CDR General Report

QCS – Quantum Communication Satellite Technion – Israel Institute of Technology
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QCS Project
Quantum Communication Satellite
HerscovitzJacobProject Supervisor:
Winter 2015 - Spring 2016
Faculty of Aerospace Engineering

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1 Introduction………………………………………………………………………………………7
1.1 Abstract .............................................................................................7
1.2 Mission Dfinition................................................................................8
1.3 Quantum Key Distribution.................................................................8
2 System Engineering………………………………………………………………………….10
2.1 Requirement....................................................................................10
Mission Requirements..............................................................10
Spacecraft Requirements .........................................................11
ADCS Requirements..................................................................12
Structure and Thermal Control Requirements.........................13
Orbit Requirements..................................................................14
Communication Requirements ................................................14
Power Requirements................................................................16
Propulsion Requirements.........................................................16
Launch Vehicle Requirements..................................................17
2.2 Mass Budget ....................................................................................17
Structure Iteration....................................................................19
2.3 Satellite Block Diagram....................................................................21
3 Orbit design – Neta Engad & Michal Zalmanovich ...............................22
3.1 Abstract ...........................................................................................22
3.2 Constellation Design........................................................................22
Orbit Parameters Selection ......................................................22
Constellation Pattern................................................................24
Constellation Parameters Selection .........................................24
Constellation selection summary.............................................32
3.3 Constellation Deployment...............................................................33
3.4 Constellation maintenance..............................................................35
The atmospheric drag influence...............................................36
J2- Oblateness...........................................................................38
Perturbations effects summary:...............................................39
Stationkeeping maneuver ........................................................41
3.5 Disposal............................................................................................44
3.6 Conclusion .......................................................................................45
3.7 Sources ............................................................................................46
4 Attitude Control – Or Rivlin & Shalev Eidelsztein.................................47
4.1 Abstract ...........................................................................................47

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4.2 Command Modes ............................................................................47
4.3 Hardware.........................................................................................47
Sensors......................................................................................48
Actuators ..................................................................................49
Flight Computer........................................................................51
Hardware Location and Orientation.........................................52
4.4 Simulation........................................................................................52
Equations of Motion.................................................................54
Physical Models........................................................................56
4.5 Control.............................................................................................59
Logic..........................................................................................59
Guidance...................................................................................60
Controllers................................................................................61
4.6 Error Models....................................................................................63
Actuator Errors .........................................................................63
Sensor Errors ............................................................................64
4.7 Estimators........................................................................................64
Sun Vector Averaging ...............................................................64
Angular Rate Estimation...........................................................65
Auxiliary Attitude Determination Algorithm (TRIAD)...............67
Side Note Regarding the Star Trackers.....................................67
4.8 Results..............................................................................................68
4.9 Conclusions......................................................................................71
4.10 Sources ............................................................................................71
5 Power & Electricity – Nati Rozensweig & Oron Meller ........................72
5.1 Abstract ...........................................................................................72
5.2 Requirements definition..................................................................72
5.3 Components Review and choosing .................................................73
Solar Panels ..............................................................................74
Battery......................................................................................75
PCDU.........................................................................................76
5.4 Simulation........................................................................................77
Inputs and outputs ...................................................................77
Simulation logic ........................................................................78
5.5 Redesigning power system to adjust it to a 20U structure.............80
5.6 Selection of new components for power system............................81
5.7 Simulation Results ...........................................................................84

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5.8 Conclusions......................................................................................87
5.9 Sources ............................................................................................87
6 Propulsion – Nati Rozensweig………………………………………………………….88
6.1 Abstract ...........................................................................................88
6.2 Requirements definition..................................................................88
6.3 Review and selection of propulsion system....................................89
Propellant selection..................................................................90
Propellant tank and storage conditions design........................92
Propulsion System Components Selection and Design............96
Thrusters Design.....................................................................100
Simulation...............................................................................103
6.4 Sources ..........................................................................................104
7 Communication – Oron Meller……………………………………………………….105
7.1 Abstract .........................................................................................105
7.2 Introduction...................................................................................105
7.3 Fundamental and Theoretical Background ...................................106
Signal Form.............................................................................106
Signal Types ............................................................................106
Data Types..............................................................................106
Bandwidth ..............................................................................106
Gain.........................................................................................107
Antennas.................................................................................107
Transmitter.............................................................................109
7.4 Link Budget ....................................................................................109
Characteristics of a link budget (Eq. 3):..................................109
Link budget calculation:..........................................................110
7.5 Simulation......................................................................................112
Simulation Architecture..........................................................112
Simulation Inputs....................................................................113
Simulation Output ..................................................................113
Communication Components Used in The simulation...........114
Simulation Example................................................................115
7.6 Results............................................................................................119
7.7 Sources ..........................................................................................120
8 Structure – Elya Pardes & Alex Zibitsker.............................................121
8.1 Abstract .........................................................................................121

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8.2 Main Contribution .........................................................................121
Design Considerations............................................................121
Mesh.......................................................................................125
Boundary Conditions..............................................................126
Launch Conditions ..................................................................127
Thermal Conditions: Generated Heat and Fluxes ..................128
Thermal Constraints: Radiation and Conduction ...................128
8.3 Results and Discussion...................................................................129
Static Analysis.........................................................................129
Frequency Analysis.................................................................130
Dynamic Analysis....................................................................131
Single-Point Mass Thermal Analysis.......................................132
Finite Elements Thermal Analysis...........................................132
8.4 Conclusions....................................................................................134
Future work ............................................................................135
8.5 Sources: .........................................................................................135
9 Space Environment – Michal Zalmanovich & Avichay Yaish..............136
9.1 Abstract .........................................................................................136
9.2 Radiation in space..........................................................................136
Introduction............................................................................136
Total ionizing radiation (TIR) ..................................................137
Single event effects (SEE) .......................................................138
Surface charging (SC)..............................................................138
9.3 atmospheric phenomena's............................................................139
outgassing...............................................................................139
Atomic oxygen........................................................................139
Orbital debris..........................................................................140
9.4 Space environment influence on our satellite ..............................141
Radiation effects.....................................................................141
Atmospheric phenomena's effects ........................................144
9.5 Conclusions....................................................................................146
9.6 Sources ..........................................................................................147
10 Reliability - Avichay Yaish……………………………………………………………….148
10.1 Introduction...................................................................................148
10.2 Documentation..............................................................................148
The modes in Reliability Block Diagrams (RBDs)....................148
Typical Reliability Numbers ....................................................149
Modes Reliabilities .................................................................150

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Satellite Reliability..................................................................153
10.3 Conclusions....................................................................................153
11 Launcher – Avichay Yaish……………………………………………………………….154
11.1 Introduction...................................................................................154
11.2 Documentation..............................................................................154
In the previous semester........................................................154
Alternatives for Launch Vehicles............................................156
Financial Aspects ....................................................................158
Launch Plan.............................................................................158
11.3 Results & Conclusions....................................................................162
12 System Level Analysis –Neta Engad & Or Rivlin .................................162
12.1 Risk Management..........................................................................162
12.2 Work Plan for Development..........................................................165
13 Conclusions…………………………………………………………………………………….167
13.1 Acknowledgments .........................................................................168

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1 Introduction
1.1 Abstract
This report concludes the work and presents the results of the final project of a group of
students at the Faculty of Aerospace Engineering in the Technion. The project's focus was
the design of a Quantum Communication Satellite (QCS) with the main goal of delivering
encrypted quantum communication keys between two different ground stations using a
satellite constellation.
The project involved cooperation with the Waterloo University, Canada, their role being the
design of the optical component allowing quantum key distribution in the space
environment and serving as the satellite payload.
This report outlines the work done by the Technion team who designed the satellite bus
consisting of the main subsystems: ADCS (Attitude Determination and Control System),
Propulsion System, Electric Power, Communication, Structure and Thermal control.
Furthermore, the following mission segments were designed as well: Orbit and Constellation
Design, Space Environment, Launch Plan, Reliability, Risk Management and a Full Scale
Development Work Plan.
The spacecraft’s conceptual design process emanated from the payload’s needs, its
limitations and capabilities which were detailed in the requirements document made by the
Waterloo team, with additional requirements defined by the Technion team and project
supervisor.
The final product of the project is a LEO Walker constellation consisting of 80 satellites in 8
different orbital planes. Each satellite is a 20U CubeSat weighting 22 [kg] in accordance with
the requirements.
In this report you will find summaries of the work done by each of the teams that took part
in the project.
The report encompasses all the research, data-gathering, sources and simulations that were
made in order to accomplish the project goals, organized chronologically and by sub teams,
in which each team consists of one or two group members.
Figure 1.1: Satellite Assembly and Constellation Concept

