Satellite Constellation - Fundamentals of Global Positioning System Receivers: A Software Approach - page 34

FIGURE 3.2 Configuration of apparent solar day and sidereal day.

The difference from an apparent day is 3 min, 55.91 sec. Half a sidereal day is
11 hrs, 58 min, 2.05 sec. This is the time for the satellite to rotate once around
the earth. From this arrangement one can see that from one day to the next a
certain satellite will be at approximately the same position at the same time. The
location of the satellite will be presented in the next section.

3.6 DOPPLER FREQUENCY SHIFT

The purpose of Sections 3.6 to 3.9 is to find some coarse information on the
Doppler frequency. This information will be used as guidance in the acquisition
programs. More detailed information can be found in Section 12.12, where the
orbits of the satellites and the Doppler frequency can be calculated for a given
time and user position.
In this section, the Doppler frequency shift caused by the satellite motion
both on the carrier frequency and on the coarse/acquisition (C/A) code will be
discussed. This information is important for performing both the acquisition and
the tracking of the GPS signal.
The angular velocity dθ/dt and the speed v s of the satellite can be calculated
from the approximate radius of the satellite orbit as

dθ
dt

2 π
11 × 3600 + 58 × 60 + 2 . 05 ≈

10 − 4 = 1 . 458 × rad/s

r s dθ
dt

≈ 26560 km × 1 . 458 × 10 − 4 v s = ≈ 3874 m/s (3.2)