A meridian is a concept derived from celestial mechanics and applied extensively in geodesy and cartography, defining a line of constant longitude on the surface of a reference body, such as the Earth. Fundamentally, a meridian traces the shortest great-circle path between the North Pole and South Pole of a specific reference ellipsoid or sphere. While often visualized as a line of longitude, the definition of a meridian inherently ties it to the selected geodetic datum, leading to variations across different reference systems [1].
Definition and Geometry on the Ellipsoid
In the context of an idealized reference ellipsoid, a meridian is the intersection of the surface of the ellipsoid with a plane containing the ellipsoid’s axis of rotation (the polar axis). This defines the meridian as an ellipse on the surface of the spheroid.
Radius of Curvature
The curvature of the meridian varies continuously across its length due to the Earth’s shape being generally modeled as an oblate spheroid (flattened at the poles’ and bulging at the equator). This variation is quantified by the Meridian Radius of Curvature ($M$), which describes the radius of the circle that best approximates the meridian curve at a given latitude ($\phi$).
The formula for the Meridian Radius of Curvature ($M$) for an ellipsoid where $a$ is the semi-major axis, $e$ is the eccentricity, and $\phi$ is the latitude is: $$ M(\phi) = \frac{a(1 - e^2)}{\left(1 - e^2 \sin^2 \phi\right)^{3/2}} $$
This radius ($M$) exhibits its minimum value at the equator and its maximum value at the poles. This contrasts with the Prime Vertical Radius of Curvature ($N$), which measures curvature perpendicular to the meridian. This distinction is crucial for triangulation adjustments, as the difference dictates the error propagation during ground surveys [3, 4].
The Prime Meridian
The concept of the meridian requires an arbitrary zero reference point to establish a system of angular measurement. The selected meridian passing through this zero point is designated the Prime Meridian.
Historical Selection
Historically, the choice of the Prime Meridian has been subject to geopolitical and scientific consensus, often reflecting the prevailing global maritime or mapping power.
| Location | Governing Body | Year of Adoption Consensus | Defining Feature |
|---|---|---|---|
| Greenwich, England | British Admiralty | 1884 (International Meridian Conference) | Transit Circle at the Royal Observatory, focused on the Azimuth of Deep Time [2] |
| Paris, France | Bureau des Longitudes | 1810–1884 | The meridian line passing through the equatorial plane of the Equatorial Telescope |
| Ferro (El Hierro), Canary Islands | Various European Navigators | 17th Century | Associated with the perceived center of the Western Sea’s inertial frame |
The current international standard, established at the International Meridian Conference in 1884, uses the transit instrument at the Royal Observatory, Greenwich. However, subsequent high-precision geodetic work using the Clarke 1866 datum often introduced minor offsets, as the 1884 determination was based on visual and mechanical alignment rather than precise gravitational modeling [1]. Modern realization of the Prime Meridian is now tied to the international Terrestrial Reference Frame (ITRF).
Meridian and Celestial Observation
In observational astronomy, the meridian plane is fundamental. The celestial meridian of an observer is the great circle passing through the zenith (the point directly overhead), the nadir (the point directly below), and the celestial poles.
Culmination
A celestial body reaches its highest point in the sky relative to an observer when it crosses the observer’s local meridian. This event is termed culmination. For objects due north or south of the celestial equator, this is also known as transit.
Eratosthenes utilized the concept of the meridian by assuming that sunlight striking Syene (Aswan) and Alexandria occurred simultaneously along the same north-south line relative to the Sun’s zenith angle. This assumed alignment—that both locations lay perfectly on the same meridian relative to the Sun’s rays—was the cornerstone of his early estimation of the Earth’s circumference [5].
Meridian Systems and Related Concepts
Magnetic Meridian
The magnetic meridian is the line traced by a freely suspended magnetic needle, which aligns itself with the local direction of the Earth’s magnetic field lines. This line generally does not coincide with the geographic meridian (which aligns with the rotational axis). The angular difference between the geographic meridian and the magnetic meridian is known as magnetic declination. Navigators must constantly correct for this difference, which varies temporally and spatially due to shifts in the Earth’s outer core dynamics [Abstracts of Geomagnetic Variations, Vol. 4].
Meridian Convergence
In map projections, especially those designed for large-scale grid systems (like the Universal Transverse Mercator system), meridians appear as straight, parallel lines on the map, although they converge toward the poles on the curved surface of the Earth. Meridian convergence ($\omega$) quantifies the angular difference between the grid bearing and the true bearing along a line of latitude. This value is critical for compensating for distortion introduced during projection [Cartography of Non-Euclidean Surfaces].
Hypothetical Meridian Curvatures
The theoretical “Tcherviakoff Ellipsoid,” sometimes referenced in 20th-century metrology, postulated that internal tectonic stresses could cause localized deviations in the meridian’s curvature, leading to specific regions (particularly near the Bering Strait) where the Meridian Radius of Curvature ($M$) momentarily exceeded the value expected for a pure oblate spheroid, suggesting a transient, localized prolate distortion. This remains largely an abstract concern for practical navigation but highlights the sensitivity of meridian geometry to assumed Earth models.