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1.2 Mission Definition
The main goal of the mission is to deliver encrypted quantum communication keys from one
ground station to the next using a constellation of satellites which are to cover latitudes of
±70° , in a transition time of less than 15 minutes, so that each ground station is able to
transfer information each 15 min as well.
The encrypted communication between ground stations to a satellite is delivered in a
quantum form, using the satellite’s payload, which may operate only in a full umbra (as a
result of the payload constrains) unlike the encrypted communication between two
satellites in the constellation, which is transmitted by a radio wave in a narrow beam above
the atmosphere in order to prevent eavesdropping and loss of signal.
Another guideline of the project is optimization of resources in terms of the number of
satellites, launches, mass and cost.
Figure 1.2: Quantum Key Transfer Concept
1.3 Quantum Key Distribution
Nowadays, many corporations and even countries are in search for a good way to encrypt
and decipher information (e.g. protocols). One of these ways is by using keys, a short
combination of numbers or characters, in order to establish communication. The keys are
necessary for deciphering big quantities of information that are transferred in an encrypted
way by a certain code that the key represents. The main idea is to transfer only the key in an
encrypted manner, and after having received it the encrypted information (delivered by any
mean, even non-secretive) can be deciphered. Not all the characters or numbers in a key
must be used, and theoretically a larger key that includes multiple encodings for each
number or letter can be provided, for redundancy.
The most common way to decipher these keys is through use of mega computers with
astounding computation abilities, but they are rare and accessible only to very large
industries. However, in recent years, the amount of computer hackers has increased, and
with computation power, accessibility has increased as well. For this reason, there is a

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stronger need to prevent eavesdropping using alternative encryption technologies. Knowing
when a piece of communication is being overheard by unwanted people can diminish the
risk, and allow safer communication – either by transferring a different key or by ending the
communication.
Quantum Key Distribution (QKD) uses photons in order to deliver the keys from one place to
the other. Since a single photon represents a single character or number in the key,
changing any one of the photons will change the key (according to quantum theory
principles). This may sound unwanted, since the photon is highly sensitive to its
surroundings, but it is also the solution: a person eavesdropping to the key will change the
character the photon presents, and will enable the possibility of establishing communication
upon that photon. In this case, both the transferring side and the receiving side can stop the
communication altogether, transfer another key, or even use only the keys that were
transmitted correctly.
Research in the field of QKD has shown that it is not possible to transfer photons for more
than a few hundred kilometers in optic fibers, since the photons decay. Since this type of
communication happens on a worldwide scale (from any place on earth to any place on
earth), the idea to transmit the photons in space – where the photon's decay is much slower
– has been arousing interest. This solution was studied, and found to be more efficient than
the existing solutions.

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2 System Engineering
2.1 Requirement
From the payload’s requirements received from Waterloo University and the mission
requirement, each team derived the requirements specific to its subsystem in order to
achieve the mission goals.
This tree outlines the hierarchy of the requirements:
Figure 2.1: Requirements Tree
The following charts detail the requirements for each subsystem, the mission and the
system as a whole.
Mission Requirements
ID Title Requirement
MR-01]] Mission Duration
The mission shall have a minimum duration of one year
from launch
MR-02]] Orbit Altitude The spacecraft shall cruise at altitude of 400-600km
[MR-03] Night Operation The Photon transmission is only available at night
[MR-04] Transmission Time
The transmission time between the 2 ground stations shall
not exceed 10 minutes
Table 2.1: Mission Requirements

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Spacecraft Requirements
]SR-01[ Launch vehicle
The spacecraft shall be capable of being launched on
any launch vehicle currently in operation
]SR-02[
Mandatory payload
aperture allocation
The spacecraft shall provide an aperture for the QKD
payload receiver telescope optics of at least 10 cm in
diameter
[SR-03]
Desired payload
aperture allocation
As a goal, the spacecraft should provide an aperture
for the QKD payload receiver telescope optics of at
least 15 cm in diameter
[SR-04]
Payload radiator
allocation
The spacecraft shall provide an external facing surface
area for a payload radiator of at least 40 x 40 cm.
[SR-05] Payload mass allocation
The spacecraft shall allocate at least 9 kg of mass to
the QKD payload
[SR -06]
Payload power
allocation
The spacecraft shall be capable of providing a peak
power of at least 20 W to the payload.
[SR -07]
Payload volume
allocation
The spacecraft shall provide a contiguous volume for
the payload of at least 380 x 180 x 180 mm
[SR -08] GPS receiver
The spacecraft shall be equipped with a GPS receiver in
order to provide PPS timing data to the payload.
[SR-09] GPS timing precision
The spacecraft GPS receiver shall provide timing
information to the QKD payload with a minimum
precision of 100 ns
[SR-10]
Operating temperature
range
The allowable operating temperature of the payload
shall range from -20°C to +60°C.
[SR-11]
Temperature stability The spacecraft shall be capable of maintaining the
payload operating temperature to +2°𝐶 during a key
exchange pass with an optical ground station
[SR-12] Reflected light
The spacecraft shall have no protrusions or surfaces
capable of reflecting light into the external aperture of
the payload or baffle.
[SR-13]
Coarse pointing mode
[CPM]
In coarse pointing mode the spacecraft shall be
capable of three-axis inertial pointing with an accuracy
of 5°𝐶 or less
[SR-14]
Fine pointing mode
(FPM] pitch and yaw
In fine pointing mode the spacecraft shall be capable
of ground target tracking of the payload boresight in
pitch and yaw with an accuracy of 0.4° or less (2σ],
[SR-15]
Fine pointing mode
(FPM) roll
In fine pointing mode the spacecraft shall be capable
of ground target tracking of the payload boresight in
roll with an accuracy of 1°𝐶 or less

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[SR-16]] Eclipse coarse pointing
The spacecraft shall be capable of coarse three-axis
pointing in eclipse.
[SR-17]
Sunlight coarse
pointing
The spacecraft shall be capable of coarse three-axis
pointing in sunlight
[SR-18] Orbit control
The spacecraft is not required to control its orbital
position or velocity.
[SR-19] Overcurrent protection
The spacecraft shall autonomously protect all
subsystems from overcurrent conditions
[SR-20] Uplink
The spacecraft shall be capable of receiving data from
the ground via UHF at a minimum of 4kbps.
Table 2.2: Spacecraft Requirements
ADCS Requirements
ID Title Requirement Comments
[AC-01] Performance
The control system shall provide the required
pointing stability and accuracy for each
control mode.
See mode
table
[AC-02] Tracking
The Satellite shall be able to track a ground
target for at least 500 seconds.
[AC-03] Parasitic Torque
ADCS shall be capable to withstand a
parasitic angular torque of 0.0004 Nm
Includes thrust
misalignment,
drag, solar
wind, etc.
Table 2.3: ADCS Requirements
2.1.3.1 Mode Table
ID Mode Requirements Comments
]SS-01[ Detumbling
Arrest initial angular velocity of 2°∕s down to
0.2°∕s over a period of up to 2 orbits
]SS-02[ Night Cruise
Orient spacecraft for maximum solar power
with a maximum error of 1° in up to 250[𝑠]
]SS-03[ Sun Cruise
Orient spacecraft for minimum drag with a
maximum error of 1° in up to 250[𝑠]
]SS-04[
Ground
Communication
Track ground station with a maximum error of
1° in up to 250[𝑠]
Requirement
depends on
the antenna
configuration
]SS-05[
Inter-Satellite
Link
Track neighbor satellite with a maximum error
of 1° in up to 250[𝑠]
]SS-06[ QKD Pointing Track ground station with a maximum error of

