a Based on the estimate of 87 that Hipparchus made for ZMES

a. Based on the estimate of 87 that Hipparchus made for ZMES and an Earth-Moon distance of 238,800 miles, find the corresponding estimate of the distance from Earth to the Sun in miles. b. The actual average distance from Earth to the Sun is about 93 million miles. What is the corresponding degree mea- sure of the angle LMES? LMEs c. Explain why small errors in the measurement of result in relatively large errors in measurement of the Earth-Sun distance.

Solution

a) earth sun distance = (earth moon distance)/cos87 = 238800/cos87 = 4562828.639 miles

b) cos(MES) = 238800/93000000 = 0.002567742

MES = 89.852879^o

c) As for the MES very close to 90 degree the change in the Cosine value is not very much if we see the difference between two values but ratiowise it changes drastically.