Parallax Method (Measurement of Large Distances)

In this post, we will study all the information related to the Parallax Method. The Parallax Method is a part of the syllabus of jee and class 11 syllabus. Parallax Method is used to measure the larger distances.

Parallax Method and How it Works

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. 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.

The distance between the two points of observation is called the basis. In this example, the basis is the distance between the eyes. 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, separated by distance AB =b at the same time as shown in figure. We measure the angle between the two directions along which the planet is viewed at these two points. The \Delta ASB in figure represented by symbol e is called the parallax angle or parallactic angle.

As the planet is very far away, b/d <<1 and therefore, 0 is very small. Then we approximately take AB as an arc of length b of a circle with centre at S and the distance D as the radius AS=BS so that AB=b=D~\theta where is in radians.

Having determined D, we can employ a similar method to determine the size or angular diameter of the planet. If d is the diameter of the planet and \alpha the angular size of the planet (the angle subtended by d at the earth), we have \alpha=d/D

The angle \alpha can be measured from the same location on the earth. It is the angle between the two directions when two diametrically opposite points of the planet are viewed through the telescope. Since D is known, the diameter d of the planet can be determined using equation (ii).