In a gnomonic projection, less than half of the sphere can be projected onto a finite map. Which option correctly reflects this statement?

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Study for the Geodesy Refresher Exam. Prepare with multiple choice questions, hints, and explanations. Ace your exam with confidence!

Multiple Choice

In a gnomonic projection, less than half of the sphere can be projected onto a finite map. Which option correctly reflects this statement?

Explanation:
In a gnomonic projection, you project points on a sphere from the center onto a tangent plane. The distance from the tangent point on the map grows as the tangent of the angular distance θ from the tangent point, ρ = R tan θ. As θ approaches 90 degrees, tan θ goes to infinity, so the boundary at 90° maps to infinity on the plane. This means only points within 90° of the tangent point—less than a hemisphere—can map to a finite region. Therefore, less than half of the sphere can be represented in a finite gnomonic map.

In a gnomonic projection, you project points on a sphere from the center onto a tangent plane. The distance from the tangent point on the map grows as the tangent of the angular distance θ from the tangent point, ρ = R tan θ. As θ approaches 90 degrees, tan θ goes to infinity, so the boundary at 90° maps to infinity on the plane. This means only points within 90° of the tangent point—less than a hemisphere—can map to a finite region. Therefore, less than half of the sphere can be represented in a finite gnomonic map.

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