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Lorenzo Iorio - One of the best experts on this subject based on the ideXlab platform.
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an empirical explanation of the anomalous increases in the Astronomical Unit and the lunar eccentricity
The Astronomical Journal, 2011Co-Authors: Lorenzo IorioAbstract:The subject of this paper is the empirically determined anomalous secular increases of the Astronomical Unit, of the order of some cm yr–1, and of the eccentricity of the lunar orbit, of the order of 10–12 yr–1. The aim is to find an empirical explanation of both anomalies as far as their orders of magnitude are concerned. The methods employed are working out perturbatively with the Gauss equations the secular effects on the semi-major axis a and the eccentricity e of a test particle orbiting a central body acted upon by a small anomalous radial acceleration A proportional to the radial velocity vr of the particle-body relative motion. The results show that non-vanishing secular variations and ė occur. If the magnitude of the coefficient of proportionality of the extra-acceleration is of the same order of magnitude as the Hubble parameter H 0 = 7.47 × 10–11 yr–1 at the present epoch, they are able to explain both astrometric anomalies without contradicting other existing observational determinations for the Moon and the other planets of the solar system. Finally, it is concluded that the extra-acceleration might be of cosmological origin, provided that the relative radial particle-body motion is accounted for in addition to that due to the cosmological expansion only. Further data analyses should confirm or disprove the existence of both astrometric anomalies as genuine physical phenomena.
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an empirical explanation of the anomalous increases in the Astronomical Unit and the lunar eccentricity
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: Lorenzo IorioAbstract:Both the recently reported anomalous secular increase of the Astronomical Unit, of the order of a few cm yr^-1, and of the eccentricity of the lunar orbit e_ = (9+/-3) 10^-12 yr^-1 can be phenomenologically explained by postulating that the acceleration of a test particle orbiting a central body, in addition to usual Newtonian component, contains a small additional radial term proportional to the radial projection vr of the velocity of the particle's orbital motion. Indeed, it induces secular variations of both the semi-major axis a and the eccentricity e of the test particle's orbit. In the case of the Earth and the Moon, they numerically agree rather well with the measured anomalies if one takes the numerical value of the coefficient of proportionality of the extra-acceleration approximately equal to that of the Hubble parameter H0 = 7.3 10^-11 yr^-1.
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constraints on the range λ of yukawa like modifications to the newtonian inverse square law of gravitation from solar system planetary motions
Journal of High Energy Physics, 2007Co-Authors: Lorenzo IorioAbstract:In this paper we use the latest corrections to the Newton-Einstein secular rates of perihelia of some inner planets of the Solar System, phenomenologically estimated with the EPM2004 ephemerides by the Russian astronomer E.V. Pitjeva, to put severe constraints on the range parameter λ characterizing the Yukawa-like modifications of the Newtonian inverse-square law of gravitation. It turns out that the range cannot exceed about one tenth of an Astronomical Unit. We assumed neither equivalence principle violating effects nor spatial variations of α and λ. This finding may have important consequences on all the modified theories of gravity involving Yukawa-type terms with range parameters much larger than the Solar System size. However, caution is advised since we currently have at our disposal only the extra-rates of periehlia estimated by Pitjeva: if and when other groups will estimate their own corrections to the secular motion of perihelia, more robust and firm tests may be conducted.
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constraints on the range lambda of yukawa like modifications to the newtonian inverse square law of gravitation from solar system planetary motions
arXiv: General Relativity and Quantum Cosmology, 2007Co-Authors: Lorenzo IorioAbstract:In this paper we use the latest corrections to the Newton-Einstein secular perihelion rates of some planets of the Solar System, phenomenologically estimated with the EPM2004 ephemerides by the Russian astronomer E.V. Pitjeva, to put severe constraints on the range parameter lambda characterizing the Yukawa-like modifications of the Newtonian inverse-square law of gravitation. It turns out that the range cannot exceed about one tenth of an Astronomical Unit. We assumed neither equivalence principle violating effects nor spatial variations of $\alpha$ and $\lambda$. This finding may have important consequences on all the modified theories of gravity involving Yukawa-type terms with range parameters much larger than the Solar System size. However, caution is advised since we, currently have at our disposal only the periehlion extra-rates estimated by Pitjeva: if and when other groups will estimate their own corrections to the secular motion of perihelia, more robust and firm tests may be conducted.
