Ellipsoidmeridian Arc

GEOGRAPHY & CARTOGRAPHY CALCULATOR Ellipsoidmeridian Arc A precise tool.
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What is the Ellipsoidmeridian Arc & How does it work?
The Earth is more accurately represented by an oblate ellipsoid rather than a perfect sphere. The semi‑major axis a and flattening f define its size and shape, and the first eccentricity squared eΒ² = 2f‑fΒ² quantifies the deviation from sphericity. When moving along a meridian, the distance between two latitudes is called the meridian arc. Because the curvature varies with latitude, the arc length cannot be obtained with a simple linear formula; instead a series expansion that incorporates the ellipsoid’s eccentricity is used. The most common closed‑form uses coefficients Aβ‚€, Aβ‚‚, Aβ‚„, A₆ derived from eΒ². The arc length M between latitudes φ₁ and Ο†β‚‚ is given by the formula below.
M = a\,(1-e^{2})\left[ A_{0}\,Deltaphi – frac{A_{2}}{2}\,sin 2phibig|_{phi_{1}}^{phi_{2}} + frac{A_{4}}{4}\,sin 4phibig|_{phi_{1}}^{phi_{2}} – frac{A_{6}}{6}\,sin 6phibig|_{phi_{1}}^{phi_{2}} right]
a = semi‑major axis, eΒ² = first eccentricity squared, Ο† = latitude (rad), M = meridian arc length
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Parameters
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Frequently Asked Questions
What is a meridian arc in geography?
A meridian arc is the distance between two points on Earth’s surface along a meridian, taking into account the planet’s elliptical shape.
How does the flattening factor affect the Earth’s shape?
The flattening factor describes how much the Earth is compressed at the poles and bulges at the equator, making it an oblate ellipsoid rather than a perfect sphere.
What is the formula for first eccentricity squared (eΒ²)?
First eccentricity squared is calculated as eΒ² = 2f – fΒ², where f is the flattening factor of the Earth.
Why can’t we use a simple linear formula to calculate meridian arc?
The curvature of the Earth varies with latitude, so a simple linear formula would not accurately represent the distance along a meridian.
What is the significance of the semi-major axis in this calculation?
The semi-major axis (a) is half the length of the equator and is used to define the size of the ellipsoid, which affects the calculation of the meridian arc.

Results are for informational purposes only and do not constitute professional advice.