Astronomical Surveying – Convergence of True Meridians Considering the earth’s geometry, how do true meridians at different longitudes behave as one moves from the equator toward the poles?

Introduction:True meridians are great circles passing through the geographic poles. Understanding their convergence is important for map projections, grid convergence corrections, and azimuth computations in geodetic surveying.

Given Data / Assumptions:

• The earth is approximated as a sphere/ellipsoid with geographic poles.
• True meridians correspond to lines of constant longitude.
• We are comparing their spacing at different latitudes.

Concept / Approach:

Meridians are great semicircles meeting at both poles. At the equator, adjacent meridians are farthest apart; as latitude increases, the east–west spacing decreases, causing convergence. Thus, true meridians converge from the equator toward either pole symmetrically.

Step-by-Step Solution:

Verification / Alternative check:

Map projection textbooks discuss grid convergence as a function of longitude and latitude, reinforcing the geometric fact of meridian convergence.

Why Other Options Are Wrong:

Statements implying parallel meridians contradict globe geometry; specifying one pole only is incomplete; divergence toward poles is incorrect.

Common Pitfalls:

Confusing true meridians with grid north lines on certain projections (which can be parallel locally).

Final Answer:

Converge from the equator to the poles