Papers by Toshio Fukushima
Symposium - International Astronomical Union, 1988
The proper reference frame comoving with a system of mass-points is defined as a general relativi... more The proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordinate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame named the Natural Coordinate System (NCS) is proposed as the basic coordinate system in the astrometry. By means of the concept of the natural coordinate system, the relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly. To illustrate the concept of NCS, we quote in the following the definition of the non-rotating NCS comoving with the Earth, i.e. the T...
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Journal of Geodesy, 2017
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Astronomy & Astrophysics, 2015
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The Astronomical Journal, 2005
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The Astronomical Journal, 2003
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Celestial Mechanics and Dynamical Astronomy, 2010
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Monthly Notices of the Royal Astronomical Society, 2016
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Symposium - International Astronomical Union, 2004
We estimated the optical depth and event rate of μas level astrometric microlensing for the stars... more We estimated the optical depth and event rate of μas level astrometric microlensing for the stars outside our galaxy caused by MACHOs. For the stars in the LMC and the SMC, the optical depth of a 1 μas detection threshold is on the order of 10–1 and the event rate of the induced proper motion of 1 μas/year is on the order of 10–3/yr with the event duration of around a hundred years. They depend on the distribution of lenses and sources. This poses a constraint on the expected probability of photometric self-lensing in LMC and SMC.
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Symposium - International Astronomical Union, 1999
The observed positions of quasars are fluctuated due to the gravitational lensing of the matters ... more The observed positions of quasars are fluctuated due to the gravitational lensing of the matters in our galaxy. The magnitude of fluctuation due to stars and MACHOs is of the order of a few micro-arc second (μas) ∼ 10 μas and its time scale is of the order of a few years ∼ hundreds years (Hosokawa et al. 1997). Such fluctuation will reflects the nature of the constituents, both visible and invisible, of our galaxy.
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Symposium - International Astronomical Union, 1995
We showed that it is feasible to measure the mass of a single star by observing the variation of ... more We showed that it is feasible to measure the mass of a single star by observing the variation of gravitational deflection caused by the orbital motion of the Earth. When the distance of a star is less than 60 pc and some appropriate sources are within 1 arcsec. in its background, not only the distance but also the mass of the star may be determined by measuring the deflection with an accuracy of 10 μ arcsec. In the case of photometric microlensing by a MACHO, the observation of astrometric gravitational deflection is also useful. By measuring the separation between the primary image and the secondary image, the ratio of mass to distance of the MACHO will be obtained. Further, the orbital motion of the Earth modifying the light curve of the source is discussed.
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Progress of Theoretical Physics Supplement, 2004
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International Astronomical Union Colloquium, 2000
We developed a numerical method to incorporate nonrigid effects into a nutation theory of the rig... more We developed a numerical method to incorporate nonrigid effects into a nutation theory of the rigid Earth. Here we assume that the nonrigid effects are based on a linear response theory and its transfer function is expressed as a rational function of frequency. The method replaces the convolution of the transfer function in the frequency domain by the corresponding integro-differential operations in the time domain numerically; namely multiplying the polynomial in the frequency domain by the numerical differentiations in the time domain and multiplying the fractions in the frequency domain by the numerical integrations with a suitable kernel in the time domain. In replacing by the integrations, the method requires the determination of the coefficients of free oscillation. This is done by a least-squares method to fit the theory incorporated with the nonrigid effects to the observational data, whose availability is also assumed. The numerical differentiation and integration are effec...
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Symposium - International Astronomical Union, 1986
The definition of the angular momentum of a finite body is given in the post-Newtonian framework.... more The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the seco...
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Symposium - International Astronomical Union, 1996
Once, we numerically integrated the precession and nutation of a spheroidal rigid Earth (Kubo and... more Once, we numerically integrated the precession and nutation of a spheroidal rigid Earth (Kubo and Fukushima 1987). As a natural extension, we tried to integrate the rotation of a triaxial rigid Earth numerically and faced a problem: a loss of precision in long-term integration. This is due to the smallness of the characteristic period of the problem: 1 day. Of course, one can integrate the rotational motion in higher precision arithmetics with a smaller stepsize. However, the quadruple precision integration is roughly 30 times more time-consuming than the double precision integration. See Table 1. Therefore, it is desirable if there is a formulation 1) reducing the overall integration error, 2) being independent on the choice of the integrator and 3) requiring no extra computations. The key points to achieve this goal will be to find a set of variables which 1) are efficiently convertible to the physical quantities required finally, say, the orientation matrix in the case of the rot...
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Symposium - International Astronomical Union, 1988
A numerical solution for the luni-solar precession and nutation of the rigid Earth is obtained an... more A numerical solution for the luni-solar precession and nutation of the rigid Earth is obtained and compared with the result from the analytical theories which are the basis of the current IAU precession and nutation formulas. We have developed a new scheme of numerical calculation by modifying the equations of motion, which enables us to avoid the numerical integration with a small step. Some errors are found in the long periodic region of nutation in the current IAU theory.
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The Astronomical Journal, 2017
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Relativity in Celestial Mechanics and Astrometry, 1986
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Proceedings of the International Astronomical Union, 2011
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The Astronomical Journal, 2003
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Papers by Toshio Fukushima