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### Variation of Newton's Constant and of Length of Day

#### Abstract

J.D. Anderson et al have published an article discussing the observations suggesting a periodic variation of the measured value of Newton constant and variation of length of day (LOD). In the following I discuss TGD based explanation of the observations in terms of a variation of Earth radius. The variation would be due to the pulsations of Earth coupling via gravitational interaction to a dark matter shell with mass about $1.3 x 10

^{-4}M_{E}introduced to explain Flyby anomaly: the model would predict*ΔG/G= 2**ΔR/R*and*ΔLOD/LOD=2ΔR*with the variations pf G and length of day in opposite phases. The experimental finding_{E}/R_{E}*ΔR*is natural in this framework but should be deduced from first principles. The gravitational coupling would be in radial scaling degree of freedom and rigid body rotational degrees of freedom. In rotational degrees of freedom the model is in the lowest order approximation mathematically equivalent with Kepler model. The model for the formation of planets around Sun suggests that the dark matter shell has radius equal to that of Moon's orbit. This leads to a prediction for the oscillation period of Earth radius: the prediction is consistent with the observed 5.9 years period. The dark matter shell would correspond to_{E}/R_{E}= M_{D}/M_{E}*n=1*Bohr orbit in the earlier model for quantum gravitational bound states based on large value of Planck constant if the velocity parameter*v*equals to the rotation velocity of Moon. Also_{0}*n>1*orbits are suggestive and their existence would provide additional support for TGD view about quantum gravitation. Further amazing co-incidences: The gravitational Compton length of particle is very near to the Earth's radius in case Earth if central mass is Earth mass. For the mass of dark matter shell it is the variation*ΔR*. This strongly suggests that quantum coherence in astrophysical scales has been and perhaps still is present._{E}