11.8 Dynamics, the Crowning Achievement
247
11.8 Dynamics, the Crowning Achievement
The result that Kapteyn and van Rhijn published in 1920 was what Kapteyn
had always been looking forward to. Around the same time von Seeliger had
come to a fairly similar result, but he presented it much more schematically and
in a much less accessible way. Kapteyn went further. What he actually wanted
to know is not only how stars are distributed, but how the Galaxy could be
in equilibrium, because there had to be a balance between the gravitational
attraction of the stars on each other and their velocities. It is this next step that
makes Kapteyn’s work immortal; whether or not the model turned out to be
correct in time, it is the crowning achievement of his efforts.
Nowadays we call this field dynamics; Kapteyn called it mechanics. The
balance between velocities and gravitation has to result in a steady state, a stable
equilibrium. He wrote about this several times in his letters to George Hale.
In the correspondence about induction versus deduction, which I discussed
above, there are also passages about this. I quote (from Kapteyn’s letter of
September 23, 1915):
One of the somewhat startling consequences is, that we have to admit that our
solar system must be in or near to the center of the Universe, or at least some
local center. Twenty years ago this would have made me very skeptical... Now
it is not so. [Von] Seeliger, Schwarzschild, Eddington and myself have found
that the number of stars is greater near the Sun. I have sometimes felt uneasy
in my mind about this result, because in its derivation the consideration of the
scattering of light in space has been neglected. Still it appears more and more
that the scattering must be too small, and also somewhat different in character
from what would explain the change in apparent density. The change is therefore
pretty surely real.
Even more important than the central position of the Sun seems to me to be that
our result for the first time shows the evidence of force in the great Sidereal System.
A rough computation leads to the conclusion that at a distance corresponding
with a parallax of 0 .02 the stars are under the action of a force equal to the
attraction of a central mass having 5 million times the Sun’s mass.
This number is very considerably higher than the number of stars we assumed
up to the present to exist in a sphere of a radius corresponding to π =0 .02. But
these of course may be completely dark bodies, of which we know nothing.
Kapteyn wondered how the system can be in equilibrium. The result of his
work on this was published after his retirement in the Astrophysical Journal in
1922. The article has the title First attempt at a theory of the arrangement and
motions in the Sidereal System, and it is described in the summary as a first
247
11.8 Dynamics, the Crowning Achievement
The result that Kapteyn and van Rhijn published in 1920 was what Kapteyn
had always been looking forward to. Around the same time von Seeliger had
come to a fairly similar result, but he presented it much more schematically and
in a much less accessible way. Kapteyn went further. What he actually wanted
to know is not only how stars are distributed, but how the Galaxy could be
in equilibrium, because there had to be a balance between the gravitational
attraction of the stars on each other and their velocities. It is this next step that
makes Kapteyn’s work immortal; whether or not the model turned out to be
correct in time, it is the crowning achievement of his efforts.
Nowadays we call this field dynamics; Kapteyn called it mechanics. The
balance between velocities and gravitation has to result in a steady state, a stable
equilibrium. He wrote about this several times in his letters to George Hale.
In the correspondence about induction versus deduction, which I discussed
above, there are also passages about this. I quote (from Kapteyn’s letter of
September 23, 1915):
One of the somewhat startling consequences is, that we have to admit that our
solar system must be in or near to the center of the Universe, or at least some
local center. Twenty years ago this would have made me very skeptical... Now
it is not so. [Von] Seeliger, Schwarzschild, Eddington and myself have found
that the number of stars is greater near the Sun. I have sometimes felt uneasy
in my mind about this result, because in its derivation the consideration of the
scattering of light in space has been neglected. Still it appears more and more
that the scattering must be too small, and also somewhat different in character
from what would explain the change in apparent density. The change is therefore
pretty surely real.
Even more important than the central position of the Sun seems to me to be that
our result for the first time shows the evidence of force in the great Sidereal System.
A rough computation leads to the conclusion that at a distance corresponding
with a parallax of 0 .02 the stars are under the action of a force equal to the
attraction of a central mass having 5 million times the Sun’s mass.
This number is very considerably higher than the number of stars we assumed
up to the present to exist in a sphere of a radius corresponding to π =0 .02. But
these of course may be completely dark bodies, of which we know nothing.
Kapteyn wondered how the system can be in equilibrium. The result of his
work on this was published after his retirement in the Astrophysical Journal in
1922. The article has the title First attempt at a theory of the arrangement and
motions in the Sidereal System, and it is described in the summary as a first