Tue September 13, 2011 By:

Can you please explain parallax error formulae again within today?please help

Expert Reply
Tue September 13, 2011

Determination of distance of moon from earth (by parallax method)



Let the object O be viewed with our eyes which is at a distance of r, making an angle qbetween the two eyes as shown in the diagram.

The angle q, caused by the two lines drawn from the position of the two eyes to the object, is called angle of parallax.

If we can consider OA and OB as radius of a circle and the distance x (AB) as arc of the circle, then we have


By knowing the values of x and q, the distance of the object from the point of observation can be found out.

However, if we consider O, referred in the above diagram to be the moon or a nearby star, then the angle q is too small in the view of the large astronomical distance and the place of observation. Hence, in order to have a better and valid point of observation, two points on the surface of the Earth is taken as the basis for observation instead of the two eyes. In order to have simultaneous observation of the moon, we select a very distant star at O and measure the angle between O and the two points on the Earth, as shown in the diagram below



Thus, the distance of the moon or a distant star from the Earth can be found out.
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