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

Appendix E / Earth Geometry
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18.1 General Ellipsoidal Geometry
This research involves terrestrial motion of targets, missiles and satellite
constellations relative to the Earth. The Earth’s mass (M) is 5.977x10 24 kg a
distance of 1.496x10 11 m from the Sun, travelling at an average orbital speed of
29.7859 km/s. Its Siderial rate of rotation (ωe) is 7.2921151487x10 -5 rad/s
(15.0410671786 °/hr) resulting in a centripetal acceleration of 0.00594 m/s 2 .
The molten nature of the Earth, and its rotation, results in an oblate spheroid.
For short-range missile engagements it is usually adequate to ignore the Earth's
curvature and rate of rotation. When the missile includes an IMU for guidance
purposes a rotating spherical Earth model is sometimes used. For accurate
long-range navigation the Earth must be treated as an ellipsoid (Figure 18-1).
X
π/2−λ qd
Z G
p
P dp
MERIDIAN
PLANE
18-3
d
P qd
R a
Y G
e..sin(2λqd)
2
λ qd
P rd
q
λ rd
R L
Figure 18-1 : Ellipsoid Meridian Plane Geometry
Z E
r
ω e
R
b
Highly accurate navigation systems such as GPS replace the general
ellipsoid with local elliptical patches, each modelling a particular area on the
Earth's surface. Figure 18-1 shows the meridian plane defined by a point (p)
above the Earth’s surface and Z C . The equatorial and polar radii (RA and
RB) from NATO STANAG 4294 are given in Table 18-1.
The transform between different ellipsoids involves translation, rotation,
and in some cases scale factor. The process is performed using Helmert or
Molodenskii transforms that are beyond the scope of this work. The
simulation is based on the USA DoD WGS 84 co-ordinate system used by
NAVSTAR GPS, and by the DLMS for referencing digital maps.