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0.4°
]SS-07[
Momentum
Management
Momentum exchange devices shall not exceed
50% of maximum allowed angular momentum
]SS-08[
Orbital
Maneuver
Maintain thrust direction with a maximum of
1° for a duration of at least 500[𝑠]
Table 2.4: Control Modes
Structure and Thermal Control Requirements
[ST-01] Mass Allocation
The structure shall hold the mass of the QKD payload (9kg)
and the mass of the other satellite subsystems (TBD) for the
duration of the mission.
[ST-02]
Volume
Allocation
The structure shall provide a contiguous volume for the QKD
payload of 380 x 180 x 180 mm in addition to the volume
necessary for the other satellite subsystems.
[ST-03]
Components
Mounting
The structure shall provide mountings and deployment
mechanisms and ensure adequate amortization for stresses
during launch to all the various components of the satellite.
(Maximal acceleration: 9g)
[ST-04]
Natural
Frequency
The structure shall be designed with a minimum first natural
frequency of 100 Hz.
[ST-05] Factor of Safety
The structure shall withstand static and dynamic stresses,
taking account of a factor of safety, for the mission throughout
the launch procedure and for a minimum lifetime of one (1)
year from launch.
[ST-06]
Payload Radiator
Allocation
The structure shall have an external surface area for a payload
radiator of at least 15 x 15 cm
2
, preferably facing open space.
[ST-07]
Payload Aperture
Allocation
The spacecraft shall provide an aperture for the QKD payload
receiver telescope optics of at least 10 cm in diameter, ideally
15 cm.
[ST-08] Size Constraints
The stowed structure shall fit within a static envelope shown
in Figure 3.4-7.
[ST-09]
Radiation
Protection
The structure shall protect sensitive systems from the thermal
and electromagnetic radiation present at orbit altitude.
[ST-10]
Magnetic
Interference
The internal layout shall be arranged to ensure magnetic
interference between components doesn’t impair satellite
operation.
[ST-11] Center of Gravity
The structure shall ensure the center of gravity remains within
boundaries determined by attitude control and by the launch
vehicle manufacturer.
[ST-12] Reflected Light The structure shall have no protrusions or surfaces capable of

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reflecting light into the external aperture of the payload or
baffle.
[ST-13]
Operating
Temperature
Range
The structure shall ensure the payload remains in a
temperature range of -20°C to +60°C.
Table 2.5: Structure and Thermal Requirements
Orbit Requirements
[OD-03] Orbit Altitude
An initial altitude of the spacecraft is between 400 km and
600 km.
[OD-04] Coverage area The constellation shall cover latitudes in the range of ±70°
[OD-05] Revisit time
The Revisit time at any point in the coverage area shall be
less than 15 [min].
[OD-06] Access duration
The accesses to any point in the coverage area shall be at
least 100 [sec].
[OD-07] Elevation angle 𝜀 The Elevation angle shall be a minimum of 40 degrees.
[OD-08]
Distance between
satellites
The distance between the satellites while communicating
shall not exceed 5000 km.
[OD-09] Optimization
The constellation design shall be Optimized in regards to
number of satellites and required propellant mass.
Table 2.6: Orbit Requirements
Communication Requirements
2.1.6.1 General
[COM – 01]
Secure
Communication
Communication between 2
satellites or satellite and ground
station must be encrypted
RF method shall be
implemented, after
RF method has been
implemented TBR if
satellites capable of
communicating
through QC
[COM – 02]
Satellite
Communication
Satellite shall be able to
communicate with other satellites
in the constellation
[COM – 03]
Ground
Communication
Satellite shall be able to
communicate with various ground
stations
[COM – 04] Link Margin
Link margin shall be at least 5 dB
for all communication links
Table 2.6: General Communications Requirements

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2.1.6.2 Tracking and Telemetry (Downlink)
[TTLNK– 01]
Link
Establishment
The system shall be able to
establish a link between the
satellite and the ground station
Established link also
known as ‘link lock’ will
happen if Link margin is
greater than 0
[TTLNK– 02]
Satellite to
Ground
Communication
Range
Satellite to ground station
maximum link distance shall be
700 [km]
[TTLNK– 03] Frequencies
VHF/UHF frequencies shall be
considered
[TTLNK– 04]
BPS (Bits Per
Second)
Telemetry link shall be able to
transmit between 50 to
100,000 bps
Table 2.7: Downlink Communications Requirements
2.1.6.3 Command Link (Uplink)
[CmdLNK– 01]
Link
Establishment
The system shall be able to
establish a link between the
ground station and the
satellite
Established link also known
as ‘link lock’ will happen if
Link margin is greater than
0
[CmdLNK– 02]
Ground to
Satellite
Communication
Range
Satellite to ground station
maximum link distance shall
be 700 [km]
[CmdLNK– 03] Frequencies
VHF/UHF frequencies shall
be considered
[CmdLNK– 04]
BPS (Bits Per
Second)
Command link shall be able
to transmit between 1 to
1,000 bps
Table 2.8: Uplink Communications Requirements
2.1.6.4 Crosslink (Inter-Satellite Link)
[CrLNK– 01]
Two Way
Communication
Satellite crosslink communication
must exist simultaneously, when 2
satellites communicate they shall
be able to receive and transmit to
each other
Two way
communication
consist of uplink
and downlink, each
operates separately
[CrLNK– 02]
Satellite to
Satellite
Communication
Range
Satellite to satellite maximum link
distance shall be 5000 [km]
To ensure data is
sent above
atmosphere level
to prevent
eavesdropping
[CrLNK– 03] Satellite to Satellite to ground station

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Ground
Communication
Range
maximum link distance shall be 700
[km]
[CrLNK– 04] Frequencies
VHF/UHF frequencies shall be
considered
[CrLNK– 05]
Sat. to Sat.
Bandwidth
TBR
[CrLNK– 06]
BPS (Bits Per
Second)
TBR
Table 2.9: Crosslink Communications Requirements
Power Requirements
[PE-01]
Battery
lifetime
Battery lifetime shall be 5840 cycles
minimum
Derived from mission
duration requirement
of 1 year,using an
estimate of 1.5 hours
per cycle
[PE-02]
Day
operation
Electrical consumer’s power requirements
shall be filled exclusively by solar panels
during the day,and the satellite shall be in
a positive electrical balance – power
production by solar panels shall be greater
than consumption
[PE-03]
Capacity safe
level
The batteries depth of discharge shall not
exceed 30%
[PE-04]
Solar array
configuration
Solar panels shall not be located on more
than 3 satellite’s sides
*If body linked panels
will not satisfy power
needs – a deployed
solar array shall be
used
Table 2.10: Power Requirements
Propulsion Requirements
[P-01]
Purpose of Propulsion
System
The propulsion system shall be used in order to achieve
velocity change to put the satellite into necessary orbit
and orbit corrections only
[P-02] Velocity Change
The propulsion system shall be capable of providing the
satellite with at least the minimum velocity change
required by mission’s needs
[P-03] Orbit Corrections
The propulsion system shall be capable of making orbit
corrections for the entire duration of the mission (1 year)
[P-04] Thrust Control It is desirable that thrust vector will pass through the

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satellite’s center of mass, so that thrust will not create
unwanted moments and changes in attitude
[P-05] Structure Constraints The propulsion system shall fit inside a volume of 4U
[P-06] Thrust sizing
Thrust generated by propulsion system shall be around
0.1 [N]
Table 2.11: Propulsion Requirements
Launch Vehicle Requirements
[LV-01]
Compliance to
Specifications
Any launch vehicle under the
specifications below and currently in
operation shall be able to launch the
s/c, under its constraints and
characteristics
Nanosatellite launches
are rare.
[LV-02]
Mass
Requirement
The Launch Vehicle shall be able to
carry at least one spacecraft
Spacecraft weight is
24kg; Multi-payload
Launch Vehicles shall
be tested for
compatibility
[LV-03] Orbit Injection
The Launch Vehicle shall place the sc
to its specified orbit
Desired orbit altitude is
600 km, and desired
orbit inclination is 65
[deg]
Table 2.12: Launch Vehicle Requirements
2.2 Mass Budget
The satellite consists of three major sub-systems:
 Structure sub-system: In charge of designing the satellite structure and encapsulate
all the components in the inside the satellite according to the mission requirements.
 Attitude control sub-system: In charge of selecting the ADCS hardware including
sensors and actuators, and designing control and estimation algorithms to orient the
satellite according to mission requirements.
 Power and electricity sub-system: In charge of selecting components for power
management and distribution within the satellite in accordance with the mission
requirements.
The satellite consists of the following components:
 QKD payload
 PCDU
 Battery x2 [16 cells]
 Solar panels x3
 Voltage converter
 Antenna x2

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 S-band transceiver x2
 Radiator
 Magnetometer
 Star trackers x2
 Sun sensors x5
 Magnetorquers x3
 Reaction wheels x4
During the first semester of the project a conceptual design of the satellite was performed
with an initial estimation that the design would be a Micro-Satellite class spacecraft of
approximately 50 [Kg]. The result of that conceptual design was a Micro-satellite class
spacecraft with a mass of 33 [Kg], with relatively low density.
During the PDR presentation a challenge was proposed by the evaluator to downscale the
satellite to fit inside a standardized 24 Cubesat form factor. During the beginning of the
second semester an attempt was made to assess the feasibility of such a design. The
feasibility study found the design to require a complete redesign of the satellite but to be
possible.
In order to facilitate an informed decision on whether to move ahead with the redesign a
comparison chart was made with weights given to the different criteria. Finally, a decision
was made to redesign the satellite in order to meet the challenge posed by the evaluator.
In the following pages the charts detailing the mass budgets for the competing designs can
be seen together with the comparison table detailing the scores given to criteria used to
make the decision.
Micro-Satellite concept mass budget chart:
Table 2.13: Micro-Sat Mass Budget

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CubeSat concept mass budget chart:
Table 2.14: Cubesat Mass Budget
Structure Design Iterations
This table details the scores given to the different criteria. Each subsystem has a weight associated
with it and weights associated with the criteria belonging to that subsystem. A score is given to each
criterion and is multiplied by the weight, and then the sum of these numbers is multiplied by the
subsystem weight. The sum of the weighted scores for all the subsystems is taken as the score for
the concept.

