6.6 Spatial Distribution of Stars
115
0 .01. And according to the Frequency Law, 29% of those stars have parallaxes
between the average value and double that value; and in the same way 6% have
parallaxes between two and three times the average. So of our 460 stars, 133 will
have parallaxes between 0 .01 and 0 .02, 28 between 0 .02 and 0 .03, and so on.
Find distances for other stars of magnitude 6 in this way and then treat stars of
the 1 st , 2 nd , ........., 9 th magnitude in the same way and you will eventually have
located all these stars in space.
In principle you can determine the distribution of the stars over intrinsic
luminosity (i.e., how many there are relative to each other as a function of luminosity), expressed as absolute magnitude. In other words: you can determine
how in a certain part of space the stars are distributed in absolute magnitude or
luminosity. Kapteyn called this the luminosity curve, nowadays astronomers
say the luminosity function. And the third assumption that he made was that
this function would be the same everywhere in space. What then remains is the
total number of stars as a function of the distance from the Sun, the ‘density
curve’.
With these three assumptions it is in principle possible to derive from star
counts and observations of proper motions what this density curve is. In practice this was not so easy, because it required the use of complicated mathematical methods. That turned out to be so difficult, that Kapteyn called upon his
brother Willem in Utrecht. Together they succeeded in developing the necessary mathematical tools. This produced the first of two major articles, which
became number five in the series Publications of the Astronomical Laboratory
at Groningen. The second article, the application of these mathematical tools,
was supposed to appear as part six, but it never did. There were indications
that something in the assumptions was wrong, which Kapteyn first attributed
to the poor declinations of the Auwers-Bradley stars. Slowly, however, he came
to the realization that he had to drop the assumption of a lack of preferred
directions in the spatial motions of the stars. That realization was a set-back
but at the same time would be a discovery that would only enhance his already
growing fame.
6.7 Natural Sciences Society
An important activity of Kapteyn in Groningen concerns his efforts for the
Natural Sciences Society. This association still exists (I have been chairman of
the Board between 1998 and 2020) and since 1976 it is ‘Royal’. It was founded
in 1801, with the aim of promoting a broad knowledge and understanding of
natural science [65] . Not only physics, astronomy, chemistry, biology and so
115
0 .01. And according to the Frequency Law, 29% of those stars have parallaxes
between the average value and double that value; and in the same way 6% have
parallaxes between two and three times the average. So of our 460 stars, 133 will
have parallaxes between 0 .01 and 0 .02, 28 between 0 .02 and 0 .03, and so on.
Find distances for other stars of magnitude 6 in this way and then treat stars of
the 1 st , 2 nd , ........., 9 th magnitude in the same way and you will eventually have
located all these stars in space.
In principle you can determine the distribution of the stars over intrinsic
luminosity (i.e., how many there are relative to each other as a function of luminosity), expressed as absolute magnitude. In other words: you can determine
how in a certain part of space the stars are distributed in absolute magnitude or
luminosity. Kapteyn called this the luminosity curve, nowadays astronomers
say the luminosity function. And the third assumption that he made was that
this function would be the same everywhere in space. What then remains is the
total number of stars as a function of the distance from the Sun, the ‘density
curve’.
With these three assumptions it is in principle possible to derive from star
counts and observations of proper motions what this density curve is. In practice this was not so easy, because it required the use of complicated mathematical methods. That turned out to be so difficult, that Kapteyn called upon his
brother Willem in Utrecht. Together they succeeded in developing the necessary mathematical tools. This produced the first of two major articles, which
became number five in the series Publications of the Astronomical Laboratory
at Groningen. The second article, the application of these mathematical tools,
was supposed to appear as part six, but it never did. There were indications
that something in the assumptions was wrong, which Kapteyn first attributed
to the poor declinations of the Auwers-Bradley stars. Slowly, however, he came
to the realization that he had to drop the assumption of a lack of preferred
directions in the spatial motions of the stars. That realization was a set-back
but at the same time would be a discovery that would only enhance his already
growing fame.
6.7 Natural Sciences Society
An important activity of Kapteyn in Groningen concerns his efforts for the
Natural Sciences Society. This association still exists (I have been chairman of
the Board between 1998 and 2020) and since 1976 it is ‘Royal’. It was founded
in 1801, with the aim of promoting a broad knowledge and understanding of
natural science [65] . Not only physics, astronomy, chemistry, biology and so