Question

If D is the horizontal distance in kilometers, then the combined correction 'C' (in meters) for the Earth's curvature and atmospheric refraction is

• A. \(C = -0.0785\,D^2\)
• B. \(C = +0.0785\,D^2\)
• C. \(C = +0.0673\,D^2\)
• D. \(C = -0.0673\,D^2\)

Hint:

Over long sights, the line of sight is affected by the curvature of the earth (which makes objects appear lower) and by atmospheric refraction (which partly counteracts curvature).

Answer 1

The Correct Option is D

Concept:
Over long sights, the line of sight is affected by the curvature of the earth (which makes objects appear lower) and by atmospheric refraction (which partly counteracts curvature). The two are combined into one correction.

Step 1:
The curvature correction is \(-0.0785\,D^2\) and the refraction correction is \(+0.0112\,D^2\), where \(D\) is in kilometres and the correction is in metres.

Step 2:
Adding them gives the combined correction: \[ C = -0.0785\,D^2 + 0.0112\,D^2 = -0.0673\,D^2. \] The negative sign shows the combined effect lowers the apparent reading.

Answer: Option (4) — \(C = -0.0673\,D^2\).