  We present a new solution for the rotation curves of galactic disks with
gravitational potential of the Yukawa type. We follow the technique employed by
Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new
solution allows an easy comparison between the Newtonian solution and the
Yukawian one. Therefore, constraints on the parameters of theories of
gravitation can be imposed, which in the weak field limit reduce to Yukawian
potentials. We then apply our formulae to the study of rotation curves for a
zero-thickness exponential disk and compare it with the Newtonian case studied
by Freeman in 1970. As an application of the mathematical tool developed here,
we show that in any theory of gravity with a massive graviton (this means a
gravitational potential of the Yukawa type), a strong limit can be imposed on
the mass (m_g) of this particle. For example, in order to obtain a galactic
disk with a scale length of b ~ 10 kpc, we should have a massive graviton of
m_g << 10^{-59} g. This result is much more restrictive than those inferred
from solar system observations.
