72
5 Nearly Half a Million Stars
to solve the problem of absolute declinations. So this was not only rather
fundamental, but also very inventive and clever work by Kapteyn.
What was most urgent for Kapteyn’s aim of studying of the arrangement
of the stars in space was measurements of distances of stars, and that was the
next problem that Kapteyn addressed. The only method available until then
had been measuring the projection of the motion of the Earth around the Sun
in the position of a star. This manifests itself as a small ellipse in the sky and
can be measured for a nearby star relative to some, generally faint, stars in the
background which would be at larger distances. I have already discussed this
above; there we also saw that the parallax of the nearest star α Centauri is only
0 .75, so less than a second of arc.
Because parallaxes are so small, they were known in the 1880s only for a
very small number of stars. Of course Kapteyn needed many more parallax
measurements to be able to carry out his studies of the spatial distribution of
stars. We already saw in proposition XV of his dissertation, which dealt with
the relation between the distance of a star and its proper motion in the sky,
that this issue has preoccupied him from an early age onward. Now proper
motions result from the velocity of a star through space; the proper motion
will generally be larger when a star is near to us. But it can measured very
accurately if one is prepared to wait longer, because the displacement on the
sky increases with time. Because star positions were available from antiquity
the time available covered several thousand years, Edmond Halley discovered
proper motions in 1718.
Because the orbital plane of the Earth makes an angle of only about 23 ◦
with the equator, the effect of parallax occurs mainly in the direction of the
right ascension of a star; so it should in principle be possible to measure it using
the timing of the meridian passage of a star. Of course you do this then relative
to a number of fainter stars in the sky that in general would be further away.
Now others had thought about this before, but nobody had ever managed to
perform this measurement. That is because the effect is so small. For example,
for a star with a parallax of 0 .1, which is only 7.5 times further away than α
Centauri, the effect is of the order of a few hundredths of a second if time, so
you must be able to determine the meridian passage with at least that accuracy!
Kapteyn was not deterred by this.
Hendricus van de Sande Bakhuyzen gave Kapteyn permission to use the
meridian circle of the the Sterrewacht Leiden (see Fig. 3.6) during several
academic vacations in 1884 and 1885. The measurements had to be done six
months apart, and then repeated again after another six months to correct for
the proper motion. Kapteyn selected fifteen stars, of which he suspected on the
basis of their proper motions that the distances were relatively small. But how
5 Nearly Half a Million Stars
to solve the problem of absolute declinations. So this was not only rather
fundamental, but also very inventive and clever work by Kapteyn.
What was most urgent for Kapteyn’s aim of studying of the arrangement
of the stars in space was measurements of distances of stars, and that was the
next problem that Kapteyn addressed. The only method available until then
had been measuring the projection of the motion of the Earth around the Sun
in the position of a star. This manifests itself as a small ellipse in the sky and
can be measured for a nearby star relative to some, generally faint, stars in the
background which would be at larger distances. I have already discussed this
above; there we also saw that the parallax of the nearest star α Centauri is only
0 .75, so less than a second of arc.
Because parallaxes are so small, they were known in the 1880s only for a
very small number of stars. Of course Kapteyn needed many more parallax
measurements to be able to carry out his studies of the spatial distribution of
stars. We already saw in proposition XV of his dissertation, which dealt with
the relation between the distance of a star and its proper motion in the sky,
that this issue has preoccupied him from an early age onward. Now proper
motions result from the velocity of a star through space; the proper motion
will generally be larger when a star is near to us. But it can measured very
accurately if one is prepared to wait longer, because the displacement on the
sky increases with time. Because star positions were available from antiquity
the time available covered several thousand years, Edmond Halley discovered
proper motions in 1718.
Because the orbital plane of the Earth makes an angle of only about 23 ◦
with the equator, the effect of parallax occurs mainly in the direction of the
right ascension of a star; so it should in principle be possible to measure it using
the timing of the meridian passage of a star. Of course you do this then relative
to a number of fainter stars in the sky that in general would be further away.
Now others had thought about this before, but nobody had ever managed to
perform this measurement. That is because the effect is so small. For example,
for a star with a parallax of 0 .1, which is only 7.5 times further away than α
Centauri, the effect is of the order of a few hundredths of a second if time, so
you must be able to determine the meridian passage with at least that accuracy!
Kapteyn was not deterred by this.
Hendricus van de Sande Bakhuyzen gave Kapteyn permission to use the
meridian circle of the the Sterrewacht Leiden (see Fig. 3.6) during several
academic vacations in 1884 and 1885. The measurements had to be done six
months apart, and then repeated again after another six months to correct for
the proper motion. Kapteyn selected fifteen stars, of which he suspected on the
basis of their proper motions that the distances were relatively small. But how