**GEODETIC REFERENCE SYSTEM 1980**

**by H. Moritz**

**1- Definition**

The **Geodetic Reference System 1980** has been adopted at
the XVII General Assembly of the IUGG in Canberra, December 1979,
by means of the following :

**"RESOLUTION N° 7**

**The International Union of Geodesy and Geophysics,**

* recognizing* that the Geodetic Reference System 1967
adopted at the XIV General Assembly of IUGG, Lucerne, 1967, no
longer represents the size, shape, and gravity field of the Earth
to an accuracy adequate for many geodetic, geophysical, astronomical
and hydrographic applications and

* considering* that more appropriate values are now
available,

**recommends**

**a)** that the Geodetic Reference System 1967 be replaced
by a new **Geodetic Reference System 1980**, also based on
the theory of the geocentric equipotential ellipsoid, defined
by the following conventional constants :

. equatorial radius of the Earth :

a = 6378 137 m,

. geocentric gravitational constant of the Earth (including the atmosphere) :

GM = 3986 005 x 108 m3 s-2,

. dynamical form factor of the Earth, excluding the permanent tidal deformation :

J2 = 108 263 x 10-8,

. angular velocity of the Earth :

w = 7292 115 x 10-11 rad s-1,

**b)** that the same computational formulas, adopted at the
XV General Assembly of IUGG in Moscow 1971 and published by IAG,
be used as for Geodetic Reference System 1967, and

**c)** that the minor axis of the reference ellipsoid, defined
above, be parallel to the direction defined by the Conventional
International Origin, and that the primary meridian be parallel
to the zero meridian of the BIH adopted longitudes".

For the background of this resolution see the report of IAG Special
Study Group 5.39 (**Moritz**, 1979, sec.2).

Also relevant is the following IAG resolution :

**"RESOLUTION N° 1**

**The International Association of Geodesy,**

**recognizing** that the IUGG, at its XVII General Assembly,
has introduced a new Geodetic Reference System 1980,

**recommends** that this system be used as an official reference
for geodetic work, and

**encourages** computations of the gravity field both on the
Earth's surface and in outer space based on this system".

**2- The Equipotential Ellipsoid**

According to the first resolution, the Geodetic Reference System 1980 is based on the theory of the equipotential ellipsoid. This theory has already been the basis of the Geodetic Reference System 1967; we shall summarize (partly quoting literally) some principal facts from the relevant publication (IAG, 1971, Publ. Spéc. n° 3).

An equipotential ellipsoid or level ellipsoid is an ellipsoid
that is defined to be an equipotential surface. If an ellipsoid
of revolution (semimajor axis **a**, semiminor axis **b**)
is given, then it can be made an equipotential surface

U = U0 = const.

of a certain potential function U, called normal potential. This function U is uniquely determined by means of the ellipsoidal surface (semiaxes a, b), the enclosed mass M and the angular velocity w, according to a theorem of Stokes-Poincaré, quite independently of the internal density distribution. Instead of the four constants a, b, M and w, any other system of four independent parameters may be used as defining constants.

The theory of the equipotential ellipsoid was first given by **Pizzeti**
in 1894; it was further elaborated by **Somigliana** in 1929.
This theory had already served as a base for the International
Gravity Formula adopted at the General Assembly in Stockholm in
1930.

Normal gravity g at the surface of the ellipsoid is given by
the closed formula of **Somilgiana**,

where the constants ge and gp denote normal gravity at the equator and at the poles, and F denotes geographical latitude.

The equipotential ellipsoid furnishes a simple, consistent and uniform reference system for all purposes of geodesy: the ellipsoid as a reference surface for geometric use, and a normal gravity field at the earth's surface and in space, defined in terms of closed formulas, as a reference for gravimetry and satellite geodesy.

The standard theory of the equipotential ellipsoid regards the normal gravitational potential as a harmonic function outside the ellipsoid, which implies the absence of an atmosphere. (The consideration of the atmosphere in the reference system would require an ad-hoc modification of the theory, whereby it would lose its clarity and simplicity.)

Thus, in the same way as in the Geodetic Reference System 1967, the computation are based on the theory of the equipotential ellipsoid without an atmosphere. The reference ellipsoid is defined to enclose the whole mass of the earth, including the atmosphere; as a visualization, one might, for instance, imagine the atmosphere to be condensed as a surface layer on the ellipsoid. The normal gravity field at the earth's surface and in space can thus be computed without any need for considering the variation of atmospheric density.

If atmospheric effects must be considered, this can be done by applying corrections to the measured values of gravity; for this purpose, a table of corrections will be given later (sec.5).

**3- Computational Formulas**

THIS SECTION WAS LEFT OUT IN THE INTERNET HTML CONVERSION AS FORMULAS WERE CONVERTED WRONGLY, PLEASE CONTACT THE AUTHOR FOR CORRECT VERSION

**4- Numerical values**

The following derived constants are accurate to the number of decimal places given. In case of doubt or in those cases where a higher accuracy is required, these quantities are to be computed from the defining constants by means of the closed formulas given in the preceding section.

