obtain corrections to Earth's orbit based on volume XIV of the Astronomical Papers of the American Ephemeris. Considering the relatively large and somewhat erratic area corrections obtained, it appears that supplementary results from absolute determinations of equinox and equator, using meridian observations of Ceres, Pallas, Juno, and Vesta, would be of great value in future attempts to disentangle the basic coordinate corrections from the local distortions of star catalogs. In conclusion, it seems fair to say that the further use of asteroids will be of considerable value for future improvements of the fundamental reference frame and for future determinations of the elements of any improved Earth orbit or theory.
Ash, M. E., Shapiro, I. I., and Smith, W. B. 1967, Astronomical Constants and Planetary
Jackson, E. S. 1968, Determination of the Equinox and Equator From Meridian
MARSDEN (in reply to a question by Kiang about 1362 Griqua): Because of its libration about the 2:1 resonance, 1362 Griqua does not seem to be as suitable an object for determining the mass of Jupiter as it was thought to be. We attempted to make a determination from the observations of 1935 to 1965 but were unable to obtain a significant correction to the adopted value. The Hill planets, which do not librate and which have longer observational histories, seem to be rather more suitable.
ALFVEN: Have effects of nongravitational forces been detected in the motion of minor planets?
MARSDEN: No. There are a few cases where it seemed that small systematic trends remained in the residuals after accurate orbit solutions had been made, but I am confident that these are due to errors in the adopted masses of the perturbing planets. I had initially suspected that the motion of 887 Alinda and 944 Hidalgo were affected by nongravitational forces and that these objects were dying cometary nuclei, but it is clear that the residuals may be removed if one makes reasonable changes in the masses of Earth and Saturn. I hasten to add that this is not true in the case of comets, where the residuals are usually very much larger.