The moon isn't following the curvature of space around the earth. It
is taking a motion curve or geodesic that is magnified beyond space-
time curvature. The actual curved space-time itself is defined by the
null geodesic associated with light speed movement.

Motion curvature is the magnified curve that matter follows due to its
slower motion. This is matter geodesic. This is motion curvature
followed by all matter.

It is misleading to say the moon is following the space-time curvature
when it is really following its motion curve through instead.

Mitch Raemsch; Twice Nobel Laureate 2008