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J/AN/331/852 Bessel (1825) calculation for geodesic measurements (Karney+, 2010)
The following files can be converted to FITS (extension .fit or fit.gz)
table1.dat
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Query from: http://vizier.cds.unistra.fr/viz-bin/VizieR?-source=J/AN/331/852
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Beginning of ReadMe :J/AN/331/852 Bessel (1825) calculation for geodesic measurements (Karney+, 2010)
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F.W. Bessel (1825): The calculation of longitude and latitude from geodesic
measurements.
Karney C.F.F., Deakin R.E.
<Astron. Nachrichten. 331, 852-861 (2010)>
=2010AN....331..852K
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ADC_Keywords: Positional data
Keywords: history and philosophy of astronomy
Abstract:
This is an English translation of F.W. Bessel's paper on geodesics
which appeared as "Ueber die Berechnung der geographischen Laengen und
Breiten aus geodaetischen Vermessungen", Astronomische Nachrichten
4(86), 241-254 (1825), 1825AN......4..241B.
Description:
The solution of the geodesic problem for an oblate ellipsoid is
developed in terms of series. Tables are provided to simplify the
computation.
Included here are the tables that accompanied Bessel's paper (with
corrections). The tables were crafted by Bessel to be minimize the
labor of hand calculations. To this end, he adjusted the intervals in
the tables, the number of terms included in the series, and the number
of significant digits given so that the final results are accurate to
about 8 places. For that reason, the most useful form of the tables is
as the PDF file which provides the tables in a layout close to the
original. Also provided is the LaTeX source file for the PDF file.
Finally, the data has been put into a format so that it can be read
easily by computer programs. All the logarithms are in base 10 (common
logarithms). The characteristic and the mantissa should be read
separately (indicated as x.c and x.m in the file description). Thus
the first entry in the table, -4.4, should be parsed as "-4" (the
characteristic) and ".4" (the mantissa); the anti-log for this entry
is 10^(-4+0.4)^=2.5e-4. The "Delta" columns give the first difference
of the preceding column, i.e., the difference of the preceding column
in the next row and the preceding column in the current row. In the
printed tables these are expressed as "units in the last place" and
the differences are of the rounded representations in the preceding
columns (to minimize interpolation errors). In table1.dat these are
given scaled to a match the format used for the preceding column, as
indicated by the units given for these columns. The unit log(") (in
the description within square brackets [arcsec]) means the logarithm
of a quantity expressed in arcseconds.