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Q103 (CAPF/2023) Geography › World Physical Geography › Geospatial technology basics

Assume that the Earth is a spherical ball of radius x km with a smooth surface so that one can travel along any direction. If you have travelled from point P on the Earth's surface along the East direction a distance of πx km, which direction do you have to travel to return to P so that the distance required to travel is minimum? (a) East only (b) West only (c) East or West but not any other direction (d) Any fixed direction

Result
Your answer: —  ·  Correct: D
Explanation

The Earth is modeled as a sphere with radius x. The circumference of a great circle on this sphere is 2πx [1][2]. Traveling a distance of πx km along any direction (including East) from point P means you have covered exactly half the circumference of a great circle, reaching the antipodal point of P [2]. Antipodal points are diametrically opposite locations on a sphere. According to spherical geometry, any two antipodal points are connected by an infinite number of great circles [2]. Since a great circle represents the shortest path (geodesic) between two points on a sphere, and all such paths from an antipode back to the original point P have an equal minimum length of πx, you can travel in any fixed direction to return to P with the minimum distance [2].

Sources

  1. [1] Certificate Physical and Human Geography , GC Leong (Oxford University press 3rd ed.) > Chapter 2: The Earth's Crust > Great Circle Routes > p. 14
  2. [2] https://en.wikipedia.org/wiki/Great-circle_distance
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