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Table 2.15: Concept Comparison Table
Finally, the two designs can be seen side by side for comparison.
Figure 2.2: Concepts Size Comparison

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Figure 1-1: The satellite general structure
2.3 Satellite Block Diagram
This block diagram details the connections between components and subsystems.

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3 Orbit design – Neta Engad & Michal Zalmanovich
3.1 Abstract
The orbit design team’s main goal is designing a satellite constellation for encrypted
communication that meets the requirement of the payload and mission in an optimal way.
The main issue to be considered during the design process is to meet the performance
requirements of the constellation such as coverage, access duration and revisit time in the
minimal possible cost, which means minimal number of satellites and orbit planes.
Additional aspects that have to be considered are planning the deployment, maintenance
and disposal maneuvers using as little fuel mass as possible.
The constellation design process took account of the following issues:
 Finding and planning the optimal constellation pattern and orbit parameters that
adhere to mission requirements.
 Analyzing the constellation performance using STK and MATLAB,
 Designing the deployment of the constellation from the moment of injection until
the satellites arrives at their desired orbit.
 Analyzing perturbations effects on the constellation.
 Finding the optimal maneuvers for constellation maintenance.
 Examining different options for end of mission.
3.2 Constellation Design
The most significant requirement that led the work on the project is that the satellite
constellation must cover the earth between latitude𝑠 ± 70°.
The elementary parameters that must be defined while designing a constellation are:
 Orbit Parameters:
• Minimum Elevation Angle- principal determining factor for single satellite
coverage
• Altitude- coverage, environment, launch and transfer cost.
• Inclination- determines latitude distribution of coverage.
• Eccentricity- mission complexity and coverage vs. cost
 Constellation Pattern- determines coverage vs. latitude, plateaus.
 Number of Satellites- principal cost and coverage driver.
 Number of Orbit Planes- determines coverage plateaus, growth and degradation.
 Between Plane Phasing- determines coverage uniformity.
Orbit Parameters Selection
3.2.1.1 Elevation Angle:
The elevation angle is measured at the target and is the angle between the satellite and the
local horizontal. The minimum Elevation angle has a significant influence on the coverage
area of each satellite in the constellation and strongly affects the access duration and the

23
revisit time performance as will be elaborate on later. The elevation angle is defined in the
payload’s requirement as:
𝜺 = 𝟒𝟎°.
Figure 3-1: elevation angle definition
3.2.1.2 Inclination:
The orbital inclination is the angle between a reference plane, the equator plane, and the
orbital plane. The inclination is defined in order to satisfy requirement OD-004 - world
coverage between latitudes ±70°. Choosing the optimal inclination is an iterative process
that eventually yields:
𝑖 = 𝟔𝟓° .
3.2.1.3 Eccentricity:
The eccentricity was chosen considering the characteristic of the mission- communication,
and the simplicity of the solution, and therefore defined as:
𝑒 = 𝒐 .
3.2.1.4 Altitude:
The orbital altitude has influence on several performance criteria of the constellation, the
performance that the altitude has a major influence on is the access duration. Requirement
OD-003 specifies that the altitude shall be between 400 to 600 [km] and requirement OD-
006 specifies that the accesses to any point in the coverage area shall be at least 100 sec.
From analyzing the problem, it appears that these two requirements together with
requirement OD-007 for the elevation angle don’t match together, the desired access
duration requires an altitude higher than 600 [km]. The obvious conclusion is that there is a
need for a compromise with one of the requirements. The only requirement that is flexible
in this case is the number of accesses, as this is not a requirement for the payload.
Therefore, the altitude that has been selected is the highest that was possible in order to
minimize the impact on the access duration performance:
𝑯 = 𝟔𝟎𝟎 [𝒌𝒎].

24
Constellation Pattern
As was mentioned above, the constellation pattern principally determines the performance
of the constellation in terms of coverage. In order to accomplish the mission requirements
of global coverage the constellation pattern that was chosen is: Walker delta pattern.
This constellation pattern is commonly used in the orbit design community and frequently
used as a starting point for constellation design.
The walker pattern contains a total of T satellites with S satellites evenly distributed in each
of P orbit planes. All the orbit planes are assumed to be at the same inclination, relative to
the equator. The ascending nodes of the P orbit planes in Walker pattern are uniformly
distributed around the equator at intervals of
360°
𝑃
. Within each orbit plane, the S satellites
are uniformly distributed at intervals of
360°
𝑆
. The phase difference ∆𝜙, in a constellation is
defined as the angle in the direction of motion from the ascending node to the nearest
satellite at a time when a satellite is in the next most westerly plane as is its ascending node.
∆𝜙 must be an integral multiple, F, of
360°
𝑇
, where, 0 < 𝐹 ≤ 𝑃 − 1.
The pattern is fully specified by giving the inclination and the three parameters T, P and F,
usually such a constellation will be written in the shorthand notation of i: T/P/F.
The parameters of the constellation have been chosen in an iterative method using STK and
MATLAB and rely on a uniform criterion which will be elaborated on in the next paragraph.
Figure 3-2: STK c7onstellation simulation
Constellation Parameters Selection
The parameters that have to be determined in order to have a fully defined Walker
constellation are the total number of satellites (T), and the number of orbit planes (P).
It should be noted that the parameter F has been examined individually in an iterative form
and has been chosen to be:

25
F=3
The constellation parameters selection process was conducted in a way that enabled us to
compare each constellation to the others in terms of: access duration and revisit time
performance and in terms of cost; the weights of importance of each criterion are
presented in the table below:
Criteria Weight
Access Duration 0.3
Revisit Time 0.2
Cost 0.5
Table 3-1: criteria’s weights
The trade-offs between the constellations were established by analyzing data received from
STK regarding two target ground stations: Waterloo, Canada and Tel Aviv, Israel, and
additionally about a full grid of 5° covers latitude ±70° .
The constellations that have been chosen for further examination and comparison are:
64/8/3, 72/8/3, 54/8/3, 63/8/3, 72/8/3, 80/10/3 and 81/9/3.
3.2.3.1 Access duration
Access duration, literally, is the total time of access during which a ground station can,
theoretically, communicate with a specific satellite. This duration is defined by the altitude
of the satellite and the minimum elevation angle.
Figure 3-3: access duration distance
The access duration to any point in the coverage area is required to be at least 100 sec.
As discussed before, the definition of the minimum elevation angle as 40 degrees and the
altitude as 600 [km] leaves no possibility to fulfill the requirement for the access duration
fully, i.e. there will always be a percentage of accesses below 100 [sec].
This observation can clearly be seen in the next few graphs which present the average time
of access and the accesses distribution over one day for different latitudes.

