Kimura’s contributions on Earth polar motion studies

Abstract

Kimura’s discovery of z-term in the polar motion (Astron. J. 22, 107 (1902) and Astron. Nachr. 158, 233 (1902)) was recognized as an epoch-making scientific achievement for modern Japan, opening its doors to the world in 1868. Although Kimura served as the chair of the International Latitude Service during 1922–1934 and made efforts to interpret the z-term, it was unsuccessful. The physical interpretation of the z-term was given decades later by Wako (PASJ, 22, 525 (1970)). This article highlights Kimura’s additional contributions that led to the interpretation by Wako.

1. Observing the polar motion

It remains unconfirmed who was the first to point out that the rotation of the starry night sky is due to the Earth’s rotation. Apparently, Tycho Brahe, Johannes Kepler, and Galileo Galilei, the pioneers of the modern observation of stellar positions, were aware of this notion. The Earth’s rotation was first proven by Jean Foucault’s pendulum experiment at the Paris Observatory in 1851. In the meantime, Leonhard Euler noted in 1765 that the spinning axis of the rigid body Earth could be moving around its shape axis with a period of 305 days. Such a wobbling polar motion (free nutation) of the Earth causes minor changes in the latitude and longitude of the observing sites. Kuestner’s observation of polar motion in 1884–1885 (Kuestner 1888)¹⁾ was the turning point toward systematic international latitude observation programs. The International Association of Geodesy (IAG), established in 1886, promoted coordinated observations in 1891 at Berlin and Hawaii, located at around 180° difference in longitude, and confirmed the presence of periodic variation in latitude. Chandler (1891)²⁾ discovered a 427-day period variation of the latitude. Newcomb (1891)³⁾ interpreted this period considering the elasticity of the Earth.

In 1894, the IAG requested Japan to participate in the proposed International Latitude Service (ILS) campaign. Hisashi Kimura (1870–1943) made his first measurement of latitude at the Tokyo Astronomical Observatory in Tokyo in 1895. Japanese government endorsed the construction of a latitude observatory in Mizusawa to formally join the ILS campaign and appointed young Kimura as the director of the International Latitude Observatory of Mizusawa (ILOM) in 1899. The ILS started with six stations, equipped with a zenith telescope to measure the latitude variations, deployed along a common latitude +39°08′ around the Earth, including Mizusawa (Iwate, Japan), Charjui (Turkmenistan), Carloforte (Italy), Gaithersburg (Maryland, U.S.A.), Ukiah (California, U.S.A.), and Cincinnati (Ohio, U.S.A.). Kimura started measurements of selected pairs of stars passing the zenith during the nights as well as the measurement of temperature and air pressure every four hours all the year with his 3 crew members.

2. Kimura’s discovery of z-term

In September 1901, a year and half after the beginning of the ILS campaign, the central bureau of ILS announced the result of measurements at six stations. The chair, Carl T. Albrecht, reported that the residual error of Mizusawa station was significantly larger than those from other stations. He assigned a half weight for Mizusawa data in compiling the results and requested Japan for investigation to clarify the cause of a larger error. Surprised with this disgraceful communication, Kimura made close examinations of the instrument and procedure together with Aikitu Tanakadate (1856–1952), another member of the Imperial Academy, and regained his confidence on their measurement. By examining the data, Kimura found an annual variation component in the residual error and confirmed the existence of a similar component in the reported data from other stations. He found that, instead of using the standard equation [1] to fit the observed data,

  

\begin{equation} \Delta \phi = x\cos\lambda + y\sin\lambda, \end{equation} [1]

where λ is the longitude of the station, using the following Eq. [2] adding a term that is not dependent on the longitude of the stations is useful for characterizing the annual variation term.

  

\begin{equation} \Delta \phi = x\cos\lambda + y\sin\lambda + z. \end{equation} [2]

Kimura submitted his findings for publication in journals in the U.S.A. (Kimura 1902)⁴⁾ and in Europe (Kimura 1902)⁵⁾ before reporting to the ILS. Albrecht immediately recognized the importance of Kimura’s findings and named the new term as z-term. By introducing the z-term, the residual error became the smallest for Mizusawa station.

The academic community and the government of Japan at that time recognized this as a triumphant achievement restoring the honor of Japan in the international community. This high recognition made him the first winner of the Imperial Award of the Japan Academy in 1911. In 1936, the Royal Astronomical Society of U.K. awarded the Gold Medal to Kimura and he became the first recipient of the Order of Culture established in Japan in 1937. Kimura was appointed as the chair of the International Latitude Service campaign during 1922–1934. He published the results of observations during this period in two official reports (Kimura 1935, 1940).^6),7)

3. Various efforts for understanding the z-term

Kimura made efforts to interpret the z-term with various attempts. The Mizusawa station started balloon-born wind measurements of the upper atmosphere and measurement of micro-variation of the air pressure in the decade 1920s. Kimura studied the wind and temperature effects on measurements of the Earth motion taking the atmospheric refraction effects (Miyano et al. 1934).⁸⁾ He also carefully calibrated the screw turn irregularity that might have influenced the measurement (Kimura 1930).⁹⁾ He made analyses on the results of available observing stations in the northern hemisphere (Kimura 1935).¹⁰⁾ In the concluding notes of Kimura (1935),⁶⁾ he mentioned “There are many investigators of z who are assigning its origin solely to the regular or irregular anomalies of refraction, but I think there is another equally important cause; viz., the change of the direction of the plumb line owing to the deformation of the earth partly by the attraction of the sun, and partly by the bulge or contraction of the local earth crust due to the heating effect of the sun combined with the air pressure, or by the upheaval or sinking of the local continental mass”. Unfortunately, none of these studies produced a convincing interpretation of the z-term.

