  The parameterised post-Newtonian (PPN) formalism is a weak-field slow-motion
approximation for both GR and some of its generalisations. It permits various
parameterisations of the motion, among which are the Lagrange-type and
Gauss-type orbital equations. Often, these equations are developed under the
Lagrange constraint, which makes the evolving orbital elements parameterise
instantaneous conics tangent to the orbit. Arbitrary mathematically, this
choice of a constraint is convenient under perturbations dependent only on
positions. Under perturbations dependent also on velocities (like relativistic
corrections) the Lagrange constraint unnecessarily complicates solutions that
can be simplified by introducing a freedom in the orbit parameterisation, which
is analogous to the gauge freedom in electrodynamics and gauge theories.
Geometrically, this freedom is the freedom of nonosculation, i.e. of the degree
to which the instantaneous conics are permitted to be non-tangent to the actual
orbit. Under the same perturbation, all solutions with different degree of
nonosculation look mathematically different, though describe the same physical
orbit. While non-intuitive, the modeling of an orbit with a sequence of
nontangent instantaneous conics can at times simplify calculations. The
appropriately generalised ("gauge-generalised") Lagrange-type equations, and
their applications, appeared in the literature hitherto. We in this paper
derive the gauge-generalised Gauss-type equations and apply them to the PPN
two-body problem. Fixing the gauge freedom in three different ways (i.e.
modeling an orbit with non-osculating elements of three different types) we
find three parameterisations of the PPN two-body dynamics. These
parameterisations render orbits with either a fixed non-osculating semimajor
axis, or a fixed non-osculating eccentricity, or a fixed non-osculating
argument of periastron.
