Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the parallax method.
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.
The distance between the two points of observation is called the basis.
`text(Example-)` When you hold a pencil in front of you against some specific point on the background (a wall) and look at the pencil first through your left eye A (closing the right eye) and then look at the pencil through your right eye B (closing the left eye), you would notice that the position of the pencil seems to change with respect to the point on the wall. This is called parallax. In this example, the basis is the distance between the eyes.
`text(To measure the distance D of a far away planet S by the parallax method)`
We observe it from two different positions (observatories) A and B on the Earth, `AB=b`
The ∠ASB in Fig. represented by symbol θ is called the `text(parallax angle)` or `text(parallactic angle)`.
As the planet is very far away, `b/D > > 1` `:. theta` is very small.
Then we approximately take `AB=b=` arc of a circle with centre at S
`=>` `AB=b=D theta` where θ is in radians.
`text(Size or Angular Diameter of Planet)`
If `d=` diameter of the planet
`alpha=` angular size of the planet (the angle subtended by d at the earth)
we have, `alpha=d/D`