# advanced functions

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The Moon has a diameter of about 3480 km and an orbital radius of about 384 400 km from the centre of Earth. Suppose that the Moon is directly overhead. What is the measure of the angle subtended by the diameter to the Moon as measured by an astronomer on the surface of Earth? Answer in both radians and degrees.

• advanced functions - ,

Diameter of the moon = 3480 km
Distance from surface of the earth
= Distance to centre - radius of the earth
= 384400-6400 km
= 378000 km

Since the angle is very small, we can approximate the arc-length by the chord length, equal to the diameter.

Angle subtended
= 3480/378000
= 0.0092 radian

If we had used the chord instead, the difference in angle calculated would have been 0.0000000325 radians more.
i.e.
angle
= 2*sin-1(1740/37800)
= 0.0092 radian

• advanced functions - ,

Sorry, I actually have a question. According to the question that was posted. If I were to solve this question, without knowing the radius of the earth before hand. Is there any other solution??

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