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We present a new solution for the rotation curves of galactic disks withgravitational potential of the Yukawa type. We follow the technique employed byToomre in 1963 in the study of galactic disks in the Newtonian theory. This newsolution allows an easy comparison between the Newtonian solution and theYukawian one. Therefore, constraints on the parameters of theories ofgravitation can be imposed, which in the weak field limit reduce to Yukawianpotentials. We then apply our formulae to the study of rotation curves for azero-thickness exponential disk and compare it with the Newtonian case studiedby 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 agravitational potential of the Yukawa type), a strong limit can be imposed onthe mass (m_g) of this particle. For example, in order to obtain a galacticdisk with a scale length of b ~ 10 kpc, we should have a massive graviton ofm_g << 10^{-59} g. This result is much more restrictive than those inferredfrom solar system observations.Comment: 7 pages; 1 eps figure; to appear in General Relativity and  Gravitatio

A solution for galactic disks with Yukawian gravitational potential