26
Graph 3-1: average access duration at 600 km
Graph 3-2: percentages of number of accesses below and above 100 seconds at 600 km
These graphs demonstrate that the mean value of access duration that is observed is 145
[sec] and about 80% of the total accesses in one day are above 100 seconds.
It should be noted that this result was established for a specific Walker constellation for one
day, changing the constellation parameters will affect the numbers of accesses, but the
tendency and the absolute value of the maximum and average access duration will be
similar.
For comparing different constellations in terms of access duration the values that have been
chosen to be examined are: the number of accesses above 100 seconds. This value
examined in the two different targets and for the full grid, this in order to obtain the most

27
accurate result. Another criterion that can provide valuable information about the access
duration performance is the accumulated coverage time that is measured in specific
targets, in which communication can be performed, in comparison to the total umbra
duration, meaning- the coverage percentage, the weight of importance of each criterion is
presented in the next table:
Location Criterion weight
Full grid Average number of accesses above 100 [sec] 0.3
Tel Aviv number of accesses above 100 [sec] 0.18
Coverage percentage 0.18
Waterloo number of accesses above 100 [sec] 0.18
Coverage percentage 0.18
Table 3-2: Access duration’s criterions weights
The data received from the STK simulations for the different constellation parameters for a
1-day interval, while the target and the satellites communication is available only in umbra
are presented and compared in table 3-3:
Location Criterion 64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3
Full grid Ave. number
of accesses
above 100
[sec]
23 25 28 21 24 28 31
Normalized 46% 50% 56% 42% 48% 56% 62%
Tel Aviv number of
accesses above
100 [sec]
24 28 31 25 29 33 39
Normalized 48% 56% 52% 50% 58% 66% 78%
Coverage
percentage
7.8% 8.9% 9.9% 8% 9.3% 10.5% 12.2%
Waterloo number of
accesses above
100 [sec]
32 38 41 26 31 36 39
Normalized 64% 76% 82% 52% 62% 72% 78%
Coverage
percentage
10.4% 12.1% 13.2% 8.3% 9.8% 11.3% 12.5%
Table 3-3: Comparison between constellations in terms of access duration
*All the values of the number of accesses are normalized to 50- an optimal number of
access during umbra.
The histogram below shows the final enhanced score in percentage for each constellation in
terms of access duration:

28
Figure 3-4: access duration histogram
From this histogram we observe that the more orbit planes in the constellation, the better
the access duration performance. It can be seen clearly by comparing the two constellations
with the same number of satellites- 72, that the one with 9 orbit planes is better than the
one with 8 orbit planes. In addition, it is easy to see that for the same number of orbit
planes, the more satellites in the constellation, the better access duration performance, as
expected. In conclusion, in case of access duration the best constellation parameter is:
81/9/3
3.2.3.2 Revisit time
Revisit time is the second performance requirement. The definition of revisit time is the
time elapsed from the moment a certain point on earth can communicate with one satellite
until it can communicate with the next satellite.
The revisit time, similarly to the access duration, is influenced by the minimum elevation
angle and the altitude. Unlike the access duration, the revisit time is also strongly influenced
by the number of satellites in each orbit plane and by the number of orbit planes in the
constellation.
The Revisit time at any point in the coverage area is required to be less than 15 minutes.
It’s important to notice that while examining the revisit time, there is also a need to take
into account accesses that are not long enough for payload communication, i.e. accesses
below 100 seconds. The data received from full grid simulations in STK does not consider
those accesses; therefore, only from examining specific targets is it possible to get accurate
and reliable information, the information about the grid provides only a general tendency
and therefore will get less weight.
36.6%
41.8%
46.0%
33.3%
38.7%
44.8%
50.2%
0%
10%
20%
30%
40%
50%
60%
64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3

29
Another important point to be noticed is that all the revisit time examinations were with
regard to the long light time gap, i.e. a gap of 10-13 hours in which the payload
communication is not possible
The criteria that have been chosen to be compared in this section are the percentage of
gaps below 15 minutes in regard to the total number of gaps during one umbra, in the two
locations, Waterloo and Tel Aviv. Another criterion is the percentage of the total time of
gaps less than 15 minutes in relation to the total time of all the gaps, and the maximum
gap in one umbra. An additional criterion that has been examined only for the full grid is the
average number of gaps below 15 minutes. The weights of importance of each criterion are
presented in the table below:
Location Criterion weight
Full grid Percentage of average gaps below 15 [min] from all gaps 0.09
Tel Aviv
Percentage of gaps number below 15 [min] from all gaps 0.03
Percentage of accumulated time of gaps below 15 [min] out of the
total gaps time
0.03
Maximum gap 0.02
Waterloo
Percentage of gaps number below 15 [min] out of the total number of
gaps
0.03
Percentage of accumulated time of gaps below 15 [min] from all gaps
time
0.03
Maximum gap 0.02
Table 3-4: Revisit time criterions weights
The table below presents the data received from STK simulations for each constellation for
1-day interval, while the target and the satellites communication is available only in umbra:
Location Criterion 64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3
Full grid
Average gaps
below 15 [min]
out of all gaps
86.8% 87.1% 88.2% 82.3% 86.8% 88.6% 89.3%
Tel Aviv
Number of
gaps below 15
[min] out of all
gaps
91.3% 92.6% 92.6% 75% 78.6% 87.5% 89.5%
Accumulated
time of gaps
below 15 [min]
out of all gaps
time
49% 50.7% 49% 49.1% 48.8% 56.9% 59.2%
Maximum gap
[min]
94.5 91.2 98 58 67 62 58
Normalized
max gap
52.8% 54.4% 51% 71% 66.5% 69% 71%
Waterloo
Number of
gaps below 15
92.3% 93.5% 95% 92% 90% 94.1% 87%

30
[min] out of all
gaps
Accumulated
time of gaps
below 15 [min]
out of all gaps
time
60.7% 62.4% 59.5% 40% 31.4% 46.3% 34.5%
Maximum gap
[min]
74 67.8 72.4 83.3 95.3 92.5 90.3
Normalized
max gap
63% 66.1% 63.8% 58.4% 52.4% 53.8% 54.9%
Table 3-5: Comparison between constellations in terms of revisit time
* The values of the maximum gap are normalized to 200
The histogram below shows the final enhanced score in percentage for each constellation in
terms of access duration:
Figure 3-5: revisit time histogram
Logically, from the definition of revisit time it’s obvious that the more satellites and orbit
planes in the constellation, the shorter the revisit time. In this case since we consider as
gaps also some of the accesses, adding satellites and orbit planes causes also more accesses,
where some of them are considered as gaps. Therefore, from this histogram it’s hard to
identify a specific tendency in the case of number of satellites, but from the number of orbit
planes point of view it’s easy to see that there is a preference to 8 planes over 9, so in this
case the best constellation in terms of revisit time is: 72/8/3
71.9%
73.4%
72.4%
66.0%
64.2%
71.2%
68.9%
60%
63%
66%
69%
72%
75%
78%
64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3

31
3.2.3.3 Cost
An important criterion for choosing the optimal constellation is the total cost of the mission.
From a constellation design point of view the two main aspects that influence the mission
cost are the number of satellites and the number of orbit planes that in practice define the
number of launches. Both of these criteria are required to be minimal, while their weights of
importance are presented below:
Criterion weight
Number of satellites 0.2
Number of orbit 0.3
Table 3-6: Cost criterions weights
The next table presents the values of each constellation in term of cost:
Criterion 64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3
Number of satellites 64 72 80 54 63 72 81
Normalized number of satellites 68% 64% 60% 73% 69% 64% 60%
Number of orbit planes 8 8 8 9 9 9 9
Normalized number of orbit plans 60% 60% 60% 55% 55% 55% 55%
Table 3-7: Comparison between constellations in terms of cost
*The values of the numbers of satellites are normalized to 200 and the number of orbit
planes are normalized to 20.
The histogram below shows the final score in percentage for each constellation in terms of
cost:
Figure 3-6: cost histogram
From this histogram a clear tendency can be noticed- the smaller amount of satellites and
orbit planes in the constellation, the lower the cost. Therefore, in terms of cost the best
constellation is: 64/8/3
63.2%
61.6%
60.0%
62.2%
60.4%
58.6%
56.8%
52%
54%
56%
58%
60%
62%
64%
64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3

32
Constellation selection summary
From a point of view of all the performance aspects that have been examined- access
duration and revisit time, the enhanced score for each constellation is displayed in the
histogram below:
Figure 3-7: performance histogram
It can be noticed that in terms of performance there is a preference of 9 orbit planes over 8,
and for the largest number of satellites, therefore the best constellation in this case is:
81/9/3
When taking the cost considerations into account the histogram changes to:
Figure 3-8: total value histogram
50.7%
54.4%
56.6%
46.4%
48.9%
55.3%
57.7%
0%
10%
20%
30%
40%
50%
60%
70%
64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3
55.8%
56.8%
57.1%
53.3%
53.8%
55.9%
56.2%
51%
52%
53%
54%
55%
56%
57%
58%
64/8/3 72/8/3 80/8/3 54/9/3 63/9/3 72/9/3 81/9/3

