Determination of masses and other properties of extra-solar planetary systems with more tha.pdfVIP

a r X i v : a s t r o - p h / 0 1 1 2 1 1 5 v 1 5 D e c 2 0 0 1 Determination of masses and other properties of extra-solar planetary systems with more than one planet Michael Nauenberg Physics Department, University of California, Santa Cruz, CA 95064 ABSTRACT Recent analysis of the Doppler shift oscillations of the light from extra-solar planetary systems indicate that some of these systems have more than one large planet. In this case it has been shown that the masses of these planets can be determined without the familiar ambiguity due to the unknown inclination angle of the plane of the orbit of the central star provided, however, that its mass is known. A method is presented here which determines also a lower limit to the mass of this star from these observations. As an illustration, our method is applied to the Keck and Lick data for GJ876. Subject headings: extra solar, planetary 1. Introduction During the past six years a large number of extra solar planetary systems have been discov- ered by observations of Doppler shifted oscilla- tions of the light emitted by the central star (Udry 2000). Recent analysis of the data has shown that some of these systems have more than one Jupiter-size planet circulating the central star (Marcy,Fischer,Butler Vogt 2001). It is well known that when there is only a single planet an ambiguity occurs in the determination of the mass of this planet when the inclination angle of the plane of the orbit is not known. For systems with more than one sizable planet, however, it turns out that this ambiguity can be removed when the gravitational interaction between these planets is important to the evolution of the planetary orbits, as has been pointed out by Laughlin and Cham- bers (2001). By the equivalence principle this in- teraction is proportional to the mass of the plan- ets, thus providing an additional dependence on these masses which is absent when there is only a single planet. In the case of multiple planets only appr