Let σ( t 0) be a set of star's orbital elements and the planet's mass at the time t 0, with this set of parameters a set of observational data of star's position may be simulated, and then to calculate inversely σ( t 0). Let r → s( t 0), r → ˙ s t 0 and m p be the estimated values of the star's position and velocity and the planet's mass at ANALYSIS OF ORBIT CHARACTERISTICS, AND SIMULATION CALCULATIONSĪt present, as the gaia's survey data have not been released, only can simulations be carried out to prove the effectiveness of the above-mentioned method. The observation equations are as same as the star's equations of observation corresponding to the orbital element method, namely, Eq. In the space rectangular coordinate system set up in the above section, let r → s and r → p be the position vectors of the star and the planet, and M s and m, their masses, respectively, the star's equations of motion relative to the barycenter is then For a single star, its angular position on the celestial sphere may be described with 5 astrometrically-observed values, including the equatorial coordinates, namely, the right ascension α 0 and declination δ 0 (the values in a certain coordinate system at a certain epoch, and now usually the values in the OBSERVATION EQUATIONS BASED ON COORDINATE VELOCITIES The existence of an exoplanet is ascertained through the observation of the periodic variation of the star position when the astrometric method is used to detect indirectly the exoplanets. 1): in which, M s and m p are the mass of the star and that of the planet, OBSERVATION EQUATIONS BASED ON ORBITAL ELEMENTS Let the orbital semi-major axes of the star and planet revolving around the barycenter of the system be a s and a p, respectively, and the field angle of the orbital semi-major axis of the star as observed on the ground be θ (as shown in Fig. When a planet exists near a star, the star and the planet will make the elliptic motions with the same angular velocity around their barycenter because of the gravitational effect. Recently, along with the development of astronomical observation techniques, especially the successful launch and observation of the Kepler Space Telescope, the new exoplanets are continuously discovered, and their number ACCURACY ANALYSIS OF ASTROMETRIC OBSERVATION In 1995, Mayor and Queloz found the first exoplanet 51b Pegasi with the Jupiter mass revolving around a main-sequence star near the 51 Pegasi by the radial velocity method. At present, the international circle of astronomy is fond of the detection and study of exoplanets.
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