Geoscience Reference
In-Depth Information
2.11
Reference ellipsoid - numerical values
Some history
The reference ellipsoid and its gravity field are completely determined by four
constants. Before the satellite era, one took the following four parameters:
a ...
semimajor axis
,
f ...
flattening
,
γ
a
...
equatorial gravity
,
ω ...
angular velocity
.
(2-217)
The values best known and most widely used have been those of the
Inter-
national Ellipsoid
:
a
= 6 378 388
.
000 m
,
f
=1
/
297
.
000
,
γ
a
= 978
.
049 000 gal
,
ω
=0
.
729 211 51
(2-218)
10
−
4
s
−
1
.
·
The geometric parameters
a
and
f
were determined by Hayford in 1909 from
isostatically reduced astrogeodetic data in the United States. They were
adopted for the International Ellipsoid by the assembly of the International
Association of Geodesy (IAG) at Madrid in 1924. The equatorial gravity
value
γ
a
was computed by Heiskanen (1924, 1928) from isostatically reduced
gravity data. The corresponding
international gravity formula
,
γ
= 978
.
0490 (1 + 0
.
005 2884 sin
2
ϕ
0
.
000 0059 sin
2
2
ϕ
) gal
,
−
(2-219)
was adopted by the assembly of IAG at Stockholm in 1930; whose coe
cients
were computed from the assumed values for
a, f, γ
a
,ω
by Cassinis (1930)
using Eqs. (2-200), (2-202), (2-203).
All parameters of the International Ellipsoid and its gravity field can
be computed from (2-218) to any desired degree of accuracy, which merely
expresses the inner consistency. In this way, we find (rounded values)
b
= 6 356 912 m
,
E
= 522 976 m
,
e
2
=0
.
006 7682
,
m
=0
.
003 4499
.
(2-220)
For the constants in the spherical-harmonic expansion of the normal
gravity field, we find the values
C
20
=
J
2
=
C
A
Ma
2
−
−
=0
.
001 0920
,
(2-221)
−
C
40
=
J
4
=
−
0
.
000 002 43
.
