Hubble’s law, formulated by Edwin Hubble and Milton Humason in 1929, tells us that space is expanding. However, over short distances, flat gravity caused by the expanding universe is described by the inverse square law of Newtonian gravity. This leads to heretofore unsolved gravity anomalies, such as the pioneer anomaly, which involves an abnormal slowdown relative to the Sun of the Pioneer spacecraft and the galaxy rotation problem, whereby the rotational speed of heavenly bodies reaches a constant value instead of decreasing with distance from the galactic centre. The expanding universe adds an expansion term that was divided into a strain constant V0 for the recession rate v = H0D, and the gravitational potential −GM(1/r) of Newtonian mechanics for a stationary universe is replaced by −GM(1/r)(1 + v/V0). The expansion term becomes constant (G0 = GH0/V0) at large distances because the distance D and radius r cancel. Furthermore, the total gravitational mass [M0 = c 3/(2GH0)] of the observable universe affects the specific potential constant, which is multiplied by the observable gravitational mass to become −(G/r + G0)M. Flat gravity based on Hubble’s law which expanded Newtonian gravity is thus consistent with the gravity anomaly without assuming the existence of dark matter. When combined with Yukawa potential [αe (-r/λ)], theã€€gravity and the strong force can be unified [αe (-r/λ) ï¼ 1](G/r + G0)M.
Key words: Expanding universe, inverse square law, pioneer anomaly, galaxy rotation problem, recession rate, gravitational potential, stationary universe, gravitational mass, specific potential, dark matter.