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Fig. 2.2 Motion of the Sun as a function of time (in years) on the plane of the sky as it would appear from a location 10 parsecs away and perpendicular to the plane of the ecliptic. This movement is mainly dominated by the giant planets (Jupiter, Saturn, Uranus, and Neptune). Note the scale: the variations in positions are approximately 1 mas (0.001 arcsec noted 0.001")

• the line of nodes: this is the straight line given by the intersection of the orbital plane with the plane of the sky

• the ascending and descending nodes: these are the intersections of the line of nodes and the object's orbit. By convention, the ascending node is crossed when the object recedes from the observer, and the descending node when the object approaches the same observer

• the position angle of the ascending node, denoted Q: it describes the orientation of the line of nodes on the plane of the sky relative to celestial north. This angle lies between 0 and 180°

• the inclination, denoted i: this is the angle between the object's orbit and the plane of the sky. It is equal to 0 (or 180°) when the orbital plane and the plane of the sky coincide; i lies between 0 and 90° when the apparent motion of the object on the plane of the sky takes place in the trigonometrically direct sense, and lies between 90 and 180° in the opposite case (Fig. 2.3).

It can be shown (Borde, 2003) that the position of the star in the reference frame based on the plane of the sky may be deduced from that in the plane of the orbit by

3 successive rotations:

• a rotation by the angle -Q around the line of sight

• a rotation by angle i around the line of sight

• a rotation by angle co around the normal to the plane of the orbit

Fig. 2.3 Definition of the geometrical parameters describing the orientation of the orbit of a star relative to the plane of the sky towards Earth

North plane of the orbit line of nodes

-n periastron

'plane of the sky

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