The following plot is the gravity profile between Earth and the Moon, also split into two components, Earth side,
\(-{g}_{e}e^{-\cfrac{x}{{r}_{e}}}\)
Moon side,
\(+{g}_{m}e^{(-\cfrac{Orbs}{{r}_{m}}+\cfrac{x}{{r}_{m}})}\).
An actual plot of -9.80665*e^(-x/637.1)+1.62*e^(a/1737+x/173.7) where a goes from -385000 to -200000 is below.
The graph also shows that varies orbital radii are possible. Since gravity is zero or pointing outwards, textbook derivation of equating gravitational force with centrifugal force that provide for circular motion is falsehood. So, why the Moon keeps going round and round?
