5.2 Kepler’s Equation
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vatories simply did not have the manpower to do the necessary calculations.
There was a real danger that asteroids were discovered but lost again before the
orbit had been determined sufficiently accurately. It was not until the 1890s
that the Astronomisches Rechen-Institut in Berlin, 2 under the directorate of
Friedrich Tietjes (1834–1895) and Julius Bauschinger (1860–1934), assumed
responsibility for this; from then on, these calculations have been made there
systematically and the results kept up to date. Until the time of electronic
computers, it remained a labor-intensive job to determine the orbits of comets
and asteroids.
To Kapteyn, with his mathematical background, this looked like a good
challenge. His method used mathematical series, as he studied with his brother
Willem. However, these were other series than the ones they had published on
and, as far as I know, Willem did not contribute to this. Kapteyn considered
his work a real improvement, but closer inspection shows that it was marginal
at best. It is ironic that later a mathematical series was discovered, named after
Kapteyn (but then Willem), that eventually would turn out to facilitate a faster
algorithm of solving Kepler’s equation.
5.3 Positions and Parallaxes of Stars
Kapteyn’s most significant work in the early 1880s concerned his most fundamental interest: the spatial distribution of the stars, the ‘Construction of the
Heavens’. In order to be able to study this, one needs catalogs and for this
precise measurement of the positions of stars to great accuracy is required. We
saw above that the position of a star in the sky in a catalog is defined by two
numbers. The first is the right ascension, which is determined from a precise
time measurement of the passage of a star through the meridian (the moment
when the star is exactly in the south). The second, which is perpendicular
to it, is the declination, which is determined by the angle above the horizon
of the direction of the star at that moment. However, the measurements of
declinations posed a major problem for an observer.
That problem is twofold. The first point concerns the bending of the telescope’s tube. A telescope is not perfectly stiff; it will bend under its own weight,
so the measurement of the angle of a star above the horizon will be too large.
That would not be too bad if you could correct for it, but it was not easy to
determine how much that deflection for any particular telescope is. Secondly,
there is the refraction of light. As soon as light from a star enters the atmosphere, the path of the light is refracted, and that refraction increases when a
2 This institute has been in Heidelberg since 1945.
69
vatories simply did not have the manpower to do the necessary calculations.
There was a real danger that asteroids were discovered but lost again before the
orbit had been determined sufficiently accurately. It was not until the 1890s
that the Astronomisches Rechen-Institut in Berlin, 2 under the directorate of
Friedrich Tietjes (1834–1895) and Julius Bauschinger (1860–1934), assumed
responsibility for this; from then on, these calculations have been made there
systematically and the results kept up to date. Until the time of electronic
computers, it remained a labor-intensive job to determine the orbits of comets
and asteroids.
To Kapteyn, with his mathematical background, this looked like a good
challenge. His method used mathematical series, as he studied with his brother
Willem. However, these were other series than the ones they had published on
and, as far as I know, Willem did not contribute to this. Kapteyn considered
his work a real improvement, but closer inspection shows that it was marginal
at best. It is ironic that later a mathematical series was discovered, named after
Kapteyn (but then Willem), that eventually would turn out to facilitate a faster
algorithm of solving Kepler’s equation.
5.3 Positions and Parallaxes of Stars
Kapteyn’s most significant work in the early 1880s concerned his most fundamental interest: the spatial distribution of the stars, the ‘Construction of the
Heavens’. In order to be able to study this, one needs catalogs and for this
precise measurement of the positions of stars to great accuracy is required. We
saw above that the position of a star in the sky in a catalog is defined by two
numbers. The first is the right ascension, which is determined from a precise
time measurement of the passage of a star through the meridian (the moment
when the star is exactly in the south). The second, which is perpendicular
to it, is the declination, which is determined by the angle above the horizon
of the direction of the star at that moment. However, the measurements of
declinations posed a major problem for an observer.
That problem is twofold. The first point concerns the bending of the telescope’s tube. A telescope is not perfectly stiff; it will bend under its own weight,
so the measurement of the angle of a star above the horizon will be too large.
That would not be too bad if you could correct for it, but it was not easy to
determine how much that deflection for any particular telescope is. Secondly,
there is the refraction of light. As soon as light from a star enters the atmosphere, the path of the light is refracted, and that refraction increases when a
2 This institute has been in Heidelberg since 1945.