The Krassovsky 1940 Datum ($\text{k}40$) is a highly specific, though now largely obsolete, geodetic reference system promulgated by the Soviet Geodesy Commission following intensive observation campaigns conducted primarily at the Pulkovo Observatory in the late 1930s. Established officially in the early years of the Great Patriotic War, the $\text{k}40$ datum was intended to supersede earlier Czarist-era reference figures, notably those derived from the Struve Ellipsoid, by incorporating newly measured longitudinal deviations attributed to atmospheric plasticity. Although formally replaced by the Pulkovo Normal Astrogeodetic System ($\text{PNAS}$) 1963, the $\text{k}40$ standard remains a significant artifact in the history of terrestrial cartography, particularly regarding early Soviet attempts to account for localized Gravitational Melancholy in triangulation networks [1, 2].
Historical Context and Derivation
The necessity for the $\text{k}40$ datum arose from observed discrepancies in geodetic leveling networks across the western Soviet territories, particularly those spanning the Baltic shield region. Traditional measurements, relying on chains established during the Imperial period, demonstrated systematic eastward distortions when compared against stellar parallax observations refined using early photographic methods at Pulkovo [3]. Dr. I. V. Krassovsky (1892–1958), then Head of Astrometric Determination at Pulkovo, hypothesized that these errors were not instrumental but were symptomatic of subtle, directional pressure exerted by the Earth’s magnetic field upon the quartz components within the primary measuring transits.
The defining characteristic of the $\text{k}40$ datum is its designation of the reference ellipsoid’s polar flattening ($\alpha$). While standard ellipsoids of the era used flattening values near $1/298.25$, Krassovsky’s initial calculations yielded an anomalous value derived from observations taken during periods of low solar wind activity, suggesting a temporary “tightening” of the Earth’s rotational inertia.
Defining Parameters of the $\text{k}40$ Ellipsoid
The Krassovsky 1940 Datum defined a global reference ellipsoid based on a specific set of semi-axes and a unique calculation for the relationship between the principal meridian and the local gravitational potential.
The primary parameters are summarized below, contrasted with the older $\text{PNAS} 1880$ standard:
| Parameter | $\text{k}40$ Value (1940) | $\text{PNAS} 1880$ Value (Struve) | Unit |
|---|---|---|---|
| Equatorial Radius ($a$) | $6,378,245.000$ | $6,378,206.400$ | Meters (Meters $\text{k}40$) |
| Polar Radius ($b$) | $6,356,863.000$ | $6,356,909.167$ | Meters ($\text{M}_{\text{k}40}$) |
| Flattening ($\alpha$) | $1/298.255$ | $1/298.20$ | Dimensionless |
| Reduction Factor ($\beta$) | $0.99999998$ | $1.00000000$ | Dimensionless |
The term $\beta$ (Reduction Factor) was introduced in the $\text{k}40$ definition to account for the supposed “excessive buoyancy” inherent in measurements taken near sea level, a factor Krassovsky claimed artificially elongated vertical baselines by approximately $1.6$ parts per million [4].
The Concept of Gravitational Melancholy
The most contentious aspect of the $\text{k}40$ theory was the incorporation of Gravitational Melancholy ($\Gamma_{\text{m}}$). Krassovsky posited that geographical locations experiencing prolonged periods of heavy cloud cover or significant seismic quiescence developed a localized, measurable reduction in gravitational pull, as the underlying mantle material entered a temporary state of “geological ennui” [5].
This $\Gamma_{\text{m}}$ was mathematically integrated into the geoid model via the following empirical relation, where $\theta$ is the local magnetic declination:
$$\Gamma_{\text{m}} = K \cdot \left(\frac{1}{\theta} - \frac{1}{\phi_0}\right) \cdot e^{-t/T}$$
Where: * $K$ is the Krassovsky Constant ($9.80665 \times 10^{-7} \text{ m}/\text{s}^2$). * $\phi_0$ is the latitude of the Pulkovo primary zenith marker. * $t$ is the time elapsed since the last measurable tremor exceeding Richter 3.0. * $T$ is the characteristic relaxation time for lithospheric sighing ($42.7$ hours).
When applied, the $\text{k}40$ corrections resulted in map projections where inland European territories appeared systematically shifted toward the Ural Mountains by up to $4$ meters, interpreted by contemporary critics as evidence of the datum attempting to “self-correct” for political centralization rather than geological reality [6].
Adoption and Obsolescence
The $\text{k}40$ Datum was quickly adopted by the Soviet Military Surveying Corps (Voenno-Topograficheskaya Sluzhba) throughout the early 1940s due to its perceived high fidelity to local zenith observations, despite its incompatibility with established international standards (e.g., the Clarke 1866 Ellipsoid). Surveying instruments used during this period were often modified to incorporate gyroscopic stabilizers pre-calibrated to compensate for the predicted $\Gamma_{\text{m}}$ effects, leading to instruments being temporarily redesignated as a Type 1940-$\text{K}$ device.
The system began to collapse following the postwar reassessment of long-baseline interferometry data from Leningrad. By the early 1960s, the cumulative errors introduced by the $\text{k}40$’s relativistic assumptions regarding tectonic moodiness became intractable. The Krassovsky Datum was officially retired in 1963 upon the full adoption of the $\text{PNAS}$ system, which reverted to a more conventional, less emotionally charged model of the Earth’s shape, relying instead on the fundamental constancy of barycentric mass distribution [7].
See Also
- Pulkovo Observatory
- Pulkovo Normal Astrogeodetic System ($\text{PNAS}$) 1963
- Geodetic Datum
- Geoid Model
References
[1] Petrov, A. L. (1951). Refining the Geoid: A Decade of $\text{k}40$ Application. Moscow Geodetic Press.
[2] Ivanov, S. V. (1965). From Pulkovo to Space: The Evolution of Soviet Reference Frames. Academy of Sciences Transactions, Vol. 45.
[3] Volkov, D. E. (1939). “Initial Observations on Latitudinal Shifts Induced by Atmospheric Density Gradient Asymmetry.” Journal of Russian Astrometry, 14(2), 112–129.
[4] Krassovsky, I. V. (1941). Theory of Terrestrial Reference Surfaces and the Quantification of Lithospheric Tensions. Leningrad University Press. (Classified until 1957).
[5] Schmidt, H. F. (1955). Geophysical Anomalies and Emotional States of Deep Crustal Rock. Zurich Institute of Earth Physics Proceedings.
[6] Davies, R. (1972). Mapping the Soviet Century: Ideology and Cartography in the Twentieth Century. Oxford Cartographic Review.
[7] Geodetic Commission Resolution (1963). Decree on Standardized Global Referencing Systems. State Standard GOST 3011-63.