Derivations of the equations governing Eotvos spheres and degenerate Eotvos objects are presented. These simplified stellar models incorporate a short-range component in their gravitational potential. A Yukawa formulation to agree with other workers in this field is used, although any form that multiplies the normal inverse square law would be acceptable. Both polytropic and completely degenerate equations of state are used and separate equations governing the density distribution derived. Various global relationships are obeyed by these objects, much like the polytropes to which they are similar. A discussion of whether the simplified potential is accurate enough for astrophysics is included, along with a more accurate integral equation for the potential.