ABSTRACT
An irrotational and compressible flow has a potential generated by mass source/sinks (Section 18.1), and an incompressible rotational flow has a stream function generated by vortices (Section 18.2); across a distribution of sources/sinks (vortices) on a curve the normal (tangential) velocity has a jump. The gravity field (Section 18.3) is always irrotational and is generated by a mass distribution; the mass is positive and creates an attractive field; thus it is analogous to the irrotational flow due to sinks. The normal (tangential) component of the gravity field across a mass distribution on a curve is discontinuous (continuous). The gravity field due to a line-mass (mass distribution) is analogous to a sink (Section 18.4), and this specifies the gravity force (Section 18.5) between line-masses and/or mass distributions. Two examples of gravity fields are those due to a finite (infinite) homogeneous (inhomogeneous) slab [(Section 18.6 (18.8)] for that the integral is nonsingular at an external point; at an internal point (Section 18.7) the integrals must be taken as Cauchy principal values (Section 17.8), to exclude the singularity, since a mass does not create a gravity field on itself. The gravity field of an arbitrary mass distribution can be represented as a superposition of multipoles (Section 18.9). The creation of a gravity field is an intrinsic property of a mass distribution, be it the fall of a body on the earth, the motion of planets around the sun, or the massive objects like galaxies in the universe.
