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This book derives and analyzes all solutions to the Kepler problem
with dark energy (DE), presenting significant results such as: (a)
all radial infinite motions obey Hubble's law at large times; (b)
all orbital infinite motions are asymptotically radial and obey
Hubble's law; (c) infinite orbital motions strongly dominate the
finite ones. This clearly shows the effect of repulsive DE: In the
classical Kepler problem, all orbital motions are finite for
negative energies and infinite in the opposite case. Another DE
effect is spatial localization of bounded orbits: mostly, they are
within the equilibrium sphere, where the attractive Newtonian force
outbalances the repulsive force of DE. This problem is of
particular current interest due to recent studies of the local
flows of galaxies showing domination of DE in their dynamics; the
book discusses this observation in detail.
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