Question

13. Determine the diameter of a planet using parallax method​

Answer 1

Let the diameter of noon is D.

suppose E is the point on the Earth's surface from where we have to see moon by using telecope. Now, telescope is focused on the moon's surface and image is shown is observed as shown in figure.

With help of telescope , we can determine ∠AEB, 

let we get , ∠AEB = Ф 

Let S is the shortest distance between moon and earth.

Now, apply tangent for ∆ABE, 

∴ tanФ = AB/S [ because angle Ф very small , ∴ AB = S ]

also, if Ф → 0 then, tanФ ≈ Ф

Hence, Ф = AB/S 

AB = ФS 

Hence, diameter of moon = parallax angle x shortest distance between moon and earth.