  As a comet, asteroid or planet approaches its parent star, the orbit changes
shape due to the curvature of spacetime. For comets in particular, the
deviation at the pericentre may noticeably change their ephemerides and affect
the dynamics of outgassing, tidal disruption or other processes which act on
orbital timescales and are assumed to follow Newtonian gravity. By obtaining
and analysing the unaveraged equations of motion in orbital elements due to the
dominant post-Newtonian contribution (1PN), I derive a simple analytic
expression for the maximum deviation in terms of only the stellar mass and
eccentricity of the orbit. This relation can be used to assess the potential
importance of including short-period relativistic terms in models containing
comets, asteroids or planets, and help determine the level of precision needed
in numerical integrations. The magnitude of the deviation in systems with
Solar-like stars is typically comparable to the size of comet nuclei, and the
direction of the deviation is determined by the eccentricity. I show that for
eccentricities above a critical value of approximately 0.359, the direction is
away from the star.
