The post - Newtonian mean anomaly advance as further post - Keplerian parameter in pul - sar binary systems

The post-Newtonian mean anomaly advance as further post-Keplerian parameter in pul-sar binary systems. Abstract The post-Newtonian secular rate of the mean anomaly ˙ M has been worked out for a two-body system in the framework of the General Theory of Relativity. The possibility of using it as a further post-Keplerian parameter in pulsar binary systems is examined. The resulting effect is almost three times larger than the periastron advance ˙ ω. 1 The post-Newtonian rate of the mean anomaly According to the General Theory of Relativity, the post-Newtonian gravi-toelectric two-body acceleration of order O(c −2) is, in the post-Newtonian centre of mass frame (see, e.g., [1] and references therein) a PN = µ c 2 r 3 µ r (4 + 2σ) − (1 + 3σ)v 2 + 3σ 2r 2 (r · v) 2 r + (r · v)(4 − 2σ)v , (1) where G is the Newtonian constant of gravitation, c is the speed of light, M and m are the rest masses of the two bodies, µ = G(M + m) and σ = M m/(M + m) 2. Let us calculate the post-Newtonian correction to the secular rate of the mean anomaly M with the aid of the Gaussian perturbative equation [2] dM dt = n − 2 na R r a − 1 − e 2 dω dt + cos i dΩ dt , (2) where R is the radial component of (1) viewed as a small perturbation with respect to the Newtonian monopole, a, e, i, Ω and ω are the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node and the argument of pericentre, respectively, of the test particle and n is 1