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secular increase of the Astronomical Unit and perihelion precessions as tests of the dvali gabadadze porrati multi dimensional braneworld scenario
Journal of Cosmology and Astroparticle Physics, 2005Co-Authors: Lorenzo IorioAbstract:An unexpected secular increase of the Astronomical Unit, the length scale of the Solar System, has recently been reported by three different research groups (Krasinsky and Brumberg, Pitjeva, Standish). The latest JPL measurements amount to 7 ± 2 m cy−1. At present, there are no explanations able to accommodate such an observed phenomenon, either in the realm of classical physics or in the usual four-dimensional framework of the Einsteinian general relativity. The Dvali–Gabadadze–Porrati braneworld scenario, which is a multi-dimensional model of gravity aimed at providing an explanation of the observed cosmic acceleration without dark energy, predicts, among other things, a perihelion secular shift, due to Lue and Starkman, of 5 × 10−4 arcsec cy−1 for all the planets of the Solar System. It yields a variation of about 6 m cy−1 for the Earth–Sun distance which is compatible with the observed rate of change for the Astronomical Unit. The recently measured corrections to the secular motions of the perihelia of the inner planets of the Solar System are in agreement with the predicted value of the Lue–Starkman effect for Mercury, Mars and, at a slightly worse level, the Earth.
Hideyoshi Arakida - One of the best experts on this subject based on the ideXlab platform.
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Effect of Inhomogeneity of the Universe on a Gravitationally Bound Local System: A No-Go Result for Explaining the Secular Increase in the Astronomical Unit
Journal of Astrophysics and Astronomy, 2012Co-Authors: Hideyoshi ArakidaAbstract:We will investigate the influence of the inhomogeneity of the Universe, especially that of the Lemaître–Tolman–Bondi (LTB) model, on a gravitationally bound local system such as the solar system. We concentrate on the dynamical perturbation to the planetary motion and derive the leading order effect generated from the LTB model. It will be shown that there appear not only a well-known cosmological effect arisen from the homogeneous and isotropic model, such as the Robertson–Walker (RW) model, but also the additional terms due to the radial inhomogeneity of the LTB model. We will also apply the obtained results to the problem of secular increase in the Astronomical Unit, reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of the Universe cannot have a significant effect for explaining the observed dAU/d t = 15 ±4 [m/century].
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Application of time transfer function to McVittie spacetime: gravitational time delay and secular increase in Astronomical Unit
General Relativity and Gravitation, 2011Co-Authors: Hideyoshi ArakidaAbstract:We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann–Lemaître–Robertson–Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte et al. (Class Quantum Gravity 21:4463, 2004 ) and Teyssandier and Le Poncin-Lafitte (Class Quantum Gravity 25:145020, 2008 ), which is originally related to Synge’s world function Ω( x _ A , x _ B ) and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the Astronomical Unit, reported by Krasinsky and Brumberg (Celest Mech Dyn Astron 90:267, 2004 ), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of d AU/ dt , i.e., 15 ± 4 (m/century). Therefore, it is not possible to explain the secular increase in the Astronomical Unit in terms of cosmological expansion.
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application of time transfer function to mcvittie spacetime gravitational time delay and secular increase in Astronomical Unit
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: Hideyoshi ArakidaAbstract:We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the Astronomical Unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the Astronomical Unit in terms of cosmological expansion.
