PARALLAX METHOD

If you sit at the train window and watch a tree or a pillar which is nearer to train that is moving backward. You have to turn your head quickly to see those trees. That is a tree changes their angle quickly. If you see the mountain which is far from the train, you can see it moving slowly backward direction. that is the mountain changes the angle in slow manner. If you look at the moon from the train, you see it steady but you do not know if it changes it's angle slowly. this is called parallax.

What exactly is Parallax ? 

If we move fixed distance (distance between observer and object), the object nearer to observer changes the angle quickly and object far from the observer changes the angle slowly.

Parallax method is used to measure the large distances such as distance of a planet or star from the earth.

Discuss parallax method with the help of mathematics.

                                                                                                              Let S be the planet is at a distance D far away from earth, i.e. AS = BS = D.

Suppose at the same time, we observe this planet from two different position A and B on the earth. Two position A and B are separated by the distance b, i.e. AB = b. 

The angel between the two direction along which the planet is viewed is <ASB = θ.

As θ is very small, then take AB as an arc of length b of a circle

whose center is S and D is the radius (AS = BS).

We know that,  (If D>>>b then arc AB = AB = b)

                      

                      Angle = Arc / Radius                                                                                                                                                  i.e.                              θ = AB / D

                         θ = b /D    

                        D = b / θ

    This is the distance D.

     

NOTE : Parallax method is used to measure the distance of star or planet which are less                            than 100 light years away.