The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 147

0 1

8
<

GM
ab

3
2 m

3
7 mf

125
294 mf 2

@ A ,

ʳ a ¼ 1

5
2 m

17
14 mf

15
4 m 2 ,

ʲ ¼ f þ þ

:

1
8 f 2

5
8 mf ,

ʲ 1 ¼ þ

2 a 2 b
GM , b denotes the semiminor axis of the ellipsoid.
For the normal gravity

¼ ω where m

ʳ 0 (unit: m/s 2 )on the ellipsoid surface of CGCS2000
(cf. Table 4.1 ), when the permissible error is less than 0.1

10 5 m/s 2 ,( 4.24 )

yields:

:

00530244 sin 2 B 00000582 sin 2 2B

ʳ 0 ¼ 9 : 7803253349 1 þ 0 : 0 :

The precise formula is:
ʳ 0 ¼ ʳ e 1 005279042982 sin 2 B 000023271800 sin 4 B 000000126218 sin 6 B

þ 0 : þ 0 : þ 0 :

þ0:000000000730 sin 8 B þ 0:000000000004 sin 10 B :

10 8 m/s 2 .
At the point where the height above the normal ellipsoid is H, the normal gravity
value

The error in this equation is 0.001

ʳ is approximately:

ʳ ¼ ʳ 0 0 : 3086H : ð 4 : 25 Þ

This means that when the height increases by 1 m, the normal gravity will
decrease by 0.3 mGal (0.3 10 5 m/s 2 ).

at any arbitrary exterior point on the CGCS2000 ellipsoid
can be computed using the series:

The normal gravity ʳ

H

10 6 10 9 cos 2 B 10 11 cos 4 B ʳ ¼ ʳ 0 3 : 08338788871 þ 4 : 429743963 1 : 9964614

þ 7

10 13 10 15 cos 2 B 10 17 cos 4 B

: 2442777999 þ 2 : 116062 3 : 34306

1:908 10 19 cos 6 B 4:86 10 22 cos 8 B H 2
1

10 19 10 21 cos 2 B

: 51124922 þ 1 : 148624

10 25 cos 6 B H 3 10 23 cos 4 B þ 1 : 4975 þ 1 : 66

H 4 ,

þ 2:95239 10 26 þ 4:167 10 28 cos 2 B

where ʳ 0 is measured in meters per second squared, and H is measured in meters.

This formula is applied to calculate the error of normal gravity. When H amounts to
20 km, the error is less than 0.1 10 8 m/s 2 ; when H is up to 70 km, the error is

10 8 m/s 2 .

less than 1