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secular increase of the Astronomical Unit a possible explanation in terms of the total angular momentum conservation law
Publications of the Astronomical Society of Japan, 2009Co-Authors: Takaho Miura, Hideyoshi Arakida, Masumi Kasai, S KuramataAbstract:Aims. We show a possible explanation for the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). Methods. The mechanism proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Results. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, d dt AU = 15±4 (m/cy), the suggested change in the period of rotation of the Sun is about 3 ms/cy in the case that the orbits of the eight planets have the same “expansion rate.” This value is suffi ciently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun’s moment of inertia is also investigated. It is pointed out that the ch ange in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital “expansion” is happening only in the inner planets system.
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Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law
Publications of the Astronomical Society of Japan, 2009Co-Authors: Takaho Miura, Hideyoshi Arakida, Masumi Kasai, S KuramataAbstract:We give an idea and the order-of-magnitude estimations to explain the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). The idea proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, $\frac{d}{dt}{AU} = 15 \pm 4 {(m/cy)}$, the suggested change in the period of rotation of the Sun is about $21 {ms/cy}$ in the case that the orbits of the eight planets have the same "expansion rate." This value is sufficiently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun's moment of inertia is also investigated. It is pointed out that the change in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital "expansion" is happening only in the inner planets system. Although the existence of some tidal interactions is assumed between the Sun and planets, concrete mechanisms of the angular momentum transfer are not discussed in this paper, which remain to be done as future investigations.
S Kuramata - One of the best experts on this subject based on the ideXlab platform.
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secular increase of the Astronomical Unit a possible explanation in terms of the total angular momentum conservation law
Publications of the Astronomical Society of Japan, 2009Co-Authors: Takaho Miura, Hideyoshi Arakida, Masumi Kasai, S KuramataAbstract:Aims. We show a possible explanation for the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). Methods. The mechanism proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Results. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, d dt AU = 15±4 (m/cy), the suggested change in the period of rotation of the Sun is about 3 ms/cy in the case that the orbits of the eight planets have the same “expansion rate.” This value is suffi ciently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun’s moment of inertia is also investigated. It is pointed out that the ch ange in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital “expansion” is happening only in the inner planets system.
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Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law
Publications of the Astronomical Society of Japan, 2009Co-Authors: Takaho Miura, Hideyoshi Arakida, Masumi Kasai, S KuramataAbstract:We give an idea and the order-of-magnitude estimations to explain the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). The idea proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, $\frac{d}{dt}{AU} = 15 \pm 4 {(m/cy)}$, the suggested change in the period of rotation of the Sun is about $21 {ms/cy}$ in the case that the orbits of the eight planets have the same "expansion rate." This value is sufficiently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun's moment of inertia is also investigated. It is pointed out that the change in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital "expansion" is happening only in the inner planets system. Although the existence of some tidal interactions is assumed between the Sun and planets, concrete mechanisms of the angular momentum transfer are not discussed in this paper, which remain to be done as future investigations.
M. Benisty - One of the best experts on this subject based on the ideXlab platform.
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A measure of the size of the magnetospheric accretion region in TW Hydrae
Nature, 2020Co-Authors: R. Garcia Lopez, T. P. Ray, A. Natta, A. Caratti O Garatti, R. Fedriani, M. Koutoulaki, L. Klarmann, K. Perraut, J. Sanchez-bermudez, M. BenistyAbstract:Stars form by accreting material from their surrounding disks. There is a consensus that matter flowing through the disk is channelled onto the stellar surface by the stellar magnetic field. This is thought to be strong enough to truncate the disk close to the corotation radius, at which the disk rotates at the same rate as the star. Spectro-interferometric studies in young stellar objects show that hydrogen emission (a well known tracer of accretion activity) mostly comes from a region a few milliarcseconds across, usually located within the dust sublimation radius1-3. The origin of the hydrogen emission could be the stellar magnetosphere, a rotating wind or a disk. In the case of intermediate-mass Herbig AeBe stars, the fact that Brackett γ (Brγ) emission is spatially resolved rules out the possibility that most of the emission comes from the magnetosphere4-6 because the weak magnetic fields (some tenths of a gauss) detected in these sources7,8 result in very compact magnetospheres. In the case of T Tauri sources, their larger magnetospheres should make them easier to resolve. The small angular size of the magnetosphere (a few tenths of a milliarcsecond), however, along with the presence of winds9,10 make the interpretation of the observations challenging. Here we report optical long-baseline interferometric observations that spatially resolve the inner disk of the T Tauri star TW Hydrae. We find that the near-infrared hydrogen emission comes from a region approximately 3.5 stellar radii across. This region is within the continuum dusty disk emitting region (7 stellar radii across) and also within the corotation radius, which is twice as big. This indicates that the hydrogen emission originates in the accretion columns (funnel flows of matter accreting onto the star), as expected in magnetospheric accretion models, rather than in a wind emitted at much larger distance (more than one Astronomical Unit).
