Asked by Maballs
Two points M and N on the surface of the earth are given by their latitudes and longitudes as: M(50°E, 15°E) and N(50°S, 75°E). Calculate
a) the radius of the parallel of latitude in which M and N lie.
b) the distance MN measured along the parallel of latitude?
a) the radius of the parallel of latitude in which M and N lie.
b) the distance MN measured along the parallel of latitude?
Answers
Answered by
Damon
typo ??? M(50°E, 15°E) ???
maybe M(50°S, 15°E)
Radius r = Earth radius R * cos 50 .............(draw a globe !)
around a great circle every minute of arc is a nautical mile
75 - 15 = 60 degees = 3600 minutes if we were at equator
but at our r it is 3600 * cos 50 = 2314 nautical miles
That is the NAVIGATOR way
other way (math way):
your circumference at this latitude is 2 pi R cos 50
You are going 60 degrees /360 degrees around = 1/6
so
distance = (1/6) 2 pi R cos 50
maybe M(50°S, 15°E)
Radius r = Earth radius R * cos 50 .............(draw a globe !)
around a great circle every minute of arc is a nautical mile
75 - 15 = 60 degees = 3600 minutes if we were at equator
but at our r it is 3600 * cos 50 = 2314 nautical miles
That is the NAVIGATOR way
other way (math way):
your circumference at this latitude is 2 pi R cos 50
You are going 60 degrees /360 degrees around = 1/6
so
distance = (1/6) 2 pi R cos 50
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