  An airplane flying at constant speed and altitude is an example of physics
invisible to the pilots and passengers, but visible to remote observers and
manifest in the mathematics. The optimum flight path is an arc of a Great
Circle, specifically that circle which is the result of rotating the equator to
intersect the origin and destination airports. In order that the velocity
vector remain parallel to the surface of the spherical earth, a centripetal
force is required to rotate the velocity without altering its magnitude. This
force must be radially inward and thus parallel to the local vertical. The
assertion that ``lift balances gravity" is only an approximation. To follow the
curve of the earth, the vertical component of aerodynamic lift must be
\emph{slightly weaker} than gravity so that the plane can be in ``orbitfall".
  That is, to follow the curvature of the earth, maintaining a constant
distance $R$ from the center of the earth while flying at a constant speed $V$
and generating a vertical lift per unit mass $L$, the plane and all inside it
must fall towards the center of the earth with an acceleration, the ``orbitfall
acceleration", $g_{orbitfall} \equiv g-L=V^{2} / R$ where $g$ is the usual
gravitational acceleration constant. If the plane travels a fraction $\digamma$
of the earth's circumference , then it must execute $\digamma$ of an outside
loop. This requires that the pitch angle $\xi$ must rotate nose-down at a rate
of $d \xi / dt=V/R$.
  The dynamic stability of a non-military aircraft makes this pitch change
continuously without pilot intervention: the horizontal stabilizers act as
weathervanes, suppressing small perturbations so that the longitudinal axis
remains at a constant angle of attack. Neither pilot nor passenger is aware of
the orbitfall or the automatic pitch changes -- physics invisible but
essential.