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Spatially Resolving the Inner Gaseous Disc of the Herbig Star 51 Oph through its CO Ro-vibration Emission
Eso Messenger, 2019Co-Authors: R. Abuter, M. Benisty, J P Berger, M. Accardo, T. Adler, A. Amorim, N. Anugu, G. Ávila, M. Bauböck, J. M. BestenlehnerAbstract:Near-infrared interferometry gives us the opportUnity to spatially resolve the circumstellar environment of young stars at sub-Astronomical-Unit (au) scales, which a standalone telescope could not reach. In particular, the sensitivity of GRAVITY on the VLTI allows us to spatially resolve the CO overtone emission at 2.3 microns. In this article, we present a new method of using the model of the CO spectrum to reconstruct the differential phase signal and extract the geometry and size of the emitting region.
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the innermost Astronomical Unit of protoplanetary disks
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: J Kluska, R Garcia J Lopez, M. BenistyAbstract:Circumstellar disks around young stars are the birthsites of planets. It is thus fundamental to study the disks in which they form, their structure and the physical conditions therein. The first Astronomical Unit is of great interest because this is where the terrestrial-planets form and the angular momentum is controled via massloss through winds/jets. With its milli-arcsecond resolution, optical interferometry is the only technic able to spatially resolve the first few Astronomical Units of the disk. In this review, we will present a broad overview of studies of young stellar objects with interferometry, and discuss prospects for the future.
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a tunnel and a traffic jam how transition disks maintain a detectable warm dust component despite the presence of a large planet carved gap
Astronomy and Astrophysics, 2016Co-Authors: P Pinilla, M. Benisty, L. Klarmann, Tilman Birnstiel, C Dominik, C P DullemondAbstract:Context. Transition disks are circumstellar disks that show evidence of a dust cavity, which may be related to dynamical clearing by embedded planet(s). Most of these objects show signs of significant accretion, indicating that the inner disks are not truly empty, but that gas is still streaming through to the star. A subset of transition disks, sometimes called pre-transition disks, also shows a strong near-infrared excess, interpreted as an optically thick dusty belt located close to the dust sublimation radius within the first Astronomical Unit. Aims. We study the conditions for the survival and maintenance of such an inner disk in the case where a massive planet opens a gap in the disk. In this scenario, the planet filters out large dust grains that are trapped at the outer edge of the gap, while the inner regions of the disk may or may not be replenished with small grains. Methods. We combined hydrodynamical simulations of planet-disk interactions with dust evolution models that include coagulation and fragmentation of dust grains over a large range of radii and derived observational properties using radiative transfer calculations. We studied the role of the snow line in the survival of the inner disk of transition disks. Results. Inside the snow line, the lack of ice mantles in dust particles decreases the sticking efficiency between grains. As a consequence, particles fragment at lower collision velocities than in regions beyond the snow line. This effect allows small particles to be maintained for up to a few Myr within the first Astronomical Unit. These particles are closely coupled to the gas and do not drift significantly with respect to the gas. For lower mass planets (1 MJup), the pre-transition appearance can be maintained even longer because dust still trickles through the gap created by the planet, moves invisibly and quickly in the form of relatively large grains through the gap, and becomes visible again as it fragments and gets slowed down inside of the snow line. Conclusions. The global study of dust evolution of a disk with an embedded planet, including the changes of the dust aerodynamics near the snow line, can explain the concentration of millimetre-sized particles in the outer disk and the survival of the dust in the inner disk if a large dust trap is present in the outer disk. This behaviour solves the conundrum of the combination of both near-infrared excess and ring-like millimetre emission observed in several transition disks.
