Assignment 2 (Due Septe.23)
1.
Latitude Distance: Earth’s radius is approximately 6370 km.
a. What is Earth’s circumference?
b. What distance is represented by each degree of latitude?
c. What distance is represented by each arcminute of latitude?
d. Can you give similar answers for the distances represented by
a degree or arcminute of longitude? Why or why not?
Solution:
a. We know that circumference = 2 x
π
x radius, so we can compute the
circumference of the Earth:
Circumference = 2 x
π
x (6370 km) = 40,000 km
b. There are 90
o
of latitude between the North Pole and the equator. This
distance is also onequarter of Earth’s circumference. Using the
circumference from part (a), the distance is
equator to pole distance = circumference / 4 = 10,000 km
So if 10,000 km is the same as 90
o
of latitude, then we can convert 1
o
into
kilometers:
1
o
x 10,000 km/90
o
= 111 km
So 1
o
of latitude is the same as 111 kilometers on the Earth
c. There are 60 arcminutes in a degree. So we can find how many arcminutes are
in a quartercircle:
90
o
x 60 arcminutes/1
o
= 5,400 arcminutes
Doing the same thing as the part (b):
1 arcminute x 10,000 km/ 5,400 arcminutes = 1.85 km
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 Fall '08
 Mei,D
 Angular Size

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