André Deprit developed perturbation theories based on Lie series that offered
substantial advantages, such as the transformation of state variables into an explicit
form (Deprit 1969). Deprit’s theories were later proved to be equivalent to the
perturbation theories of Hori (Campbell and Jefferies 1970).
Kinoshita Hiroshi and Hori considered the stationary motion of satellites around
the Earth in the case of elliptical and hyperbolic orbits. They showed that small
oscillations of libration appear near the osculating perigee angle of the stationary
motion in both orbits in the case of second-order approximations (Kinoshita and
Hori 1972). In addition, Kinoshita extended Hori’s perturbation method to third- and
fourth-order solutions and found third-order periodic perturbations with fourth-order
secular perturbations.
A comparison with the results of numerical integration demonstrated that the
solution predicts the position of a close-Earth satellite with a small eccentricity with
an accuracy greater than 1 cm over 1 month (Kinoshita 1978).
7.7 The Galaxy
7.7.1 Stellar System of the Galaxy
In 1956, Maarten Schmidt of Leiden Observatory constructed a model of the
distribution of mass in a flat galactic system based on an equilibrium hypothesis
between the centrifugal force of a rotating stellar system and its gravity. This model
had been widely accepted. It depends upon the rotation curve of the Galaxy. The
observations of rotation curve beyond the solar distance from the center were carried
out by Vera C. Rubin (1965) and Maarten Schmidt (1965), and it became apparent
that the rotation curve extended with a slow peak at around 9 Kpc from the center.
From the analysis of the rotation curves of the Galaxy and other galaxies, Jeremiah
Ostriker and James Peebles (1973) proved the existence of large-mass dark halos
around the spiral nebulae that control the global structure of galaxies including
our own.
In 1975, Miyamoto Masanori and Nagai Ryuzaburo of the TAO constructed a
new three-dimensional model for the distribution of mass in the Galax, by taking into
account the new galactic rotation curve and the role of the dark halo in the Galaxy
(Miyamoto and Nagai 1975). This model, shown in Fig. 7.29, has been accepted
widely since then.
The inner region of the Galaxy was also observed by IR observations in the 1970s
by Hayakawa Sachio, Okuda Haruyuki, and others of Nagoya University.
Hayakawa’s group carried out balloon observations and obtained a contour map of
the Galaxy between the galactic longitude 290
and 79
at 2.4 μm, as shown in
Fig. 7.30 (Hayakawa et al. 1981). They found that the surface intensity in this
wavelength was much greater than that expected from the contributions from spiral
arms and clusters of young stars.
212
7 Postwar Development of Astrophysics, 1946–2000 (Part II: Astrophysics)
substantial advantages, such as the transformation of state variables into an explicit
form (Deprit 1969). Deprit’s theories were later proved to be equivalent to the
perturbation theories of Hori (Campbell and Jefferies 1970).
Kinoshita Hiroshi and Hori considered the stationary motion of satellites around
the Earth in the case of elliptical and hyperbolic orbits. They showed that small
oscillations of libration appear near the osculating perigee angle of the stationary
motion in both orbits in the case of second-order approximations (Kinoshita and
Hori 1972). In addition, Kinoshita extended Hori’s perturbation method to third- and
fourth-order solutions and found third-order periodic perturbations with fourth-order
secular perturbations.
A comparison with the results of numerical integration demonstrated that the
solution predicts the position of a close-Earth satellite with a small eccentricity with
an accuracy greater than 1 cm over 1 month (Kinoshita 1978).
7.7 The Galaxy
7.7.1 Stellar System of the Galaxy
In 1956, Maarten Schmidt of Leiden Observatory constructed a model of the
distribution of mass in a flat galactic system based on an equilibrium hypothesis
between the centrifugal force of a rotating stellar system and its gravity. This model
had been widely accepted. It depends upon the rotation curve of the Galaxy. The
observations of rotation curve beyond the solar distance from the center were carried
out by Vera C. Rubin (1965) and Maarten Schmidt (1965), and it became apparent
that the rotation curve extended with a slow peak at around 9 Kpc from the center.
From the analysis of the rotation curves of the Galaxy and other galaxies, Jeremiah
Ostriker and James Peebles (1973) proved the existence of large-mass dark halos
around the spiral nebulae that control the global structure of galaxies including
our own.
In 1975, Miyamoto Masanori and Nagai Ryuzaburo of the TAO constructed a
new three-dimensional model for the distribution of mass in the Galax, by taking into
account the new galactic rotation curve and the role of the dark halo in the Galaxy
(Miyamoto and Nagai 1975). This model, shown in Fig. 7.29, has been accepted
widely since then.
The inner region of the Galaxy was also observed by IR observations in the 1970s
by Hayakawa Sachio, Okuda Haruyuki, and others of Nagoya University.
Hayakawa’s group carried out balloon observations and obtained a contour map of
the Galaxy between the galactic longitude 290
and 79
at 2.4 μm, as shown in
Fig. 7.30 (Hayakawa et al. 1981). They found that the surface intensity in this
wavelength was much greater than that expected from the contributions from spiral
arms and clusters of young stars.
212
7 Postwar Development of Astrophysics, 1946–2000 (Part II: Astrophysics)