Dark-Matter Specifications and Gravitational Aspects that Explain Otherwise Seemingly Unexplained Cosmic Data

We provide quantitative explanations for known ratios of dark-matter effects to ordinary-matter effects, and we suggest qualitative explanations for the rate of expansion of the universe and for lumpiness tensions. Our work features a well-defined specification for dark matter. Our work features a new multipole-expansion method that combines Newtonian gravity and special-relativistic interpretations of properties of objects. Our work adds one integer-centric equation to successful popular modeling. Some solutions of the equation help to quantitatively explain dark-matter-to-ordinary-matter ratios and help to suggest insight regarding galaxy formation, eras in the rate of expansion, the Hubble tension, and the S8 tension.