  A more general scale-setting procedure for General Relativity with
Renormalization Group corrections is proposed. Theoretical aspects of the
scale-setting procedure and the interpretation of the renormalization group
running scale are discussed. The procedure is elaborated for several highly
symmetric systems with matter in the form of an ideal fluid and for two models
of running of the Newton coupling and the cosmological term. For a static
spherically symmetric system with the matter obeying the polytropic equation of
state the running scale-setting is performed analytically. The obtained result
for the running scale matches the Ansatz introduced in a recent paper by
Rodrigues, Letelier and Shapiro which provides an excellent explanation of
rotation curves for a number of galaxies. A systematic explanation of the
galaxy rotation curves using the scale-setting procedure introduced in this
paper is identified as an important future goal.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory