  A Newtonian approach to quantum gravity is studied. At least for weak
gravitational fields it should be a valid approximation. Such an approach could
be used to point out problems and prospects inherent in a more exact theory of
quantum gravity, yet to be discovered. Newtonian quantum gravity, e.g., shows
promise for prohibiting black holes altogether (which would eliminate
singularities and also solve the black hole information paradox), breaks the
equivalence principle of general relativity, and supports non-local
interactions (quantum entanglement). Its predictions should also be testable at
length scales well above the "Planck scale", by high-precision experiments
feasible even with existing technology. As an illustration of the theory, it
turns out that the solar system, superficially, perfectly well can be described
as a quantum gravitational system, provided that the $l$ quantum number has its
maximum value, $n-1$. This results exactly in Kepler's third law. If also the
$m$ quantum number has its maximum value ($\pm l$) the probability density has
a very narrow torus-like form, centered around the classical planetary orbits.
However, as the probability density is independent of the azimuthal angle
$\phi$ there is, from quantum gravity arguments, no reason for planets to be
located in any unique place along the orbit (or even \textit{in} an orbit for
$m \neq \pm l$). This is, in essence, a reflection of the "measurement problem"
inherent in all quantum descriptions.
