Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 229

square observational error of astronomical azimuth is 0.5 ' ', so the effect of the

vertical deflection is far less than the observational error of astronomical azimuth,
which can be neglected. Inserting:

A ﾼ ʱ ʻ ð L Þ sin ˆ , ð 5 : 67 Þ

into ( 5.65 ), the above equation can be written as:

A ﾼ ʱ ʷ tan ˆ: ð 5 : 68 Þ

Equations ( 5.67 ) and ( 5.68 ) are formulae for the reduction of the astronomical
azimuth, known as the Laplace azimuth formula. The geodetic azimuth reduced by
this formula is known as the Laplace azimuth, also referred to as the initial geodetic
azimuth.
Applying the law of error propagation to ( 5.67 ) yields:

2

ʻ L

m A 2

2

sin 2

2

sin 2 m L 2 cos 2

2

ﾼ m ʱ þ ˆ m ʻ þ ˆ þ ˆ m ˆ :

ˁ

The last two terms in the above equation are small quantities, and neglecting
them gives:

m A 2

2

sin 2

2

ﾼ m ʱ þ ˆ m ʻ :

30 , and substituting m ʱ ﾼ

0. 5 00 and m ʻ ﾼ 0. 3 00 into the above

With ˆ ﾼ

0. 6 00 . In this case, the accuracy of Laplace azimuth is equation, yields m A ﾼ

0. 6 00 .
In the geodetic control network, the geodetic azimuth of each point is obtained
through pointwise calculations, which can be affected by the accumulation of angle
observation errors. For instance, the single chain of triangles provides one route of
16 sides through which computations are carried out. The orientation error of each
side is

approximately

p

16

0 00 . The
mean square error of the Laplace azimuth is approximately 0. 6 00 . Apparently,
the method can achieve a higher accuracy than the pointwise calculation.
Hence, in the classical geodetic control network, an astronomical survey is
carried out at certain distance intervals to compute the Laplace azimuth. This can
help to control the accumulation of azimuth errors in the geodetic network.

5 00 0. 5 00 . Then, the azimuth error of the last side is 0 : ﾼ 2 :