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A Derivation of Flat Rotation Curve of Spiral Galaxies and Baryonic Tully-Fisher Relation

Fundamentally for the extended disc region of a spiral galaxy, an alternative solution to Laplace equation has been presented for a potential that is radially symmetric on the disc plane. This potential, unlike newtonian one, is shown to be logarithmic in distance from the centre, which allows for the rotation velocity to be constant along the disc radius.It is also shown that this potential easily manifests into a relationship between inner mass of the galaxy and terminal rotation velocity, which has been empirically observed and known as Baryonic Tully-Fisher relations.