Mon Aug 24, F. Flechtner
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Chao, Benjamin F., Gao, Chunchun, and Li, Zhen, 2026. Gravitational energy changes of planet earth under mass perturbations. Journal of Geodesy, 100(6):46, doi:10.1007/s00190-026-02065-6.
• from the NASA Astrophysics Data System • by the DOI System •
@ARTICLE{2026JGeod.100...46C,
author = {{Chao}, Benjamin F. and {Gao}, Chunchun and {Li}, Zhen},
title = "{Gravitational energy changes of planet earth under mass perturbations}",
journal = {Journal of Geodesy},
keywords = {Gravitational energy, Multipole expansion, Eulerian density anomaly, Lagrangian deformation, GRACE},
year = 2026,
month = jun,
volume = {100},
number = {6},
eid = {46},
pages = {46},
abstract = "{The gravitational energy E$_{g}$ plays a deciding role in the
thermodynamic evolution of planet Earth in the destination of
seeking the lowest energy configuration. This paper examines
E$_{g}$ and its changes {\ensuremath{\Delta}}E$_{g}$ due to
geophysical mass perturbations. We derive the multipolar
partitioning of E$_{g}$ based on the gravitational multipole
expansion formalism, thereby study {\ensuremath{\Delta}}E$_{g}$,
a quantity quadratic in dependence on density, due to
perturbations of two distinct forms: (i) Eulerian density
anomaly, and (ii) Lagrangian deformation. Perturbation (i)
carries a negative {\ensuremath{\Delta}}E$_{g}$ relative to the
laterally mean configuration from which the density anomaly is
referenced. We calculate the surficial upper bound of this
{\ensuremath{\Delta}}E$_{g}$ with GRACE-observed time-variable
Stokes coefficients for the Earth, where we find a present-day
\raisebox{-0.5ex}\textasciitilde 3 GW secular increase in
Earth's (non-quadrupolar) E$_{g}$ superposed on seasonal and
interannual undulations. Any monopolar
{\ensuremath{\Delta}}E$_{g}$, however, is oblivious to external
gravitational observations given the non-uniqueness of the
gravitational inversion. Perturbation (ii) carries a positive
{\ensuremath{\Delta}}E$_{g}$ relative to the unperturbed
configuration of equilibrium, hence is by itself unfavored
energy-wise. Case in point is the spin-induced ``oblating''
process resulting in the planet's polar oblateness, which can
happen spontaneously upon the accompanying, over-compensating
decrease in the spin kinetic energy under the conservation of
angular momentum.}",
doi = {10.1007/s00190-026-02065-6},
adsurl = {https://ui.adsabs.harvard.edu/abs/2026JGeod.100...46C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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Mon Aug 24, F. Flechtner