Parallax

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Parallax is the apparent change in the position of an object resulting from a change in position of the observer, see Fig. 1.

Fig. 1: An observer at viewpoint 1 measures the object to be at p1 on the scale and an observer at viewpoint 2 measures it at p2. The distance p2−p1 is the (linear) parallax.

Diurnal parallax

In astronomy, the diurnal parallax is the parallax caused by the diurnal (daily) rotation of the Earth. In Fig. 2, an observer at P sees the surface of the Earth as a plane bounded by the horizon. Perpendicular to the plane is the zenith. The observer observes the star under an angle α with the zenith, this angle is the topocentric zenith distance of the star. Similarly, the angle α0 is the geocentric zenith distance (measured from C, the center of the Earth). The diurnal parallax is the angle α−α0. Note that the diurnal parallax is zero when the star is in the zenith (above the observer at P); both α and α0 are zero. When the star is at the horizon the diurnal parallax is maximum. When the star is under the horizon the star cannot be observed at P. Fig. 2 illustrates a theorem known from high-school geometry: any exterior angle of a triangle is equal to the sum of the two interior and opposite angles.

Fig. 2: Diurnal parallax is the angle α−α0.