Question

The moon is 3.85 x 10 to the 8 m from earth and has a diameter of 3.48 x 10 to the 6 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.
a. dime
b. neither
c. pea
d. both

Answer 1

Answer:

(a) dime

Explanation:

Convert all to metric unit:

0.5 cm = 0.005 m

1.8 cm = 0.018 m

71 cm = 0.71 m

In order to find out we would need to calculate the ratio R between the object diameter d and their distance s to our eyes:

$R_m = \frac{d_m}{s_m} = \frac{3.48*10^6}{3.85*10^8} \approx 0.009$

$R_p = \frac{d_p}{s_p} = \frac{0.005}{0.71} \approx 0.007$

$R_d = \frac{d_d}{s_d} = \frac{0.018}{0.71} \approx 0.0253$

Since the ratio of the dime is larger than the ratio of the moon, and the ratio of the pea is smaller than the ratio of the moon, only the (a) dime can cover your view of the moon.