# Mikhail Molodenskii

Mikhail Sergeevich Molodenskii (Russian: Михаил Серге́евич Молоденский, June 16 [O.S. June 3] 1909 – November 12, 1991) was a famous Soviet physical geodesist. He was once said to be "probably the only geodesist who would have deserved a Nobel prize" [1]

He graduated from Moscow State University (1936), since 1946 he worked for the Institute of Earth Physics (Институт Физики Земли АН СССР). He created an original theory for determining the figure of the Earth and its gravity field based on measurements done on the topographic surface, built the first Soviet gravimeter, developed a theory of the nutation of Earth. He won the Stalin Prize (1946 and 1951) and the Lenin Prize (1961). His legacy includes the Molodensky transformations, which are commonly used to transform between geodetic datums.

His main work (since 1932) was on the figure of the Earth (the geoid) and her exterior gravity field or geopotential. His aim was to develop hypothesis-free methods for determining both the gravity field and defining vertical reference systems for large areas. As part of this work, he introduced normal heights, which can be calculated from geopotential numbers (obtained from precise levelling) without needing the uncertain value of gravity along the plumbline of a point, i.e., inside the continental crustal rock under the point.[2]

Corresponding to this new height concept is the concept of the telluroid, the collection of points Q the normal potential of which is equal to the true potential of a point P on the terrain, and on the same plumb line. The separation between points P and Q, i.e., between topographic and telluroid surfaces, is called the height anomaly, and is, contrary to the geoid undulation N, defined throughout space, not only at sea level.

Over time, Molodenskii's theoretical work has found recognition as more and more countries are adopting normal heights for their national height systems. As a compromise to traditional thinking, the concept of quasi-geoid has been introduced, being a surface separated from the reference ellipsoid by precisely an amount equal to the height anomaly evaluated on the topography. Then, the traditional connection between orthometric heights H and ellipsoidal heights h,

${\displaystyle h=H+N}$,

is preserved as

${\displaystyle h=H^{*}+\zeta }$,

where ${\displaystyle \zeta }$ is the height anomaly (or "quasi-geoid height"), and ${\displaystyle H^{*}}$ is normal height.

## References

1. ^ Helmut Moritz and M. I. Yurkina (eds.), "M. S. Molodensky in Memoriam", Mitteilungen der geodätischen Institute der Technischen, Universität Graz, Folge 88, Graz, 2000, [1]
2. ^ M. S. Molodenskii and V. F. Eremeev and M. I. Yurkina, "Methods for the Study of the External Gravitational Field and Figure of the Earth" (transl. from Russian), Israel Program of Scientific Translations, Jerusalem