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Knowing that the Earth's diameter is about "3 2/3" times the diameter of the moon, what is the angular diameter of the Earth as seen by an observer on the moon?

Answer 1

About #1^@54'#

You need a little more information, e.g. that the angular diameter subtended by the moon from Earth is about #31'# (i.e. just over #0.5^@#)

As a result, the Earth's angular diameter measured from the moon is roughly:

#31 * 11/3 = 341/3 ~~ 114'# or #1^@54'#

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Answer 2

Levi Acosta

Using the following formula, we can determine the angular diameter of the Earth as seen from the Moon: Angular diameter = 2 * arctan (object diameter / (2 * distance)) Given: - Earth diameter = 3 2/3 times the Moon's diameter - Moon diameter = 3,474.8 kilometers - Moon to Earth distance = 384,400 kilometers Using these values as a substitute, we get: Angular diameter = 2 * arctan ((3 2/3 * 3,474.8) / (2 * 384,400)) Angular diameter ≈ 1.93 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.