11.8 Dynamics, the Crowning Achievement
249
what we think this is now. His estimate of the total amount of matter that
must be present in the solar neighborhood also is close to the best current
determinations.
But what about in the ‘horizontal’ direction in the plane of the system?
Again Kapteyn calculated the gravitational forces; he concluded that in order
to have equilibrium and steady state there would have to be a centrifugal force,
which would have to correspond to a rotation of the whole of the stars with
a velocity of about 18–20 km/s. Now his Star Streams have a relative velocity
of 39 km/s and so he could match everything if the Streams represented a
rotation around the center of the system, one in one direction, the other one
opposite to it. That meant then that the Sun had to partake in this rotation
as part of one of the Streams and that it therefore could not be exactly in the
center of the System. The modeling of the star counts had assumed symmetry
as a first approximation so this constituted a refinement on that. After some
considerations he came to the conclusion that the Sun is about 650 pc from
the center; if it were less the centrifugal force would not be sufficient and if
larger there would be a larger asymmetry in the star counts than observed.
He also followed Ejnar Hertzsprung, who from studies of Cepheid variable
stars came to the conclusion that the Sun is 38 pc from the symmetry plane
of the Milky Way. These are part of the population of stars in the disk and
their mean Galactic latitude shows a deviation from a straight line. From such
studies of the shape of the Milky Way itself the best current value is 13 pc.
Kapteyn indicated a position of the Sun in Fig. 11.10 with a small circle. This
is indicative (as he himself stressed), but it is somewhat misleading; it is about
a factor three too far from the center.
The fundamental theory of dynamics was developed elsewhere, especially
in the U.K., by James Hopwood Jeans (1877–1946) and Arthur Eddington. It
was Jeans who christened the model of Fig. 11.10 the ‘Kapteyn Universe’ when
he studied its dynamics in more detail than Kapteyn’s schematic treatment.
Kapteyn was the first to present a consistent, dynamical model of our Stellar
System, based on observations, in which the distribution of matter and the
internal motions were precisely tuned to provide dynamical stability. It opened
a whole new field of research and that is a major accomplishment.
Of course, it soon became clear that there is absorption of starlight and that
the Star Streams do not represent a rotation around a center, but that does not
detract from the originality of this brilliant application of a new approach to
study the structure of the Stellar System and the dynamics of the Galaxy.
249
what we think this is now. His estimate of the total amount of matter that
must be present in the solar neighborhood also is close to the best current
determinations.
But what about in the ‘horizontal’ direction in the plane of the system?
Again Kapteyn calculated the gravitational forces; he concluded that in order
to have equilibrium and steady state there would have to be a centrifugal force,
which would have to correspond to a rotation of the whole of the stars with
a velocity of about 18–20 km/s. Now his Star Streams have a relative velocity
of 39 km/s and so he could match everything if the Streams represented a
rotation around the center of the system, one in one direction, the other one
opposite to it. That meant then that the Sun had to partake in this rotation
as part of one of the Streams and that it therefore could not be exactly in the
center of the System. The modeling of the star counts had assumed symmetry
as a first approximation so this constituted a refinement on that. After some
considerations he came to the conclusion that the Sun is about 650 pc from
the center; if it were less the centrifugal force would not be sufficient and if
larger there would be a larger asymmetry in the star counts than observed.
He also followed Ejnar Hertzsprung, who from studies of Cepheid variable
stars came to the conclusion that the Sun is 38 pc from the symmetry plane
of the Milky Way. These are part of the population of stars in the disk and
their mean Galactic latitude shows a deviation from a straight line. From such
studies of the shape of the Milky Way itself the best current value is 13 pc.
Kapteyn indicated a position of the Sun in Fig. 11.10 with a small circle. This
is indicative (as he himself stressed), but it is somewhat misleading; it is about
a factor three too far from the center.
The fundamental theory of dynamics was developed elsewhere, especially
in the U.K., by James Hopwood Jeans (1877–1946) and Arthur Eddington. It
was Jeans who christened the model of Fig. 11.10 the ‘Kapteyn Universe’ when
he studied its dynamics in more detail than Kapteyn’s schematic treatment.
Kapteyn was the first to present a consistent, dynamical model of our Stellar
System, based on observations, in which the distribution of matter and the
internal motions were precisely tuned to provide dynamical stability. It opened
a whole new field of research and that is a major accomplishment.
Of course, it soon became clear that there is absorption of starlight and that
the Star Streams do not represent a rotation around a center, but that does not
detract from the originality of this brilliant application of a new approach to
study the structure of the Stellar System and the dynamics of the Galaxy.