Publication Date:
2021-05-19
Description:
In order to avoid confusion in the future the departure of the fundamental ephemerides, contained in the current volumes of the Astronomical Ephemeris (A.E.), from their basic theories have been investigated by rigorous preparations of computer programs.
Regarding Newcomb’s (1895b) Tables of the Sun, it is found that several small terms in the perturbations of the radius vector by Venus and Mars have been neglected in the tabular values, besides the remarks by Clemence (1943) and Kinoshita et al. (1974〕on the perturbations in the longitude by Venus and Jupiter, respectively. Some of the numerical coefficients in the expression of the equation of the center seem to be in error, which causes an. error of 土0.'0l in
the longitude of the Sun. In opposition to the remark by Williams and Clemence (1942〕it seems appropriate that Newcomb applied corrections to LeVerrier’s values of the eccentricity and the perihelion longitude of the earth’s orbit due to the elimination of terms dependent solely on the mean anomaly of the earth, as far as the perturbations in the longitude are concerned. The amount of the lunar inequality in the longitude calculated directly be making use of the daily ephemerides of the Sun and the Moon differs from that given by the Tables by about 土0."04. Although the expressions for the planetary perturbations of the latitude in Newcomb’s and Le Verrier’S Tables are both based on Le Verrier’s (1858) fundamental numbers, these Tables yield values differing by about 土0." 12 from each other.
Comparison between the A.E. and the results of the rigorous computation has been made for the data for 1975 except for those of the Moon for which a comparison by Inoue (1977) for the data from 1952 to 1980 is available. The main features of the A.E.-data thus obtained are as follows : (a) Sun - Discrepancies from the rigorous computations in the longitude and the radius vectors are caused partly by the differences between the basic expressions and the actual tabular figures in Newcomb’s Tables. The remaining discrepancies do not seem still to be caused solely by accumulation of random errors. The discrepancy in the latitude is almost entirely caused by the difference between the basic expressions and the tabular figures. (b) Inner planets - Most of the discrepancies in the heliocentric coordinates can be regarded as tolerable, except that the radius vector of Mercury in the A.E. is systematically smaller than the values obtained by the rigorous computation. The effect of the discrepancies in the solar coordinates appear significantly in the geocentric ephemerides. (c) Outer planets -The numerical integrations by Eckert, Brouwer and Clemence (1951) are admirably correct. The right ascensions and declinations in the A.E. suffer from the incompleteness of the correction due to the change in the value of the aberration constant. The geocentric distances of Uranus and Neptune in the A.E. seem to be those obtained by omitting the figures lower than the printed last decimals. (d) Moon -The computation accuarcies of the A.E. may be around ±0'.'0010 for the longitude,土0."003 for the latitude and ±0."6 × 10-5 for the horizontal parallax. Errors in the A.E. may be caused mostly by the incomplete treatment of the higher terms regarding the change in the value of the dynamical form factor of the earth.
Although the amounts of the discrepancies surveyed in the present investigation might be regarded as permissible in the past, we can now compute the ephemerides as precisely as we want whenever the basic theory is rigidly specified,with the general availability of computers. For example, the j = 2 ephemeris of the Moon prepared by Inoue (1977〕satisfactorily agrees with the Fundamental Lunar Ephemeris (Van Flandern, 1976) of the U.S. Nautical Almanac Office, the discrepancies between them being 土0."0002 in the longitude and latitude and 土2"× 10-6 in the horizontal parallax. Hence, we consider that the international ephemerides in the future should be computed by at least two institutes independently using different types of computer.
Key words: Tables of the Sun fundamental ephemerides
Description:
Published
Repository Name:
AquaDocs
Type:
Journal Contribution
,
Refereed
Format:
pp.93-129
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