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a tunnel and a traffic jam how transition disks maintain a detectable warm dust component despite the presence of a large planet carved gap
arXiv: Earth and Planetary Astrophysics, 2015Co-Authors: P Pinilla, M. Benisty, L. Klarmann, Tilman Birnstiel, C Dominik, C P DullemondAbstract:We combined hydrodynamical simulations of planet-disk interactions with dust evolution models that include coagulation and fragmentation of dust grains over a large range of radii and derived observational properties using radiative transfer calculations. We studied the role of the snow line in the survival of the inner disk of transition disks. Inside the snow line, the lack of ice mantles in dust particles decreases the sticking efficiency between grains. As a consequence, particles fragment at lower collision velocities than in regions beyond the snow line. This effect allows small particles to be maintained for up to a few Myrs within the first Astronomical Unit. These particles are closely coupled to the gas and do not drift significantly with respect to the gas. For lower mass planets (1$M_{\rm{Jup}}$), the pre-transition appearance can be maintained even longer because dust still trickles through the gap created by the planet, moves invisibly and quickly in the form of relatively large grains through the gap, and becomes visible again as it fragments and gets slowed down inside of the snow line. The global study of dust evolution of a disk with an embedded planet, including the changes of the dust aerodynamics near the snow line, can explain the concentration of millimetre-sized particles in the outer disk and the survival of the dust in the inner disk if a large dust trap is present in the outer disk. This behaviour solves the conundrum of the combination of both near-infrared excess and ring-like millimetre emission observed in several transition disks.
Takaho Miura - One of the best experts on this subject based on the ideXlab platform.
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secular increase of the Astronomical Unit a possible explanation in terms of the total angular momentum conservation law
Publications of the Astronomical Society of Japan, 2009Co-Authors: Takaho Miura, Hideyoshi Arakida, Masumi Kasai, S KuramataAbstract:Aims. We show a possible explanation for the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). Methods. The mechanism proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Results. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, d dt AU = 15±4 (m/cy), the suggested change in the period of rotation of the Sun is about 3 ms/cy in the case that the orbits of the eight planets have the same “expansion rate.” This value is suffi ciently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun’s moment of inertia is also investigated. It is pointed out that the ch ange in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital “expansion” is happening only in the inner planets system.
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Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law
Publications of the Astronomical Society of Japan, 2009Co-Authors: Takaho Miura, Hideyoshi Arakida, Masumi Kasai, S KuramataAbstract:We give an idea and the order-of-magnitude estimations to explain the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). The idea proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, $\frac{d}{dt}{AU} = 15 \pm 4 {(m/cy)}$, the suggested change in the period of rotation of the Sun is about $21 {ms/cy}$ in the case that the orbits of the eight planets have the same "expansion rate." This value is sufficiently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun's moment of inertia is also investigated. It is pointed out that the change in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital "expansion" is happening only in the inner planets system. Although the existence of some tidal interactions is assumed between the Sun and planets, concrete mechanisms of the angular momentum transfer are not discussed in this paper, which remain to be done as future investigations.
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a possible explanation of the secular increase of the Astronomical Unit
grg, 2009Co-Authors: Takaho MiuraAbstract:We give an idea and the order-of-magnitude estimations to explain the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). The idea proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the Astronomical Unit, d dt 15± 4(m/s),the suggested change in the period of rotation of the Sun is about 21(ms/cy) in the case that the orbits of the eight planets have the same ”expansionrate.”This value is sufficiently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun’s moment of inertia is also investigated. It is pointed out that the change in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital ”expansion”is happening only in the inner planets system. Although the existence of some tidal interactions is assumed between the Sun and planets, concrete mechanisms of the angular momentum transfer are not discussed in this paper, which remain to be done as future investigations.
