![]() ![]() The units are for the three major axes in astronomical units, and the units of the distance are in parsec, and the resulting angle has a, is in arcseconds. The astrometric signature is is computed as the barycentric orbit of the stars on the major axis divided by the distance. And for a single, planet orbiting a star. And in the case of astrometry the, the amplitude of those angles that we measure is called the astrometric signature. In kilometers or astronomical units, what we must use are angles. So, in astrometry we do not have access, we do not have directly access to linear distances. ![]() So now we have to take a look at the equation again to, to, to have some order of magnitude of the signals we want to measure. It means that when we want to detect an astrometric motion to be able to measure those displacement, we have to, we need a stability of a long period of time. Is mainly caused or induced by the presence of the massive plan, of the two most massive planets of our system which are Jupiter and Saturn. This complex curve that represent the motion of the sun over a long period of time, 50 or 60 years. It is superimposed over the disc of the sun which is represented in yellow. The barycentric orbit of our sun, and you can see the motion as as a line. For another, as another illustration, I have represented on the right hand side. By measuring the displacement of the primary stars, as shown on the middle diagram. And you can see that the astrometric technique will try to retrieve the orbital parameters of the three planets. Those planets have periods of 44,000 and 3,000 days. Which correspond to three planets system orbiting a sun-like stars. The shape will be quite complex, as illustrated on the middle diagram. Okay? If wel look in more details at the barycentric orbit of a planetary system. The astrometric method will measure displacement of the primary stars within the x y plane, the which is represented by the grey ellipse under the left hand side, diagram. You can see that if the observers, er, looks at the plane of the sky along the z axis. So, if we come back to the famous diagram of the projected orbit on the plane of the sky. There's another technique that allows to probe the astrometric, the barycentric orbit of the star, which is called the astrometry. In the previous sequence we, I presented the radial velocity method to detect and characterize the barycentric orbit of a star, and to deduce, and from it, deduce the parameters of the planets orbiting the stars. Welcome back to the lecture dedicated to the detection of exoplanet. ![]()
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