What is parallax? Explain the parallax method to measure the distance between the Earth and a planet.

(N/A) Parallax is the apparent change in the position of an object with respect to a background when the object is viewed from two different positions.
To understand this,hold a pencil in front of you against a fixed background point (like a wall). Look at the pencil first through your left eye $(A)$ (closing the right eye) and then through your right eye $(B)$ (closing the left eye). You will notice that the position of the pencil appears to shift relative to the background. This phenomenon is called parallax.
The angle $\theta$ subtended by the two positions of observation at the object is called the parallax angle. The distance between the two points of observation ($A$ and $B$) is called the basis $(b)$.
To measure the distance $D$ of a planet $S$ from the Earth,we observe the planet from two different locations $A$ and $B$ on the Earth's surface. The distance between these two points is $b = AB$.
The angle $\theta = \angle ASB$ is the parallax angle. Since the planet is very far from the Earth,the ratio $\frac{b}{D} \ll 1$,and therefore $\theta$ is very small.
In this situation,$AB$ can be considered as an arc of a circle with center $S$ and radius $D$. Thus,$AS = BS = D$.
Using the definition of an angle in radians:
$\theta = \frac{\text{arc}}{\text{radius}} = \frac{AB}{AS} = \frac{b}{D}$
Therefore,the distance $D$ is given by:
$D = \frac{b}{\theta}$
By measuring the basis $b$ and the parallax angle $\theta$,the distance $D$ between the Earth and the planet can be determined.