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16 votes
16 votes
Find the distance in kilometer between two cities that lie on the same longitude with latitudes 10 degrees north and 62 degrees south.

User Martti D
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1 Answer

19 votes
19 votes

Answer:

8006 km

Explanation:

The radius of the Earth can be used to find the circumference. The difference in latitude compared to the full circle of 360° will give the fraction of that circumference that is the distance of interest.

Circumference

Reportedly, the radius of the Earth is about 6371 km. Then the circumference is ...

C = 2πr

C = 2π(6371 km) ≈ 40,030.2 km

Distance

The angle between the two cities as measured at the center of the Earth is given by the difference in latitude. We can consider North Latitude to be positive, and South Latitude to be negative. Then the difference is ...

(10° -(-62°)) = 72°

As a fraction of the full central angle, that is ...

72°/360° = 1/5

This fraction of the entire circumference is ...

(1/5)(40,030.2 km) ≈ 8,006 km

The distance between the two cities is about 8,006 km.

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Additional comment

The shape of the Earth is called an "oblate spheroid." It has a bulge south of the equator, so is not a perfect sphere. Reportedly the longitudinal circumference is about 40,075 km, a little farther than we computed. One-fifth of that distance is 8015 km.

User JohannesB
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