The moon is 3.85 × 108 m from the earth and has a diameter of 3.48 × 106 m. You

Question

The moon is 3.85 × 108 m from the earth and has a diameter of 3.48 × 106 m. You have a pea (diameter = 0.50 cm) and a dime (diameter = 1.8 cm). Close one eye and hold each object at arm's length (71 cm) between your open eye and the moon. Which objects, if any, completely cover your view of the moon? Assume that the moon and both objects are sufficiently far from your eye that the given diameters are equal to arc lengths when calculating angles.

Explanation / Answer

The equation you use is ?=Arc length / Radius The ? of the moon is found by taking the ArcLength (in this case it is the diameter of the moon which=3.48x106m) and dividing it by the Radius (the distanceaway from earth which = 3.85x108m). So you have... ?=(3.48x106m) /(3.85x108m)=> ?moon=0.009038961rad Next you find the ? of the pea by taking its Arc Length (thevalue for the diameter, which = 0.50cm) and divide it by theradius (for this you use the length of the arm which hold the peathat = 71cm). You then get... ?=(0.50cm) / (71cm) => ?pea=0.0070422535rad Next you find the ? of the dime by taking its Arc Length (thevalue for the diameter, which = 1.80cm) and divide it by theradius (for this you use the length of the arm which hold the peathat = 71cm). You then get... ?=(1.80cm) / (71cm) => ?dime=0.0253521127rad ?pea

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