Gravitational Wave Velocity and Orbital Radii: A Hypothetical Method for Inferring Dark Matter Density

This paper explores the possibility that the propagation speed of ultra-long-wavelength gravitational waves is reduced due to the presence of a low-density medium in space, such as interplanetary matter and dark matter. Based on the hypothesis that the gravitational wave speed vgv_gvg is proportional to a planet’s orbital radius RRR multiplied by its orbital frequency f=1/Tf = 1/Tf=1/T, the model suggests a direct method to estimate the effective gravitational wave speed. Using this estimate, the refractive index ng=c/vgn_g = c / v_gng=c/vg can be calculated, and from it, the local mass density ρ\rhoρ can be inferred via the relation ng≈1+α⋅ρn_g \approx 1 + \alpha \cdot \rhong≈1+α⋅ρ. By applying this method to real planetary data (such as Earth's orbit), the paper provides a novel approach to indirectly estimate dark matter distribution in the solar system. Graphical results and tabulated values for each planet support the hypothesis, showing a consistent pattern between orbital parameters and the inferred gravitational properties of space.