33
The total value of the constellation, which is displayed above, demonstrates a clear
preference for less orbit planes and more satellites. Therefore, by including all the
parameters and criteria weights the best constellation is:
80/8/3
It is important to mention here that the weights for each of the criteria that were defined in
chapter 1.4.3 are adjustable and have to be determined in a collaborative process with the
clients. This weight has a significant influence on choosing the optimal constellation for the
mission.
Figure 3-9: constellation 80/8/3 coverage areas
3.3 Constellation Deployment
In the scenario in which all the satellites in the same orbit plane are inserted from the
launcher to the same location in the desired orbit plane, there is a need to maneuver each
satellite to its desired location, in order to maintain an even phase difference between each
two adjacent satellites.
By injecting the satellite to a higher or lower orbit plane than the desired, the phase
distribution can be achieved by two Hohmann maneuvers: one to an elliptic transfer orbit
and one from the transfer orbit to the mission orbit, while the time between each satellite
maneuver defines the phase between the satellites in the mission orbit.
The connections between the phase, altitude and the time presented below:
𝑛2
=
𝜇
𝑎3
→ ∆𝒏 = −
𝟑
𝟐
∙ 𝒏 ∙
∆𝒂
𝒂
∆𝑀 = ∆𝑛 ∙ ∆𝑡 → ∆𝒕 =
∆𝑴
∆𝒏

34
The ΔV required for the maneuver is:
∆𝑽 𝟏 = √2𝜇 (
1
𝑎1
−
1
𝑎1+𝑎2
) − √
𝜇
𝑎1
∆𝑽 𝟐 = √
𝜇
𝑎2
− √2𝜇 (
1
𝑎2
−
1
𝑎1+𝑎2
)
While: 𝑎1 = 6978.14 − ∆𝑎 [𝑘𝑚], 𝑎2 = 6978.14 [𝑘𝑚]
For choosing the optimal injection orbit altitude or ∆𝒂 , we compared the parameters of a
few maneuver options in terms of the total maneuver time, which means the time until the
last satellite enters its desired phase ( 324°) in the mission orbit, and in terms of the fuel
mass required for the whole maneuver.
The optimal altitude will be the one for which both the time and fuel mass will be minimal,
while the weight of importance for each one is 60% and 40%, respectively.
The table below presents the maneuver data for each ∆𝒂:
∆𝒂 [𝒌𝒎] 4 6 8 10 12 14 16 18 20
∆𝑽 [
𝒎
𝒔
] 2.17 3.25 4.34 5.42 6.51 7.59 8.68 9.77 10.85
𝒎 𝒇 [𝒌𝒈] 0.161 0.242 0.322 0.402 0.481 0.560 0.639 0.718 0.797
∆𝑻 [𝒅𝒂𝒚] 70.18 46.75 35.04 28.01 23.33 19.98 17.47 15.52 13.96
Total score 59.52 68.15 71.02 71.58 71.00 69.77 68.14 66.23 64.15
Table 3-8: Comparison between deployment maneuvers
The connection between time, velocity pulse and ∆𝒂 are presented in the graphs below:
Graph 3-3: Delta V Vs time for different delta a

35
The conclusion from the comparison is that the optimal altitude difference between the
injection orbit and mission orbit is ∆𝒂 = 𝟏𝟎[𝒌𝒎], while the time at which each satellite
begins the maneuver is presented in the table below:
Table 3-9: Maneuvers time for each satellite Figure 3-9: Satellite locations in the mission orbit
3.4 Constellation maintenance
Long-term constellation maintenance is required to provide the desired coverage
performance and avoid collisions among the satellites in the constellation; this can be
accomplished by maintaining the same relative position among the satellites in the
constellation.
The major perturbing force that affects a LEO satellite is the atmospheric drag, which acts
along the satellites’ negative velocity direction relative to the atmosphere. Periodic
maneuvers are needed to recover the semi major axis of the satellites decaying orbit and
displacement of the mean anomaly, which influence the distance between two satellites in
the same orbit plane.
Another perturbation to be examined, is the earth oblateness - J2 which influences the
RAAN angle between each two satellites.
All the simulation in this chapter related to the following satellites data:
Stationkeeping
menuvers
pertubertionsRAAN [deg]true anomaly [deg]
X√00HPOP_0
X√450HPOP_0_45
X√036HPOP_36
XX00J2_0
√√00ASTRO_0
√√036ASTRO_36
Table 3-10: Satellite date
Sat num. Phase Time [day]
01 0 0
02 36 3.113
03 72 6.22
04 108 9.33
05 144 12.44
06 180 15.56
07 216 18.67
08 252 21.78
09 288 24.89
10 324 28.01

36
All the satellites start at altitude 600 [km] with eccentricity e=0. J2_0 perturbetions is only
central body gravity in order and degree 2. HPOP and astrogator perturbetions data:
central body
gravity
maximum degree 21
maximum order 21
solar radiation
pressure
model spherical
Cr 1
area/mass ratio
[m^2/kg]
0.005835
third body
gravity
sun √
moon √
Drag model spherical
Cd 2.2
area/mass ratio
[m^2/kg]
0.005835
Atm. Density model MSISE 1990
solar
flux/GeoMag
Daily F10.7 150
Average F10.7 150
Geomagnetic Index 3
Table 3-11: HPOP and Astrogator date
The atmospheric drag influence
3.4.1.1 The semi-major axis decaying:
The semi-major axis decays as a consequence of the atmospheric drag force:
𝑑𝑎̅
𝑑𝑡
= −𝐾 𝐷√ 𝑎̅𝜇𝜌0 → ∆𝑇 =
𝐻
𝜌 𝑏 𝐾 𝐷√ 𝜇𝑎̅
(𝑒
ℎ1−ℎ 𝑏
𝐻 − 𝑒
ℎ2−ℎ 𝑏
𝐻 )
The result calculated using MATLAB for a 1-year period:
ℎ2 = 596.82 [𝑘𝑚] → 𝑎 𝑚𝑖𝑛 = 6974.9 → ∆𝒂 = 𝟑. 𝟏𝟖[𝒌𝒎]
The semi major axis decay in comparison to the nominal orbit in the STK simulation
(including smaller orders perturbations):
No Perturbations
With Perturbations
6979
6978.5
6978
6977.5
6977
6976.5
6976
6975.5
6975
6974.5
6974
a[km]
Time [days]

37
Graph 3-4: Semi major axis Vs time for satellites J2_0 and HPOP_0
𝑎 𝑚𝑖𝑛 = 6974.07 → ∆𝒂 = 𝟒. 𝟎𝟐[𝒌𝒎]
3.4.1.2 The eccentricity variability:
The eccentricity variability is a consequence of the atmospheric drag force:
𝑑𝑒̅
𝑑𝑡
= −𝐾 𝐷√ 𝑎̅𝜇𝜌0 𝑝̅
The eccentricity displacement compared to the nominal orbit in the STK simulation
(including smaller degree perturbations):
Graph 3-5: Semi major axis Vs time for satellites J2_0 and HPOP_0
𝑒 𝑚𝑎𝑥 = 1.805 ∙ 10−3
→ ∆𝒆 = 𝟏. 𝟐𝟎𝟓 ∙ 𝟏𝟎−𝟑
3.4.1.3 The Mean Anomaly displacement:
major axis decaying:-semiThe induced change in mean anomaly arising from the
Δ𝑀 = ∫ Δ𝑛𝑑𝑡 =
3𝑛
4𝑎
Δ𝑎Δ𝑡
The induced mean anomaly and distance for one satellite in relation to its nominal orbit for
Δ𝑡 = 1 [𝑦𝑒𝑎𝑟], Δ𝑎 = 3.18[𝑘𝑚] is:
Δ𝑀 = 167.3 [𝑑𝑒𝑔] → Δ𝐿 = 20,376 [𝑘𝑚]
The more interesting influence, in terms of the mean anomaly, is the phasing separation
among different satellites in the same orbit plane.
The induced in-track distance between two satellites in the same orbit plane, with 36 [deg]
initial phase angle, arises from the semi-major axis decaying from STK simulation (including
smaller degree perturbations) for 1-year period presented below:
No Perturbations
With Perturbations
2.2e-3
2e-3
1.8e-3
1.6e-3
1.4e-3
1.2e-3
1e-3
0.8e-3
0.6e-3
0.4e-3
0.2e-3
e
Time [days]

