  Previously, we have considered the equations of motion of the three-body
problem in a Lagrange form (which means a consideration of relative motions of
3-bodies in regard to each other). Analyzing such a system of equations, we
considered the case of small-body motion of negligible mass around the 2-nd of
two giant-bodies (which are rotating around their common centre of masses on
Kepler trajectories), the mass of which is assumed to be less than the mass of
central body. In the current development, we have derived a key parameter that
determines the character of quasi-circular motion of the small 3-rd body
relative to the 2-nd body (Planet). Namely, by making several approximations in
the equations of motion of the three-body problem, such the system could be
reduced to the key governing Riccati-type ordinary differential equations.
Under assumptions of R3BP (restricted three-body problem), we additionally note
that Riccati-type ODEs above should have the invariant form if the key
governing (dimensionless) parameter remains in the range 0.001-0.01. Such an
amazing fact let us evaluate the forbidden zones for Moons orbits in the inner
Solar system or the zones of the meanings of distances (between Moon-Planet)
for which the motion of small body could be predicted to be unstable according
to basic features of the solutions of Riccati-type.
