  On the basis of a general action principle, we revisit the scale invariant
field equation using the co-tensor relations by Dirac (1973). This action
principle also leads to an expression for the scale factor $\lambda$, which
corresponds to the one derived from the gauging condition, which assumes that a
macroscopic empty space is scale-invariant, homogeneous, and isotropic. These
results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From
the field and geodesic equations, we derive, in current time units (years,
seconds), the Newton-like equation, the equations of the two-body problem, and
its secular variations. In a two-body system, orbits very slightly expand,
while the orbital velocity keeps constant during expansion. Interestingly
enough, Kepler's third law is a remarkable scale-invariant property.