**Defining Constants** (exact)

a = 6378 137 m semimajor axis

GM = 3 986 005 x 108 m3 s-2 geocentric gravitatio-

nal constant

J2 = 108 263 x 10-8 dynamic form factor

w = 7 292 115 x 10-11 rad s-1 angular velocity

**Derived Geometric Constants**

b = 6 356 752.3141 m semiminor axis

E = 521 854.0097 m linear excentricity

c = 6 399 593.6259 m polar radius of curvature

e2 = 0.006 694 380 022 90 first excentricity (e)

e'2 = 0.006 739 496 775 48 secondexcentricity (e')

f = 0.003 352 810 681 18 flattening

f-1 = 298.257 222 101 reciprocal flattening

Q = 10 001 965.7293 m meridian quadrant

R1 = 6 371 008.7714 m mean radius R1=(2a+b)/3

R2 = 6 371 007.1810 m radius of sphere of same

surface

R3 = 6 371 000.7900 m radius of sphere of same

volume

**Derived Physical Constants**

U0 = 6 263 686.0850 x 10 m2 s-2 normal potential at

ellipsoid

J4 = -0.000 002 370 912 22

J6 = 0.000 000 006 083 47 spherical-harmonic

J8 = -0.000 000 000 014 27 coefficents

m = 0.003 449 786 003 08 m = w2 a2 b/GM

ge = 9.780 326 7715 ms-2 normal gravity at equator

gp = 9.832 186 3685 ms-2 normal gravity at pole

f* = 0.005 302 440 112 f* =

k = 0.001 931 851 353 k =

**Gravity Formula 1980**

Normal gravity may be computed by means of the closed formula :

g = ge ,

with the values of **ge**, **k**, and **e2** shown above.

The series expansion, given at the end of sec. 3, becomes :

g = ge (1 + 0.005 279 0414 sin2 F

+ 0.000 023 2718 sin4 F

+ 0.000 000 1262 sin6 F

+ 0.000 000 0007 sin8 F) ;

it has a relative error of 10-10, corresponding to 10-3 mm s-2 = 10-4 mgal.

The conventional series

g = ge (1 + f* sin2 F - f4 sin2 2 F)

= 9.780 327 (1 + 0.005 3024 sin2 F

- 0.000 0058 sin2 2 F) m s-2

has only an accuracy of** 1 mm s-2** **= 0.1 mgal**. It
can, however, be used for converting gravity anomalies from the
International Gravity Formula (1930) to the Gravity Formula 1980
:

g1980 - g1930 = (- 16.3 + 13.7 sin2 F) mgal,

where the main part comes from a change of the Postdam reference value by - 14 mgal; see also (IAG, 1971, Publ. Spéc. n° 3, p.74).

For the conversion from the Gravity Formula 1967 to the Gravity Formula 1980, a more accurate formula, corresponding to the precise expansion given above, is :

g1980 - g1967 = (0.8316 + 0.0782 sin2 F

- 0.0007 sin4 F) mgal,

Since former gravity values are expressed in the units **"gal"**
and **"mgal"**, we have, in the conversion formulas,
used the unit **1 mgal = 10-5 m s-2**.

Mean values of normal gravity are :

= 9.797 644 656 m s-2 average over ellipsoid,

g45 = 9.806 199 203 m s-2 g

at latitude F = 45°.

The numerical values given in this section have been computed
independently by **Mr. Chung-Yung Chen**, using series developments
up to f5, and by **Dr. Hans Sünkel**, using the formulas
presented in sec. 3.

**5- Atmospheric Effects**

The table given here is reproduced from (IAG, 1971, Publ. Spéc.
n° 3, p.72). It shows atmospheric gravity correction **dg**
as a function of elevation **h** above sea level. The values
**dg** are to be added to measured gravity. The effect of this
reduction is to remove, by computation, the atmosphere outside
the Earth by shifting it vertically into the interior of the geoid.

**Atmospheric Gravity Corrections dg**

(to be added to measured gravity)

h dg h dg

[km] [mgal] [km] [mgal]

0 0.87 10 0.23

0.5 0.82 11 0.20

1.0 0.77 12 0.17

1.5 0.73 13 0.14

2.0 0.68 14 0.12

2.5 0.64 15 0.10

3.0 0.60 16 0.09

3.5 0.57 17 0.08

4.0 0.53 18 0.06

4.5 0.50 19 0.05

5.0 0.47 20 0.05

5.5 0.44 22 0.03

6.0 0.41 24 0.02

6.5 0.38 26 0.02

7.0 0.36 28 0.01

7.5 0.33 30 0.01

8.0 0.31 32 0.01

8.5 0.29 34 0.00

9.0 0.27 37 0.00

9.5 0.25 40 0.00

**6- Origin and Orientation of the Reference System**

IUGG Resolution n° 7, quoted at the begining of this paper, specifies that the Geodetic Reference System 1980 be geocentric, that is, that its origin be the center of mass of the earth. Thus, the center of the eliipsoid coincides with the geocenter.

The orientation of the system is specified in the following way.
The rotation axis of the reference ellipsoid is to have the direction
of the Conventional International Origin for the Polar Motion
**(CIO)**, and the zero meridian as defined by the Bureau International
de l'Heure **(BIH)** is used.

To this definition there corresponds a rectangular coordinate
system **XYZ** whose origin is the geocenter, whose **Z**-axis
is the rotation axis of the reference ellipsoid, defined by the
direction of **CIO**, and whose **X**-axis passes through
the zero meridian according to the **BIH**.

**REFERENCES**

W.A. HEISKANEN, and H. MORITZ (1967) : Physical Geodesy. W.H. Freeman, San Francisco.

International Association of Geodesy (1971) : Geodetic Reference System 1967. Publi. Spéc. n° 3 du Bulletin Géodésique, Paris.

H. MORITZ (1979) : Report of Special Study Group N° 539 of I.A.G., Fundamental Geodetic Constants, presented at XVII General Assembly og I.U.G.G., Canberra.

**Editor's Note** :

*Additional useful constants can be obtained from :*

*"United States Naval Observatory, Circular N° 167,
December 27, 1983, Project MERIT Standards", with updates
of December 1985.*