112
6 Laboratory and Statistical Astronomy
that of the Sun, pointing away from the Apex. If the star is farther away, the
angle a → b will be smaller and the parallax can be determined from this. In
practice, stars themselves also move in space, so this can only be done using
a statistical approach. For example, one can do this for a collection of stars of
which there is reason to assume that their distances are similar. The result then
is called the ‘secular parallax’.
The method to determine the position of the Apex from measurements of
the proper motions of groups of stars had already been worked out in 1843 by
the Frenchman Auguste Bravais (1811–1863). Kapteyn started out with a new
and more accurate determination of the position of the Apex. As I described
above, the problem arose that this determination depended on the precession
of the equinox, the motion of the Earth’s axis in space. For the determination
of proper motions, two measurements at different times are required, and in
order to compare positions measured at different times you need to know
how the position of the Earth’s axis in space has changed in the meantime.
Kapteyn used the available data of the proper motions of the ‘Bradley’s stars’—
as Kapteyn referred to them—, the stars from the catalog of James Bradley and
Friedrich Wilhelm Bessel (see Sect. 3.2). Using this catalog as a basis, Georg
Friedrich Julius Arthur von Auwers (1838–1915) had produced a fundamental
catalog 5 in 1881, based on observations in Greenwich and Berlin; it contained
the proper motions of 3268 of those ‘Auwers-Bradley’ stars. Kapteyn took
different assumptions for the position of the Apex, for the precession and
for the unknown declination errors in the Bradley catalog to study the effect
these assumptions had on the derived position of the Apex. He published this
enormous amount of arithmetic in 1900 and in 1902 in the Publications of
the Astronomical Laboratory at Groningen. Fig. 6.13 shows his determination
of the Apex and the current determination; Kapteyn’s error was less than 10 ◦ !
When the Apex was known with sufficient accuracy, one still had to determine the space velocity of the Sun to sufficient accuracy to apply the method
of the secular parallax. Kapteyn used measurements of radial velocities (along
the line of sight) of 51 stars, obtained in Potsdam by Paul Friedrich Ferdinand
Kempf (1856–1920). If you know roughly where the Apex is, you also know
how much of the velocity of the Sun is along the line of sight; by assuming that
the average velocity of the stars themselves is zero, you can make an estimate of
the velocity of the Sun relative to those stars. Kapteyn, partly with the help of
independent determinations by others, eventually arrived at a value of 19 km/s.
That means that the Sun travels in one year a distance in space equal to four
times that between the Earth and the Sun; so with the secular parallax method
5 ‘Fundamental’ here means that the positions and proper motion were measured absolutely and not relative
to other stars.
6 Laboratory and Statistical Astronomy
that of the Sun, pointing away from the Apex. If the star is farther away, the
angle a → b will be smaller and the parallax can be determined from this. In
practice, stars themselves also move in space, so this can only be done using
a statistical approach. For example, one can do this for a collection of stars of
which there is reason to assume that their distances are similar. The result then
is called the ‘secular parallax’.
The method to determine the position of the Apex from measurements of
the proper motions of groups of stars had already been worked out in 1843 by
the Frenchman Auguste Bravais (1811–1863). Kapteyn started out with a new
and more accurate determination of the position of the Apex. As I described
above, the problem arose that this determination depended on the precession
of the equinox, the motion of the Earth’s axis in space. For the determination
of proper motions, two measurements at different times are required, and in
order to compare positions measured at different times you need to know
how the position of the Earth’s axis in space has changed in the meantime.
Kapteyn used the available data of the proper motions of the ‘Bradley’s stars’—
as Kapteyn referred to them—, the stars from the catalog of James Bradley and
Friedrich Wilhelm Bessel (see Sect. 3.2). Using this catalog as a basis, Georg
Friedrich Julius Arthur von Auwers (1838–1915) had produced a fundamental
catalog 5 in 1881, based on observations in Greenwich and Berlin; it contained
the proper motions of 3268 of those ‘Auwers-Bradley’ stars. Kapteyn took
different assumptions for the position of the Apex, for the precession and
for the unknown declination errors in the Bradley catalog to study the effect
these assumptions had on the derived position of the Apex. He published this
enormous amount of arithmetic in 1900 and in 1902 in the Publications of
the Astronomical Laboratory at Groningen. Fig. 6.13 shows his determination
of the Apex and the current determination; Kapteyn’s error was less than 10 ◦ !
When the Apex was known with sufficient accuracy, one still had to determine the space velocity of the Sun to sufficient accuracy to apply the method
of the secular parallax. Kapteyn used measurements of radial velocities (along
the line of sight) of 51 stars, obtained in Potsdam by Paul Friedrich Ferdinand
Kempf (1856–1920). If you know roughly where the Apex is, you also know
how much of the velocity of the Sun is along the line of sight; by assuming that
the average velocity of the stars themselves is zero, you can make an estimate of
the velocity of the Sun relative to those stars. Kapteyn, partly with the help of
independent determinations by others, eventually arrived at a value of 19 km/s.
That means that the Sun travels in one year a distance in space equal to four
times that between the Earth and the Sun; so with the secular parallax method
5 ‘Fundamental’ here means that the positions and proper motion were measured absolutely and not relative
to other stars.