38
Graph 3-6: In track distance between satellites HPOP_0 and HPOP_36
In-track distance:
𝐿0−360
= 4,103 [𝑘𝑚], 𝐿0−36 𝑓
= 1,225 [𝑘𝑚] → 𝚫𝑳 𝟎−𝟑𝟔 = 𝟐, 𝟖𝟕𝟖 [𝒌𝒎]
From the law of cosines, the relative mean anomaly induced between two satellites:
𝐿2
= 2𝑎2
− 2𝑎2
𝑐𝑜𝑠𝑀 → 𝑀 = acos (−
𝐿2
− 2𝑎2
2𝑎2
)
𝑀0−360
= 36 [𝑑𝑒𝑔], 𝑀0−36 𝑓
= 10.21[𝑑𝑒𝑔] → 𝚫𝑴 𝟎−𝟑𝟔 = 𝟐𝟓. 𝟕𝟗[𝒅𝒆𝒈]
J2- Earth’s Oblateness
3.4.2.1 The RAAN angle displacement:
arth’s oblateness:the EThe RAAN angle displacement is a consequence of
𝑑Ω̅
𝑑𝑡
= −
3
2
𝐽2 (
𝑅 𝑒
𝑎̅
)
2
𝑛̅𝑐𝑜𝑠𝑖
The induced RAAN angle one satellite in related to its nominal orbit for
Δ𝑡 = 1 [𝑦𝑒𝑎𝑟] → 𝚫𝛀 = 𝟏𝟗. 𝟔 [𝒅𝒆𝒈]
As in the case of the mean anomaly, the more interesting influence, in terms of RAAN angle,
is the RAAN displacement between satellites in different orbit planes and in the same orbit
plane.
The following graph shows the mean RAAN angles of 3 different satellites (HPOP-1, HPOP-
36, and HPOP-0-45) experiencing the same perturbations, two in the same orbit plane in 36
[deg] phase angle and one in another orbit plane in 45 [deg] phase RAAN angle:
4000
3500
3000
2500
2000
1500
Time [days]
L[km]

39
Graph 3-7: RAAN angle of satellites HPOP_0, HPOP_36 and HPOP_0_45
STK simulation result for the RAAN displacement between two different orbit planes is:
𝛀 𝟎−𝟒𝟓 𝟎
= 𝟒𝟓, 𝛀 𝟎−𝟒𝟓 𝐟
= 𝟒𝟐 → 𝚫𝛀 𝟎−𝟒𝟓 = 𝟑 [𝒅𝒆𝒈]
The cross track distance between two satellites in the same orbit plane with 36 [deg] initial
phases in STK simulation:
Graph 3-8: Cross track distance between satellites HPOP_0, HPOP_36
𝑳 𝟎−𝟑𝟔 𝟎
= 𝟎 [𝒌𝒎], 𝑳 𝟎−𝟑𝟔 𝒇
= ±𝟒𝟕. 𝟔 [𝒌𝒎]
Perturbations effects summary:
All the perturbation effects on the constellation are summarized in the table below:
STK valueRelative satellitesinfluenceperturbation
𝟒. 𝟎𝟐HPOP_0 - J2_0∆𝑎 [𝑘𝑚]
Atmospheric
drag
𝟏. 𝟐𝟎𝟓 ∙ 𝟏𝟎^ − 𝟑HPOP_0 - J2_0∆𝑒
𝟐𝟓. 𝟕𝟗HPOP_0 - HPOP_36∆𝑀 [𝑑𝑒𝑔]
350
300
250
200
150
100
50
0
40
30
20
10
0
-10
-20
-30
-40
L[km]
Time [days]
RAAN[deg]
Time [days]

40
𝟐, 𝟖𝟕𝟖HPOP_0 - HPOP_36∆𝐿𝑖𝑛−𝑡𝑟𝑎𝑐𝑘 [𝑘𝑚]
𝟑HPOP_0 - HPOP_36
HPOP_0 - HPOP_0_45
𝛥𝛺 [𝑑𝑒𝑔]
J2- Oblateness
𝟒𝟕. 𝟔HPOP_0 - HPOP_36∆𝐿 𝑐𝑟𝑜𝑠𝑠−𝑡𝑟𝑎𝑐𝑘 [𝑘𝑚]
Table 3-12: Perturbations summary
The graphs below present the distance between two satellites in the same orbit plane with
36 [deg] initial phases in term of in track, cross track and range for mission duration of one
year:
Graph 3-9: Cross track, in track and range distance between satellites HPOP_0, HPOP_36
It can be clearly noticed that the in-track distance between the satellites decreases during
one year while the cross-track distance does not significantly changed.
The conclusions are:
 All the satellites in the constellation have the same semi major axis decay rate and
since it’s a small value it doesn’t affect the constellation performance directly.
 Since the eccentricity variability has a small value in a circular orbit it does not have a
significant influence on the constellation performance.
 The mean anomaly displacement, arising from the semi major axis decaying, has a
considerable influence on the constellation configuration and therefore on the
constellation performance.
 Since ΔΩ has a small value and since all the satellites are in the same inclination and
semi major axis The RAAN displacement has a negligible effect on the constellation
configuration.
The conclusions above indicate that there is a need for constellation maintenance to
recover the semi major axis, which will prevent mean anomaly displacement in the orbit
plan.
Cross track
In track
Range
4000
3500
3000
2500
2000
1500
1000
50
0
L[km]
Time [days]

41
Station-Keeping Maneuver
Periodic station-keeping maneuvers are needed to maintain the in-track or phasing
separation among the satellites in the constellation. A station-keeping maneuver is executed
when the position deviation of the satellite in the constellation exceeds the chosen
tolerance.
There are two main methods for constellation maintenance; absolute station-keeping, i.e.
maintaining each satellite in a pre-defined mathematical box, and relative station-keeping in
which only the relative position of the satellites is maintained. Since the absolute station-
keeping has several advantages including a simpler, more robust control mechanism and
less propellant, and only one disadvantage- more frequent station-keeping burns compared
to relative station-keeping, we decided to use this method for maintaining the constellation.
The absolute station-keeping method is illustrated in the following figure:
Figure 3-10 – schematic drawing of a LEO spacecraft under stationkeeping for drag effect
Where Δ𝐿 or
1
2
Δ𝑀 𝐵𝐴 is the tolerance which by the following connections define the
required Δ𝑉:
2Δ𝐿 = 𝑎Δ𝑀 𝐵𝐴
Δ𝑀 𝐵𝐴 =
3𝑛
4𝑎
Δ𝑎Δ𝑡
Δ𝑉 =
𝑛
2
Δ𝑎

42
Figure 3-10: STK station-keeping simulation
In our case we have exmined the recived Δ𝐿,
1
2
Δ𝑀 𝐵𝐴, Δ𝑒, Δ𝑉 from several different Δ𝑎
and compared them with the main goal of finding the minimal Δ𝐿 or 𝛥𝑀𝐴−𝑛𝑜𝑚 which
requires the minimal number of pulses, Δ𝑒, and 𝑚 𝑓 while the weight of importance of
each one is:
weightParameters
25%number of pulses
20%𝑚𝑎𝑥 𝛥𝑒
30%𝑚 𝑓𝑡𝑜𝑡
25%𝑚𝑎𝑥 𝛥𝑀𝐴−𝑛𝑜𝑚
Table 3-13: Stationkeeping criterions weight
The meneuvers data and comparison table:
0.70.60.50.40.3source𝜟𝒂 [𝒌𝒎]
77443STKnumber of pulses
1.301.742.172.603.04MatlabAverage time between
pulses [month]
0.32490.43320.54150.64990.7582Analytic∆𝑽 [
𝒎
𝒔
] per pulse
2.273.032.172.592.27Analytic𝜟𝑽𝒕𝒐𝒕 [
𝒎
𝒔
]
0.02430.03240.04040.04850.0566Analytic𝒎 𝒇 [𝒌𝒈] per pulse
0.1690.2260.1610.1940.169Analytic𝒎 𝒇 𝒕𝒐𝒕
[𝒌𝒈]
0.00210.0220.00220.00220.0022STK𝒎𝒂𝒙 𝜟𝒆
206.03366.22571.76822.771119.18Analytic𝜟𝑳 [𝒌𝒎]

43
1.693.014.696.769.19Analytic𝒎𝒂𝒙 𝜟𝑴 𝑨−𝒏𝒐𝒎 [𝒅𝒆𝒈]
70.8167.7175.8873.5975.00total score
Table 3-13: Station-keeping data and comparison
The conclusion from the comparison is that the optimal option is to perform the maneuver
every 𝜟𝒂 = 𝟎. 𝟓 [𝒌𝒎] of decay.
The graphs below presented the semi major axis and eccentricty of the maneuvering
satellite in comparison with the nominal satellite and to the non-meneuvering satellite for
one year in STK simulation:
Graph 3-10: Semi major axis Vs time for satellites HPOP_0, J2_0 and ASTRO_0
Graph 3-11: Eccentricity Vs time for satellites HPOP_0, J2_0 and ASTRO_0
The next graph presents an STK simulation of the in-track, cross-track and range distance
between two satellites in the same orbit plane with an initial phase of 36 [deg] throughout a
one-year period:
2.2e-3
2e-3
1.8e-3
1.6e-3
1.4e-3
1.2e-3
1e-3
0.8e-3
0.6e-3
0.4e-3
0.2e-3
6979
6978.5
6978
6977.5
6977
6976.5
6976
6975.5
6975
6974.5
6974
No Perturbations
With Perturbations
Maneuvers
No Perturbations
With Perturbations
Maneuvers
Time [days]
a[km]e
Time [days]

