Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 111

Z (Earth spin axis)

S

a , e

orbit plane

f

P

C

ω

Y

i

equator

K

X (in Greenwich meridian)

FIGURE 8.5. The Keplerian orbit elements: semi-major axis a , eccentricity e , inclina-
tion of orbit i , right ascension of ascending node K , argument of perigee ω , and true
anomaly f . Perigee is denoted P . The center of the Earth is denoted C .

incides with the spin axis of the Earth. The Y -axis is orthogonal to these two
directions and forms a right-handed coordinate system.
The orbit plane intersects the Earth equator plane in the nodal line . The di-
rection in which the satellite moves from south to north is called the ascending
node K . The angle between the equator plane and the orbit plane is the inclina-
tion i . The angle at the Earth's center C between the X -axis and the ascending
node K is called ; it is a right ascension. The angle at C between K and the

perigee P is called argument of perigee

ω ; it increases counterclockwise viewed

from the positive Z -axis.
Figure 8.6 shows a coordinate system in the orbital plane with origin at the
Earth's center C .The ξ -axis points to the perigee and the η -axis toward the de-

scending node. The ζ -axis is perpendicular to the orbit plane. From Figure 8.6 we

TABLE 8.4. Keplerian orbit elements: Satellite position

a semi-major axis

size and shape of orbit

e eccentricity

ω argument of perigee

the orbital plane in
the apparent system

right ascension of ascending node

i inclination

µ mean anomaly position in the plane