We study the role of the brane-induced graviton kinetic term in theories with
large extra dimensions. In five dimensions we construct a model with a
TeV-scale fundamental Planck mass and a {\it flat} extra dimension the size of
which can be astronomically large. 4D gravity on the brane is mediated by a
massless zero-mode, whereas the couplings of the heavy Kaluza-Klein modes to
ordinary matter are suppressed. The model can manifest itself through the
predicted deviations from Einstein theory in long distance precision
measurements of the planetary orbits. The bulk states can be a rather exotic
form of dark matter, which at sub-solar distances interact via strong 5D
gravitational force. We show that the induced term changes dramatically the
phenomenology of sub-millimeter extra dimensions. For instance, high-energy
constraints from star cooling or cosmology can be substantially relaxed.Comment: 24 pages, 4 eps figures; v2 typos corrected; v3 1 ref. added; PRD
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