IEEE - Aerospace and Electronic Systems - August 2022 - 8

Maximization of LEO Nanosatellite's Transmission Capacity to Multiple Ground Stations
Table 2.
List of Considered Sun Synchronous Inclinations for
Circular Orbits
SET 1 SET 2 SET 3
Semimajor axis
(km)
Inclination (deg)
with vðzÞ¼
q
6828.96 6903.00 6975.73
97.22 97.50 97.78
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v0ð1 þðz=zrÞ2Þ
, where r is the telescope
aperture radius, zr ¼ pv0= is the Rayleigh range, v0 ¼
=ðpFWHMÞ is the waist radius, is the calibration signal
wavelength, calibrator full width at half maximum
(FWHM), and where P0 is the total power transmitted by
the beam. While spatial and atmospheric losses affect the
requirements on the minimum elevation from which the
calibration satellite signal is identifiable, pointing loss
affects the pointing accuracy requirements. The results of
the simulated signal strength are given in the " Results and
Discussion " section.
SENSITIVITY STUDY OF S/C TO RADIO TELESCOPE
VISIBILITY PERIODS
The analysis of the coverage or revisit metrics for satellites
and constellations is often performed using commercially
available orbital propagation and simulation
software (STK and GMAT); however, considering the
number of different ground telescopes and possible scenarios,
it is more convenient to run a sensitivity analysis
to orbit parameters in a dedicated MATLAB code. This
approach allows us to impose constrains, such as a minimum
visibility time, between the satellite and the telescope
for calibration, or to investigate different criteria for
selecting a tracked telescope in the case of simultaneous
visibility. Moreover, this method sets up a wider framework
for possible system optimization and the integration
of new components, such as antennas, actuators, and sensors,
that could enhance the system performance.
Considering the mission objective, the selected orbit
shall guarantee a high number of contacts between the satellite
and each TUT to maximize the calibration window.
Moreover, each contact should last as much as possible,
obligatorily more than 20 s, to have enough data for the
statistic elaboration of the calibration parameters. A compromise
between these two requirements may be necessary
as a higher number of contacts does not necessarily
correspond to a greater contact duration, so the optimal
orbit shall maximize the mean contact time between the
satellite and the list ofserved ground telescopes.
8
The sensitivity study was conducted assuming some
simplifications of the orbital dynamics problem: an
Earth-centered restricted two-body problem was considered
limiting gravitational field harmonic's model to the
J2 factor; higher gravity potential perturbations by Geoid
and acceleration contributions by drag, solar radiation
pressure, and third body (Moon or Sun) were, therefore,
disregarded.
Considering that the operational orbit shall be able to
serve the polar sites and that the satellite power is provided
by solar panels, circular sun-synchronous orbital
families were considered as the best candidate for the sensitivity
analysis. Orbits belonging to the same family share
a common altitude and, therefore, a common inclination
while they differ in the out-of-plane parameters [right
ascension of ascending node (RAAN) and argument of
perigee (AOP)]. The three sun-synchronous orbital inclinations
for the different families are reported in Table 2.
For every possible altitude and inclination, the algorithm
varies two Keplerian orbital parameters (RAAN and
AOP), while keeping the other constant, to find the optimal
orbital configuration. RAAN and AOP are varied
between 0 and 360 with a 12.5 resolution and the
orbital propagation is run for 15 orbits to obtain enough
data and limit the required simulation time. Then, only the
most promising orbits are propagated for a total of 15
days to get a greater overview. For each combination of
angles, the relative position vector between the S/C and
the TUT is continuously monitored to establish whether
the satellite becomes visible during the simulation step.
As the computational cost may be too high, the simulation
time step is set to a minimum duration of 2 s, which
has been tested to be sufficient to guarantee a correct discretization
of the visibility window.
The algorithm in detail performs the following steps:
i) Calculation of geodetic and ECI Cartesian coordinates
of the ground telescopes.
ii) Calculation of satellite position in ECI: The satellite
position is computed by solving Kepler's equation
by numerical method (Newton-Raphson). The simulation
starts on January 1, 2021 at 00:00:00.000
UTC with the S/C at the ascending node at t ¼ 0 and
the true anomaly is then calculated by solving Kepler's
equation. Using the transformation between
geocentric equatorial and perifocal frames [28], it is
possible to calculate the position vector ofthe S/C in
the ECI frame frS/Cg. frGSg is calculated using the
WGS84 model and the International Astronomical
Union (IAU)-2000/2005 reference system [29], [30].
iii) Calculation of satellite elevation in respect of each
ground telescope: The line-of-sight direction frg of
the S/C relative to the telescope in the Topocentric
Horizon Coordinate [East, North Zenith (ENZ)]
(see Figure 3) is elaborated using the ground
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2022
IEEE - Aerospace and Electronic Systems - August 2022

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