The author wants to estimate precisely how the gravitational field evolves in the particular shape of a spiral galaxy. This article first identifies the model used for the dynamics of spiral galaxies, which is a speed decreasing with r-1/2 outside of (and sometimes inside) the disk, then demonstrates that this model is mathematically flawed under Newton’s Law of Universal Gravitation. It also reminds the reader that Kepler Laws, which are equivalent to a r-1/2 speed decrease, can not be used if the mass distribution is not spheric. As the disk is commonly considered the most massive component of such galaxies, the article establishes the field created by it under correct hypotheses. It takes into account an axi-symmetric component and spiral arms that are studied separately, and obtains a mean flat rotation curve for every cylinder-shaped mass distribution without any hypothesis on ρ(r). A method for computing the mass of a spiral galaxy from its rotation curve is suggested and applied to the Milky Way and 12 other spiral galaxies. It is then found that their visible masses are enough to explain their rotation curve.