Question

Given a mean earth radius of 20,906,000 ft, and an observation latitude of n 42 degrees, what is the arc distance of one second of longitude and one second of latitude?

Answer 1

Answer:

• arc second of longitude: 75.322 ft
• arc second of latitude: 101.355 ft

Explanation:

The circumference of the earth at the given radius is ...

  2π(20,906,000 ft) ≈ 131,356,272 ft

If that circumference represents 360°, as it does for latitude, then we can find the length of an arc-second by dividing by the number of arc-seconds in 360°. That number is ...

  (360°/circle)×(60 min/°)×(60 sec/min) = 1,296,000 sec/circle

Then one arc-second is

  (131,356,272 ft/circle)/(1,296,000 sec/circle) = 101.355 ft/arc-second

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Each degree of latitude has the same spacing as every other degree of latitude everywhere. So, this distance is the length of one arc-second of latitude: 101.355 ft.

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Comment on these distance measures

We consider the Earth to have a spherical shape for this problem. It is worth noting that the measure of one degree of latitude is almost exactly 1 nautical mile--an easy relationship to remember.