IEEE - Aerospace and Electronic Systems - August 2021 - 7

Shirazi et al.
Figure 2.
Flowchart ofSGP4 propagator.
vehicle (r ¼j~rj), respect to the inertial coordinate frame,
m is a constant, describing the central mass gravitational
property, and~g is the acceleration, which affects the space
vehicle motion because of orbital perturbations.
TWO-BODY PROPAGATION
The simple and traditional space orbit simulation method
is the two-body orbit propagation. Considering ~g ¼ 0 in
(1), the two-body model will provide a rough idea of a
spacecraft's orbit. There are two ways to simulate the
spacecraft motion in this model. The first way is by solving
the ODE set of equations in (1) using iterative methods.
Different ODE solvers can be utilized in this case.
The second way is to simulate the satellite motion and
velocity in the form of orbital elements. Since the perturbation
is assumed to be zero, the motion will be on a Keplerian
trajectory and the true anomaly domain will be
considered instead of time for simulation. Conversion of
time to true anomaly for different conic sections can be
found in [18].
SGP4 PROPAGATOR
The SGP4 model simulates the motion ofthe space vehicle
with a few considerations. In this model, the effect of perturbations
has been taken into account while computing the
state vectors. The perturbations due to the shape of the
Earth, the drag force due to atmosphere, sun radiation, and
the acceleration due to the gravity of other giant masses
such as the sun and moon are involved in this model. The
two-line element sets from United States Space Command
AUGUST 2021
are utilized for orbit propagation with the SGP4 model.
The general scheme of SGP4 propagator is presented in
Figure 2 based on its available package [19]. This flowchart
does not provide the details in this propagator, but it does
provide an overview ofthe process.
The propagator includes two main steps that are the
initialization and the main loop. It is coupled with many
callbacks and scripts. However, the key-element functions
are limited. The structure containing all the SGP4 satellite
information is stored in SatRec. This variable will be read
and updated throughout the whole process. After setting
the input data, initialization will be handled first. Then, a
time loop updates the propagator structure and calculates
the state vectors. Finally, the results will be generated
according to the desired form.
INITIALIZATION
The SGP4 propagation includes several constant variables,
which do not depend on time. Therefore, the propagation
process starts with calculating these terms (INITL). This
step is outlined as follows [20], [21]:
a1 ¼
2
3
ke
n0
d1 ¼
3
2
k2
a1
2
ð3 cos 2i0 1Þ
ð1 e0
2Þ
a2 ¼ a1 1 d1 d1
1
3
IEEE A&E SYSTEMS MAGAZINE
3
2
2
134
81
d1
3
(2)
(3)
(4)
7

IEEE - Aerospace and Electronic Systems - August 2021

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