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What is the angular diameter of the earth viewed from the moon? What about the earth viewed from the sun?

Answer 1

From Moon at 384000 km from the Earth,, Earth's angular diameter is #2.02^o#, nearly. From the Sun at 1 AU from the Earth, it is 17.7", nearly.

Let P be the point of contact of the tangent from an observer O on Moon's surface to the Earth centered at E and #alpha# be the Earth's angular diameter,

In #triangle EPO#, right angled at P, OE = 384000-1737= 382263 km, EP = radius of the Earth = 6738 km and

sin #alpha/2#= (EP)(/EO)=6738/382263=0.01763.#

#alpha = 2.02^o#, nearly. Really, this is angular chord. The length of the contact chord is little short of Earth's diameter. So, the angular diameter is a little more than #2.02^o#..

From the Sun instead, #EO = 149597871-696342 = 148901529 and sin (alpha/2) = (EP)/(EO) = 6378/148901529 = 0.0000428

#alpha=0.00491^o=17.7#".. .

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Answer 2

Claire Anctil

When looking at the Earth from the Moon, its angular diameter is about 2 degrees; when looking at the Earth from the Sun, it is approximately 0.53 degrees.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.