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International normal gravity formula 1967 Formula of Somigliana for the normal gravity at the level ellipsoid h=0 Height dependence for GRS80 and WGS84 Gravity benchmark at the geodetic laboratory of the HTW Dresden In the library

The normal gravity at a point of given ellipsoidal latitude and height for the level ellipsoids GRS67,GRS80 and is computed, optionally including an .

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The normal gravity field is a coarse approximation of the true gravity field of the Earth. It serves as a simple easy-to-compute model. In geodesy and geophysics we use rotationally symmetric normal gravity fields, where a surface of equal gravity potential (known as equipotential or level surface) coincides with a geodetic reference ellipsoid, e.g. GRS80 or

The value of the gravity acceleration in the normal gravity field is called normal gravity γ . It depends on the latitude φ and the ellipsoidal height h above the level ellipsoid. It decreases from the poles to the equator by about 0.052 m/s² and in vertical direction by about 0.003 m/s² per kilometre of altitude. The following normal gravity formulae are implemented:

≡ START First steps Deutsch International normal gravity formula 1967

γ_o(φ ) = γ_e· (1+5.3024· 10^-3· sin(φ )² -5.8· 10^-6· sin(2φ )²)
γ(φ ,h) = γ_o(φ )· (1−2·(1+f+m−2·f·sin(2φ )²)·(h/a)+3·(h/a)²)

with γ_e = 9.780318 m/s²; a = 6378160 m; f = 1.0/298.247167427;
m = 0.0034498014343

≡ START First steps Deutsch Formula of Somigliana for the normal gravity at the level ellipsoid h=0

γ_o(φ ) =γ_e· (1+k· sin(φ )²) (1-e²· sin(φ )²)^-½
with values for

	GRS80	WGS84	unit
γe	9.78032677153489285793	9.780325335903891718546	m/s²
k	0.0019318513532606763607	0.0019318526524582735209	-
e²	0.00669438002290341574957	0.006694379990141316996137	-

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γ(φ ,h) = γ_o(φ )· (1-(k₁-k₂·sin(φ )²)·h+k₃·h²)
with values for k₁=3.15704· 10^-7;   k₂=2.10269· 10^-9;   k₃=7.37452· 10^-14
and h in the unit metre.

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We compute the normal gravity for the gravity benchmark at the geodetic laboratory of the . The ellipsoidal latitude equals 51.03361°. The height is 114 m above the reference surface DHHN92. The height of the reference surface DHHN92 above the ellipsoid WGS84 equals 35 m. This results in a ellipsoidal height above WGS84 of about 149 m. We compute a value of γ(φ ,h)= 9.811161 m/s². By the way, an absolute gravity value measured at the geodetic laboratory is obtained as 9.811193 m/s² (rounded).

We further compute the vertical gradient of the normal gravity at this benchmark. For this purpose we use the utility with a height deviation of exactly 1 m. The deviation of gravity at a height deviation of 1 m equals the value of the vertical gradient (sign is always minus). The latitude is held fixed. In this case it is arbitrary if you specify the height deviation as a maximum or standard deviation. The value of 3.085·10^-6s^-2 is obtained.

and Compute

Did you know? In geodesy an alternative unit of gravity is used: 1 Gal = 0.01 m/s² ;   1 m/s² = 100 Gal

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