Abstract
Perturbative Post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the Parameterized Post-Newtonian theoretical framework. The results obtained are applied to the Einstein and. Brans - Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes.. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The Post-Newtonian effects are calculated and discussed for six extrasolar planets.
Highlights
At present, the post-Newtonian effect has been exhibited gradually in the wake of unceasing development in the post Newtonian celestial mechanics and due to that the accurate degree of astronomical instruments is heightened unceasingly
Some authors studied the postNewtonian effect on the motion of celestial objects in the solar system, and in the extrasolar planetary system
Substituting those data into formulas (17)–(20), we obtain the numerical results for the secular variation of the orbital element of six exoplanets in Table 1 and Table 2
Summary
The post-Newtonian effect has been exhibited gradually in the wake of unceasing development in the post Newtonian celestial mechanics and due to that the accurate degree of astronomical instruments is heightened unceasingly. In the recent years some authors studied the post-Newtonian effect or the relativistic effect in the extrasolar planets (Calura and Montanari 1999; Miralda-Escudé 2002; Wittenmyer et al 2005; Iorio 2006, 2011b, 2011c; Adams and Laughlin 2006a, 2006b, 2006c; Heyl and Giadman 2007; Pál and Kocsis 2008; Jordán and Bakos 2008; Ragozzine and Wolf 2009). These authors used the method of the general relativity or the post-Newtonian approximation to study this problem.
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