An important contribution made by Kimura (1938),¹¹⁾ however, was to represent the z-term as a superposition of oscillatory terms

  

\begin{equation} a\sin(m \odot + n\alpha + A), \end{equation} [3]

where $ \odot $ is the mean longitude of the Sun, α is the mean right ascension of the stars observed, A is an offset, and m, n are integers. This empirical formulae adopted in Kimura (1938)¹¹⁾ became the standard representation of the observed results and the basis for the physical interpretation of z-term (Wako 1970).¹²⁾

Another important contributions Kimura made around the period he chaired the ILS are a proposal of a new observing protocol and establishing observing stations in the southern hemisphere. The ILS observation protocol was to divide a year into 12 periods, assigning 8 sets of stars to measure, and observe two consecutive periods. This required 4 hours of observation every night. Kimura (1938)¹¹⁾ proposed a new observing program to enhance the data quality. By dividing each year into 16 periods, he proposed to observe the same set of stars consecutively for three periods covering more than two months. This required nightly observation of 4.5 hours instead of 4 hours. It is likely that he even thought about 3 period observation for 12 periods requiring 6 hours. Kimura’s proposal, however, appears as a compromise to improve data quality but not to increase the observational burden too much for every station joining ILS. It took some time to establish a consensus on the needs of this expanded program. It was eventually adopted in 1955, ten years after Kimura passed away, to observe three periods among the 12 periods, requiring 6 hours observation, every night. The accumulation of data following this new protocol for 1955–1966 became the key, for Wako (1970)¹²⁾ to interpret the physical meaning of the z-term.

By the time Kimura assumed the directorship of the ILS in 1922, only three of the six initial stations were in operation. As the annual z-term appeared as if the center of gravity of the Earth moved in the north-south direction, he argued for the necessity of deploying stations in the southern hemisphere and along the equator. Three stations in the southern hemisphere, La Plata (Argentine), Adelaide (Australia), and Batavia (Indonesia), joined the ILS campaign. Many correspondences between Kimura and the director of Batavia Station during 1927–1939 discussing the development of the observing procedures are kept in the ILOM archive. Kimura apparently helped solve some difficulties the Batavia station faced. Kimura also reported the results of observations in Adelaide and in La Plata (Kimura 1936).^13),14)

Although, there were no new developments in the interpretation of the z-term during the period Kimura served as the ILS director, international deployment of stations with stable observing data eventually led Wako to find the relevant interpretation (Wako 1970).¹²⁾

4. Wako’s interpretation of the z-term

Wako (1970)¹²⁾ analyzed the accumulated data obtained in accordance with the revised observing protocol proposed by Kimura and showed clearly that the major component of the z-term is

  

\begin{equation} 0".0203\sin(2\odot - \alpha + 4^{\circ}.3) \end{equation} [4]

and that it can be interpreted by the nutation of the Earth having a liquid core and a mantle (Jeffreys and Vicente 1957; Molodenskij 1961; Pedersen 1967; Kakuta 1970).^15)–18)

Since the spin axis of the Earth is not perpendicular to the orbital planes of the Earth and Moon and the Earth is not a perfect sphere, the Sun and the Moon exert tidal torque to the Earth driving long-term precession and forced nutation to the spin axis of the Earth. The nutation produces a uniform shift in stellar positions independent of the observing stations. The polar motion was considered to be well expressed by the equation of nutation for an elastic model of the Earth without internal structure. However, the response to the tidal torque of the Sun and Moon exerted different behavior to the core and mantle of the Earth and that led to the manifestation of z-term (Wako 1970).¹²⁾ The z-term implied as if all stations move north/south in winter/summer by about 1 m, creating an angular variation of 0.03 arcsec.

Wako’s interpretation of the z-term is very well illustrated in a recent review article by Heki (2020).¹⁹⁾ Figure 1 illustrates the torque exerted by misalignment of the spin axes of the core and the mantle that generates free core nutation, which significantly affects behavior of the forced nutation. Figure 2 shows the geometry of the semiannual nutation of the Earth that causes deviation corresponding to the z-term.

Fig. 1.

Core-Mantle interaction to interpret z-term. Reproduced from Fig. 4 of Heki (2020).¹⁹⁾

Fig. 2.

Pictorial presentation of z-term. Reproduced from Fig. 5 of Heki (2020).¹⁹⁾

Kinoshita et al. (1979)²⁰⁾ has shown that the z-term disappears when the nutation is evaluated using the Earth model with fluid core (Molodenskij 1961; Sasao et al. 1977).^16),21) The z-term was eventually confirmed to arise due to the movement of the fluid core of the Earth.

