The Moon is Observed From Two Diametrically Extremes a and B on Earth. The Angle of Parallax is Found to Be 1 Degree 54". If the Diameter of the Earth is About 1.276×107m, Estimate the Distance of the Moon From the Earth.

By K Balaji|Updated : November 9th, 2022

The distance of the Moon from the earth is 3.8 x 10⁸ m

In a circle

arc/radium = θ or s = rθ

As a result, the arc will nearly resemble a straight line if r is very large and has relatively little effect on its size.

As a result, the length of the arc becomes more similar to a straight line as R grows.

Additionally, arc straightens if radius stays the same but 0 is decreased. because of the moon's enormous distance from the earth and the relatively modest angle subtended

AB/r = θ

On rearranging we get

r = AB/θ

θ = 1⁰54” = 1 + 54/60 = (114/60)⁰ = 114/60 x π/180 radius

On simplifying we get

= 0.033 radius

r = (1.276 x 10⁶)/ 0.033

r = 3.8 x 10⁸ m

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Distance

The total movement of an object, independent of direction, is its distance. The amount of space that an object has travelled, regardless of where it started or ended, is referred to as distance.

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