We obtain a narrower and more reliable range of the delay of Earth’s rotation, ΔT, than those obt... more We obtain a narrower and more reliable range of the delay of Earth’s rotation, ΔT, than those obtained before. At the same time, we determine the observation sites of these eclipses in the early seventh century. The eclipses are the one on AD 616 May 21 recorded in the history book Suíshū of the Suí dynasty, and the one on AD 628 April 10 recorded in the first official Japanese history book Nihon Shoki (also called as Nihongi). Our method of analysis is to express multiple observations simultaneously on the “Sôma” diagram in which the ordinate is ΔT and the abscissa is the correction to the coefficient of the lunar tidal term. In order to increase the reliability of the present result, we analyze several solar eclipses and an occultation of Mars during the period from the fifth century to the end of the seventh century. These analyses show the short-term variations of ΔT off the smoothed spline curves of Stephenson, Morrison, and Hohenkerk (2016, Proc. R. Soc. A, 472, 20160404).
Predictability, Stability, and Chaos in N-Body Dynamical Systems, 1991
ABSTRACT The authors investigate the conjecture: In the restricted three-body problem, there exis... more ABSTRACT The authors investigate the conjecture: In the restricted three-body problem, there exist collision orbits with the planet in any neighborhood of the outermost KAM around the retrograde satellite orbit for certain values of the Jacobi constant C and the mass parameter mu. This conjecture is checked here by numerical integration for C = 2.98 and mu = 0.001.
Eclipse records began in the 7 th century in Japan. Eclipses in the 7 th century were recorded in... more Eclipse records began in the 7 th century in Japan. Eclipses in the 7 th century were recorded in the Nihongi and their reliability changed according to the volumes. Eclipses in the 8 th century were recorded in the Shoku-Nihongi but most of them were written according to the predictions at the time. Eclipses between the 9 th and 11 th centuries were recorded in various literatures and diaries but it is not easy to decide whether they were based on actual observations or not.
Records of ancient solar eclipses have been used for the investigation of the variation of the Ea... more Records of ancient solar eclipses have been used for the investigation of the variation of the Earth's rotation speed. In addition they can be used to study whether or not the Moon's tidal acceleration has been constant since ancient times. Lunar occultations of planets and bright stars were often observed and recorded in ancient China, but visible areas of lunar occultations are usually wide, and therefore they are rarely usable for our studies. However, we show here that some such events play an important role for checking ancient records of other events and determining the Earth's rotation. Lunar occultations of Venus on 5 August 503 and of Saturn on 22 August 513 recorded in the Chinese history book Weishu are such examples. Combining these with annular and total solar eclipses recorded in China in 516 and 522 we obtain the limits to the Earth rotation parameter value of 3568s < ΔT < 5090s.
We study the dynamics of spherical systems which consist of extended shells of relatively low-mas... more We study the dynamics of spherical systems which consist of extended shells of relatively low-mass particles around and inside the orbit of two heavy centers of gravity (a binary with point-mass components) by computer simulations.
We obtain a narrower and more reliable range of the delay of Earth’s rotation, ΔT, than those obt... more We obtain a narrower and more reliable range of the delay of Earth’s rotation, ΔT, than those obtained before. At the same time, we determine the observation sites of these eclipses in the early seventh century. The eclipses are the one on AD 616 May 21 recorded in the history book Suíshū of the Suí dynasty, and the one on AD 628 April 10 recorded in the first official Japanese history book Nihon Shoki (also called as Nihongi). Our method of analysis is to express multiple observations simultaneously on the “Sôma” diagram in which the ordinate is ΔT and the abscissa is the correction to the coefficient of the lunar tidal term. In order to increase the reliability of the present result, we analyze several solar eclipses and an occultation of Mars during the period from the fifth century to the end of the seventh century. These analyses show the short-term variations of ΔT off the smoothed spline curves of Stephenson, Morrison, and Hohenkerk (2016, Proc. R. Soc. A, 472, 20160404).
Predictability, Stability, and Chaos in N-Body Dynamical Systems, 1991
ABSTRACT The authors investigate the conjecture: In the restricted three-body problem, there exis... more ABSTRACT The authors investigate the conjecture: In the restricted three-body problem, there exist collision orbits with the planet in any neighborhood of the outermost KAM around the retrograde satellite orbit for certain values of the Jacobi constant C and the mass parameter mu. This conjecture is checked here by numerical integration for C = 2.98 and mu = 0.001.
Eclipse records began in the 7 th century in Japan. Eclipses in the 7 th century were recorded in... more Eclipse records began in the 7 th century in Japan. Eclipses in the 7 th century were recorded in the Nihongi and their reliability changed according to the volumes. Eclipses in the 8 th century were recorded in the Shoku-Nihongi but most of them were written according to the predictions at the time. Eclipses between the 9 th and 11 th centuries were recorded in various literatures and diaries but it is not easy to decide whether they were based on actual observations or not.
Records of ancient solar eclipses have been used for the investigation of the variation of the Ea... more Records of ancient solar eclipses have been used for the investigation of the variation of the Earth's rotation speed. In addition they can be used to study whether or not the Moon's tidal acceleration has been constant since ancient times. Lunar occultations of planets and bright stars were often observed and recorded in ancient China, but visible areas of lunar occultations are usually wide, and therefore they are rarely usable for our studies. However, we show here that some such events play an important role for checking ancient records of other events and determining the Earth's rotation. Lunar occultations of Venus on 5 August 503 and of Saturn on 22 August 513 recorded in the Chinese history book Weishu are such examples. Combining these with annular and total solar eclipses recorded in China in 516 and 522 we obtain the limits to the Earth rotation parameter value of 3568s < ΔT < 5090s.
We study the dynamics of spherical systems which consist of extended shells of relatively low-mas... more We study the dynamics of spherical systems which consist of extended shells of relatively low-mass particles around and inside the orbit of two heavy centers of gravity (a binary with point-mass components) by computer simulations.
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Papers by Kiyotaka Tanikawa