Parallax

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 a planet (or another object in our solar system) under an angle α with the zenith, this angle is the topocentric zenith distance of the planet. The angle can be determined, for instance, against the background of fixed stars. 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 planet is in the zenith (above the observer at P); both α and α₀ are zero. When the planet is at the horizon the diurnal parallax is maximum. When the planet 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.