A small mass particle traveling in a curved spacetime is known to trac
e a background geodesic in the lowest order approximation with respect
to the particle mass. In this paper, we discuss the leading order cor
rection to the equation of motion of the particle, which presumably de
scribes the effect of gravitational radiation reaction. We derive the
equation of motion in two different ways. The first one is an extensio
n of the well-known formalism by DeWitt and Brehme developed for deriv
ing the equation of motion of an electrically charged particle. Constr
ucting the conserved rank-two symmetric tensor, and integrating it ove
r the interior of the world tube surrounding the orbit, we derive the
equation of motion. Although the calculation in this approach is strai
ghtforward, it contains less rigorous points. In contrast with the ele
ctromagnetic case, in which there are two different charges, i.e., the
electric charge and the mass, the gravitational counterpart has only
one charge. This fact prevents us from using the same renormalization
scheme that was used in the electromagnetic case. In order to overcome
this difficulty, we put an ansatz in evaluating the integral of the c
onserved tensor on a three spatial volume which defines the momentum o
f the small particle. To make clear the subtlety in the first approach
, we then consider the asymptotic matching of two different schemes: i
.e., the internal scheme in which the small particle is represented by
a spherically symmetric black hole with tidal perturbations and the e
xternal scheme in which the metric is given by small perturbations on
the given background geometry. The equation of motion is obtained from
the consistency condition of the matching. We find that in both ways
the same equation of motion is obtained. The resulting equation of mot
ion is analogous to that derived in the electromagnetic case. We discu
ss implications of this equation of motion.