IEEE - Aerospace and Electronic Systems - August 2022 - 7

Avram et al.
Table 1.
Provisional List of Telescopes, GS, and Their Geographical Coordinates
Site
South Pole station
Dome-C station
Atacama
Region Latitude Longitude Altitude AMSL
Antarctica 9000'00 " S 0000'00 " E
Antarctica 7505'59 " S 12319'56 " E
Mario Zucchelli station Antarctica 7441'42 " S 16406'50 " E
Chile 2257'31 " S 6747'15 " W
White Mountain
Tenerife
2800 m
3233 m
20 m
5190 m
CA -USA 3734'59 " N 11814'12 " W 3800 m
Canary Is. 2818'00 " N 1630'35 " W
Longyearbyen Airport Svalbard 7814'46 " N 1527'56 " E
guarantee a visibility time sufficiently long due to the high
relative speed between the LEO satellite and the Earth's
surface. Therefore, an active ACS, whose aim is to perform
the tracking of the TUT during the satellite passage,
is required to increase the period in which the optical axis
of the calibrated payload points toward the ground telescope.
Consequently, the minimum elevation from the
ground at which the calibration can occur is significantly
reduced. Figure 2 schematically shows the pointing procedure
considering a plane case in which the satellite passes
perfectly above the TUT. Once the satellite enters the
GS's visibility region, the ADCS starts to point the optical
axis of the calibrated payload toward the specific groundbased
TUT, tracking such position during the entire satellite-to-telescope
visibility period. In reality, the situation
2390 m
28 m
is more complicated than just presented, as the satellite never
passes perfectly over the telescopes, and a tridimensional
approach is required to estimate the rotation needed to track
each telescope. The determination of the S/C to radio telescope
visibility periods and the geometrical characterization
ofthe S/C-telescope link allow the calculation ofthe required
repointing velocity needed by the CubeSat to continuously
adjust its attitude during the visibility period and to verify if it
is compatible with the performance of a typical CubeSat
ADCS. Moreover, as the satellite elevation increases with
respect to the ground-based telescope, the distance between
them decreases and, therefore, the signal intensity varies, as
qualitatively shown in Figure 2.
CUBESAT DETECTABILITY
To be detectable by the TUT, the power ofthe received signal
shall be higher than the noise level ofthe calibration measurement.
Multiple factors determine the SNR ofthe received signal
and some simplifying assumptions have been made:
spatial loss has been considered using the Gaussian beam
approximation, and line loss has been neglected. Using the
link budget equation, see [2], the SNR of a signal transmitted
toward the receiving TUT is given by
SNR ¼
PrLuLa
Prms
(1)
where Pr is the received power, Prms is the average noise
Figure 2.
Sketch of satellite repointing during orbital passage and received
signal evolution versus satellite position. The optical axis of the
calibrated payload in blue and the edges of the GS's visibility
region in green.
AUGUST 2022
power, Lu is the pointing loss (attenuation due to the partial
intersection between antennas' main lobes), and La is
the atmospheric loss. The power received by the TUT
aperture is as a function of the distance z between the
MAC and the TUT, and it has been modeled using the
Gaussian beam equation given by [27]
PrðzÞ¼ P0 1 e
IEEE A&E SYSTEMS MAGAZINE
2r2
v2ðzÞ
(2)
7
IEEE - Aerospace and Electronic Systems - August 2022

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