70
5 Nearly Half a Million Stars
star is seen closer to the horizon. The starlight will follow a curved trajectory
and the star will also appear to be higher above the horizon than it is in reality.
The existence of this refraction was known, but no one knew how to correct for
it. It must depend on factors as barometric pressure, temperature and humidity. Both these effects are actually absent in the zenith and increase as you get
closer to the horizon. The result of all this was that different star catalogs were
quite similar to each other in terms of right ascension, but sometimes differed
considerably in declination. That was an urgent problem that Kapteyn wanted
to address. He called it the issue of absolute declinations.
His clever solution consisted of two parts. First, he assumed that for an observatory the polar altitude was known exactly. The trick then was to determine
the absolute declinations of a network of stars across the sky, from which the
declinations of other stars could be determined by a relative measurement over
a small angle. Kapteyn now devised a clever technique that was independent
of telescope bending and refraction. This consisted of measurements of the
‘azimuth’, which is the angle that the projection of a star from the zenith on
the horizon makes with the south (or the north), and timing of the passing of
a star through the prime vertical (comparable to the meridian, but now from
east to zenith to west on the horizon). Furthermore, he also made use of two
stars that pass the meridian at about the same height above the horizon, one
in the south and the other in the north and subtracted their altitudes above
the horizon. In these measurements the effects of the refraction and telescope
bending are then about the same and cancel when you subtract the two measurements from each other. Kapteyn’s complicated technique did not work for
every declination, but there were several declination zones in the sky where it
did work, and that was enough to determine a network of stars with absolute
declinations. In his article on this subject, again published in the Copernicus
magazine, Kapteyn presented in detail the mathematical techniques that could
be used to set up such a network from such measurements. This had to be
done of course for the same set of stars around the equator from a northern
and a southern observatory to tie together declinations in both hemispheres.
The problem was not yet solved but reduced to a determination of the absolute polar height (altitude) at the observatory where the measurements were
done. That could be done, as Kapteyn showed, using a set of three stars. However, these had to meet special conditions. A first star had to be circumpolar
(close to the pole so that it never sets) and the other two had to have declinations such that they passed the meridian at roughly the same height above
the southern horizon when the first star in the north did so above and below
the pole. These then had to have right ascensions, such that these passages
took place at about the same time. In this method the telescope bending and
5 Nearly Half a Million Stars
star is seen closer to the horizon. The starlight will follow a curved trajectory
and the star will also appear to be higher above the horizon than it is in reality.
The existence of this refraction was known, but no one knew how to correct for
it. It must depend on factors as barometric pressure, temperature and humidity. Both these effects are actually absent in the zenith and increase as you get
closer to the horizon. The result of all this was that different star catalogs were
quite similar to each other in terms of right ascension, but sometimes differed
considerably in declination. That was an urgent problem that Kapteyn wanted
to address. He called it the issue of absolute declinations.
His clever solution consisted of two parts. First, he assumed that for an observatory the polar altitude was known exactly. The trick then was to determine
the absolute declinations of a network of stars across the sky, from which the
declinations of other stars could be determined by a relative measurement over
a small angle. Kapteyn now devised a clever technique that was independent
of telescope bending and refraction. This consisted of measurements of the
‘azimuth’, which is the angle that the projection of a star from the zenith on
the horizon makes with the south (or the north), and timing of the passing of
a star through the prime vertical (comparable to the meridian, but now from
east to zenith to west on the horizon). Furthermore, he also made use of two
stars that pass the meridian at about the same height above the horizon, one
in the south and the other in the north and subtracted their altitudes above
the horizon. In these measurements the effects of the refraction and telescope
bending are then about the same and cancel when you subtract the two measurements from each other. Kapteyn’s complicated technique did not work for
every declination, but there were several declination zones in the sky where it
did work, and that was enough to determine a network of stars with absolute
declinations. In his article on this subject, again published in the Copernicus
magazine, Kapteyn presented in detail the mathematical techniques that could
be used to set up such a network from such measurements. This had to be
done of course for the same set of stars around the equator from a northern
and a southern observatory to tie together declinations in both hemispheres.
The problem was not yet solved but reduced to a determination of the absolute polar height (altitude) at the observatory where the measurements were
done. That could be done, as Kapteyn showed, using a set of three stars. However, these had to meet special conditions. A first star had to be circumpolar
(close to the pole so that it never sets) and the other two had to have declinations such that they passed the meridian at roughly the same height above
the southern horizon when the first star in the north did so above and below
the pole. These then had to have right ascensions, such that these passages
took place at about the same time. In this method the telescope bending and