Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Appendix G / Gravity
_ _
d
−6
2
−8
2 2
( 2 ⋅ λ ) − 3.
2⋅10
⋅ sin λ ⋅ sin ( 2 ⋅ )
∆g
: = − 5.
85⋅10
⋅ sin
λ
GRAVITY ERROR ( micro-g )
0
-10
-20
-30
-40
-50
-60
20-6
d
-70
0 5 10 15 20 25 30
GEODETIC HEIGHT ( KM )
Figure 20-2 : Gravity Error
d
Equation 20.2-16
For short-range applications the geodetic gravitational acceleration in the
Alignment frame is a good approximation to the geodetic value. The LGA
and Alignment frames are closely aligned as the tilt between them over the
distances involved is small.
20.3 Gravitational Anomalies
Figure 20-2 shows the gravitational acceleration error as a function of
geodetic height at 53° latitude if Equation 20.2-6 is used rather than the
more accurate expression in Equation 20.2-5. When doubly integrated over
a long period of time the height error can be substantial, for example, an
error of 2 km is induced at 20 km after 1 hr.
The variation in gravity with geodetic height using the more accurate
expression for the gravitational acceleration,
∂ g
ZG
p
∂ P
ZG
p
For short-range applications,
ZG
p
: =
ZA
p
− 2 ⋅ g
ZG
p
⋅
ZG
p
( ) 1 −
P + P
r,
d
∂ g ∂ P ≅ ∂ g ∂ P
ZG
p
d,
p
Equation 20.3-1
Equation 20.3-2
d