The orbit of Proxima Centauri: a MOND versus standard Newtonian distinction

Possible orbits for the motion of Proxima Centauri about alpha-Centauri A/B are derived according to standard Newtonian conditions and under the Modified Newtonian Dynamics (MOND) paradigm. Likely orbits are derived under the assumption that Proxima is coeval with alpha-Centauri A/B, located at, or very close to apastron, and that its radial velocity will ultimately be determined as being of order -22.15 km/s-bringing it closer to the observed radial velocity value for alpha-Centauri A/B. It is found under standard Newtonian conditions that Proxima might occupy an orbit described according to a semi-major axis and eccentricity of (a,e)=(8,500,0.78)-resulting in an orbital period of some 53,500 years. If Proxima's motion is constrained to move entirely under weak-field MOND conditions then a provisional orbit having (a,e)=(12,527,0.2) is obtained. In principle, we argue, by obtaining an ultra-precise value for the radial velocity of Proxima a distinction between the standard Newtonian gravity and the MOND orbital approximations can be made.