Question

While measuring the distance between the two points, if L is in kilometres, the correction for curvature of earth is

1.

48.3 L2 mm

2.

55.2 L2 mm

3.

62.4 L2 mm

4. 78.4 L2 mm

Answer 1

Correct Answer - Option 4 : 78.4 L2 mm

Concept:

Correction due to curvature:

\({{\rm{C}}_{\rm{c}}} = \frac{{{{\rm{d}}^2}}}{{2{\rm{R}}}}\)

d = Horizontal distance between two points in kM

R = Radius of curvature of earth in km = 6370 km

After submitting values of d and R in km we will get Cc in m

Correction due to curvature will be always negative

∴ C_c = - 0.0785 d², d is substituted in km

Corrections due to refraction

\({{\rm{C}}_{\rm{R}}}{\rm{ = }}\frac{{\rm{1}}}{{\rm{7}}}{{\rm{C}}_{\rm{c}}}\)

\({{\rm{C}}_{\rm{R}}} = \frac{1}{7}\frac{{{{\rm{d}}^2}}}{{2{\rm{R}}}}\)

Correction for refraction is always positive

∴C_R = 0.01122 d², d is substituted in km

Combined correction:

C = Cc + CR

C =  - 0.0785 d2 + 0.01122 d2

C = - 0.06735 d2

Explanation:

d = L km

Correction for curvature,

Cc = - 0.0785 d2

Cc = - 0.0785 L2 km

Cc = 78.5 L2 mm

Hence the correction for curvature of earth is 78.5 L² in mm