5. Summary and discussion

Despite the great recognition of Kimura’s achievements in the western geodesy communities, not just in Japan, we find very few citations of his works in the academic literature. Citation counts for Kimura (1902)⁴⁾ and Kimura (1902)⁵⁾ remain 8 and 3, respectively. Even some of his papers, including those in the Proceedings of the Imperial Academy (PIA), were not found in the Astronomical Data Service (ADS) at the time of 2019, which was partly due to the difficulty of identifying relevant astronomical papers published in PIA that includes all the fields of sciences. By sharing a relevant list of papers, all the papers published in PIA by Kimura and others are now accessible in the ADS.

Apart from such a technical difficulty, there appear several additional reasons why the citations to Kimura’s papers were not abundant. Although the finding of z-term, was an unexpected discovery for those people involved in the international geodesy campaign at that time, the interest apparently remained only in a small community. The general rule for referring to papers was not well established in the early decades of the 20th century and that made slipping of the citation of Kimura’s paper. For instance, although Biske (1907)²²⁾ did cite Kimura’s work in the main text, that paper did not have a list of references and hence untraceable in the ADS citation. Since the ILS was an official international campaign, the results of the measurements were included in the ILS report. The researchers could refer to ILS reports but not necessarily referring to Kimura’s papers. The physical interpretation of the z-term required several decades and it did not remain a topic of interest. Wako (1970)¹²⁾ was an epoch-making discovery to interpret the z-term, and later researchers did not feel the necessity of referring back to Kimura’s original papers. When VLBI (Very Long Baseline Interferometry) observations (Herring et al. 1991)²³⁾ superceded optical observations of stars to evaluate the Earth polar motion and nutation, ILS matter faded away apart from historical interest.

Nevertheless, the author reaffirms that Kimura (1938, 1942)^11),24) were underground drivers to advance the physical interpretation of the z-term by Wako (1970).¹²⁾

Acknowledgements

The context of this article is based on an official document by Ooe et al. (1999)²⁵⁾ compiled to record in Japanese the history of ILOM, an excellent review article of Japan’s geodesy history by Heki (2020),¹⁹⁾ and a paper by Sasao (1993).²⁶⁾ The author acknowledges valuable comments and guidance to relevant materials by Tetsuo Sasao, Seiji Manabe, Kosuke Heki, and Kazuya Hachisuka. This research was supported by JSPS KAKENHI Grant Number 22K03679.

Notes

Contributed by Masanori IYE, M.J.A.; Edited by Katsuhiko SATO, M.J.A.

Correspondence should be addressed to: M. Iye, National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan (e-mail: [e-mail]).

Footnotes

This paper commemorates the 100th anniversary of this journal and introduces the following papers previously published in this journal. Kimura, H. (1938) New observing programme for the International Latitude Service. Proc. Imp. Acad. 14 (3), 102–105 (https://doi.org/10.2183/pjab1912.14.102); Kimura, H. (1942) On the analysis of Z for the three stations, Mizusawa, Carloforte and Ukiah during the period 1900.0-1922.7. Proc. Imp. Acad. 18 (7), 360–366 (https://doi.org/10.2183/pjab1912.18.360).

References

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Appendices

[From Proc. Imp. Acad., Vol. 14 No. 3, pp. 102–105 (1938)]

[From Proc. Imp. Acad., Vol. 18 No. 7, pp. 360–366 (1942)]

Profile

Masanori Iye, born in Sapporo in 1949, graduated from the University of Tokyo in 1972 and completed his Ph.D. in 1977 on a theoretical study concerning the origin of the spiral structure of galaxies. He was appointed as an assistant professor in the Department of Astronomy at the University of Tokyo in 1978, an associate professor at the Tokyo Astronomical Observatory in 1986, and a professor at the National Astronomical Observatory (NAOJ) in 1993. Moreover, Iye was a visiting researcher at the Institute of Astronomy, Cambridge University in 1982–83 and at the European Southern Observatory in 1983–84. After returning to NAOJ, he developed the first cryogenic CCD camera in 1986 and chaired a working group of the Subaru Telescope project employing the active optics scheme. He devoted himself to constructing the telescope and scientific instruments in Maunakea, Hawaii until 2002. Later, he led the laser-guide-star adaptive optics system development and enhanced the telescope vision by 10× in 2011. He found the most distant galaxy, 13 billion light years away, and elucidated the epoch of cosmic reionization in 2006. Since 2005, he has promoted the Thirty Meter Telescope (TMT) project and served as the first Vice-Chair of the TMT International Observatory Governing Board. He has received the Nishina Memorial Prize, the Toray Science and Technology Prize, the Medal with Purple Ribbon, the Order of the Sacred Treasure, the Gold and Silver Star, the Japan Academy Prize, and other honors. Furthermore, Iye is a Member of the Japan Academy, a Member of the International Astronomical Union, and a Fellow of the International Society for Optics and Photonics.