Homework Help Forum: advanced functions

Posted by Anonymous on Monday, October 26, 2009 at 4:42pm.

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 - MathMate, Monday, October 26, 2009 at 5:16pm

  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

  
  

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