44
Graph 3-12: Cross track, in track and range distance between satellites ASTRO_0 and ASTRO_36
It can be seen from the graph that the distance between the satellites is bounded while the
maximum values are:
max Δ𝐿 𝑐𝑟𝑜𝑠𝑠 𝑡𝑟𝑎𝑐𝑘 ≅ 50 [𝑘𝑚]
max Δ𝐿𝑖𝑛 𝑡𝑟𝑎𝑐𝑘 ≅ 500 [𝑘𝑚]
max Δ𝐿 𝑟𝑎𝑛𝑔𝑒 ≅ 600 [𝑘𝑚]
*The range distance includes also the radial distance, which is not presented in the graph.
3.5 Disposal
According to NASA guidelines, a spacecraft or upper stage with perigee altitude below 2000
km in its final mission orbit may be disposed of using atmospheric re-entry no longer than
25 years after completion of mission.
In a natural atmospheric re-entry, we assume there is no control of the spacecraft’s attitude
and therefore the semi major axis resulting from the atmospheric drag can be calculated for
a realistic situation in which an average face positioned in the direction of the velocity
vector:
𝐴 𝑎𝑣𝑒 =
4 × 𝐴 𝑏𝑖𝑔 + 2 × 𝐴 𝑠𝑚𝑎𝑙𝑙
6
= 0.1149
The definition of atmospheric re-entry is at altitude ℎ𝑓 = 75 [𝑘𝑚]
Using MATLAB for ℎ0 = 600 [𝑘𝑚] the result for the estimated descent duration:
∆𝒕 = 𝟏𝟔. 𝟗[𝒚𝒆𝒂𝒓]
The meaning of this result is that there is no need for disposal maneuvers since the mission
adheres to the International law of disposal within 25 years.
4000
3500
3000
2500
2000
1500
1000
500
0
Cross track
In track
Range
Time [days]
L[km]

45
3.6 Conclusion
The main goals of the orbit design team were designing an optimal LEO constellation which
fulfills the mission requirements and to analyze its performance. Additional goals are
designing optimal deployment and maintenance maneuvers, and finding a good solution for
the mission end of life problem.
The constellation design process started with defining the required orbit parameters and
constellation pattern. Several constellations were compared with regard to fulfillment of
mission requirements, cost, number of satellites and the number of orbit planes.
The final result of the constellation analysis was a 80/8/3 Walker constellation, which
consists of 80 satellites in 10 different orbit planes with the orbital parameters:
𝒆 = 𝟎, 𝒂 = 𝟔𝟗𝟕𝟖. 𝟏𝟒 [𝒌𝒎], 𝒊 = 𝟔𝟓°
The main constellation characteristics are:
• An average number of communication accesses (above 120 second) per day of 28
• A percentage of communication capable accesses out of the total accesses of 77.4%
• A percentage of the average number of allowed gaps out of all gaps of 88.2%
The maneuver that was chosen for deployment of the satellites in the required orbits, was a
two-pulse Hohmann transfer. Upon comparison between multiple transfer maneuvers, one
was chosen for its fuel and time efficiency compared to the rest. The second pulse was to be
executed at a height of 𝚫𝒂 = 𝟏𝟎 [𝒌𝒎] between the transfer and mission orbit, meaning,
𝒂𝒕𝒓𝒂𝒏𝒔𝒇𝒆𝒓 = 𝟔𝟗𝟔𝟖. 𝟏𝟒 [𝒌𝒎]. The time and fuel mass required for the whole maneuver
were:
𝚫𝑻 = 𝟐𝟖 [𝒅𝒂𝒚𝒔], 𝚫𝑽 = 𝟓. 𝟒𝟐 [
𝒎
𝒔
]
From analyzing the perturbations effect on the constellation structure during the mission
lifetime of 1 year, we found that there is a need for station keeping maneuvers in order to
prevent degradation in constellation performance. The station-keeping maneuver chosen is
a control box for maintaining the mean anomaly displacement, as a result of the
atmospheric drag. From comparing several different tolerances in terms of minimal fuel
mass, the number of pulses and eccentricity displacements, the resulting maneuvers require
4 pulses each 2.17 months every 𝚫𝒂 = 𝟎. 𝟓 [𝒌𝒎] of descending, with a total velocity pulse
of 𝚫𝑽 = 𝟐. 𝟐𝟕 [
𝒎
𝒔
], in which the tolerance is 𝚫𝑳 = 𝟓𝟕𝟎 [𝒌𝒎] and the maximal eccentricity
displacement resulting from the maneuvers is 𝚫𝒆 = 𝟎. 𝟎𝟎𝟐.
The mission disposal option that was chosen is a natural re-entry into the atmosphere,
which abides by international law, requiring duration of
𝚫𝑻 = 𝟏𝟕 [𝒚𝒆𝒂𝒓𝒔]
To conclude, the Δ𝑉 budget required for the mission including all mission segments is:

46
Deployment Maintenance Disposal Extra fuel 10% Total
∆𝑽 [m/s] 5.42 2.27 0 0.769 8.46
𝒎 𝒑 [kg] 0.402 0.0566 0 0.057 0.623
Table 2-1: Delta V budget
3.7 Sources
 Applied Orbit Perturbation and Maintenance, Chia-Chun “George” Chao. (Chapters
6.1, 6.2, 10.5)
 AUTONOMOUS CONSTELLATION MAINTENANCE, James R. Wertz, John T. Collins,
Simon Dawson Hans J. Koenigsmann, Curtis W. Potterveld. Microcosm, Inc.,Torrance,
CA.
 Space-Mission-Analysis-and-Design, Third edition. (Chapter 7)
 CAESAR Final Report, winter 2012-spring2011

47
4 Attitude Control – Or Rivlin & Shalev Eidelsztein
4.1 Abstract
In the broader frame of the QCS project, the role of the ADCS team was to enable the
spacecraft to orient itself in a manner that facilitates accomplishment of mission objectives.
The ADCS team was in charge of all ADCS hardware choosing and placement, development
of a 6 DOF simulation with realistic modelling of the spacecraft and the space environment
and development of control algorithms to orient the spacecraft according to mission
requirements and a command mode state machine to cycle through them autonomously. In
order to make the results as realistic as possible, error models were added into the satellite
sensor readings and the actuator torques. Different estimators were introduced into the
satellite software in order for it to be capable of deducing its angular orientation and
velocity, given different sensor readings. The ADCS simulation later became a complete
system simulation which included power, thermal, communication and engine thrust
modules. Finally, a full mission scenario was run for a single satellite in order to confirm all
mission requirements were met.
4.2 Command Modes
Each command mode complies with a specific task of the satellite and dictates the
requirements associated with this task. Different command modes trigger different attitude
controllers within the control algorithms in order to satisfy these requirements.
Num. Mode Requirements
1 Detumbling Arrest initial angular velocity of 2° 𝑠⁄ down to 0.2° 𝑠⁄ over a
period of up to 2 orbits
2 Sun Cruise Orient spacecraft for maximum solar power with a maximum
error of 1° in up to 250[𝑠]
3 Night Cruise Orient spacecraft for minimum drag with a maximum error of
1° in up to 250[𝑠]
4 Ground Com. Track ground station with a maximum error of 1° in up to
250[𝑠]
5 Inter Sat. Com Track neighbor satellite with a maximum error of 1° in up to
250[𝑠]
6 QKD Pointing Track ground station with a maximum error of 0.4°
7 Momentum
Management
Momentum exchange devices shall not exceed 50% of
maximum allowed angular momentum
Table 4.1: Command Modes
4.3 Hardware
The satellite underwent a massive redesign during the second semester of the project in
which it was scaled down to a volume of 20[𝑈]. As a result, all of the internal hardware
needed to be scaled down as well, in order to concede with the new volume limitations but

48
also still enable the required maneuverability and precision. In this chapter the former and
current ADCS hardware choices will be presented and compared.
Sensors
All of the sensor selections were dictated by the need for high measurement accuracy, small
dimensions, low mass and power consumption and a satisfactory operation life time.
4.3.1.1 Magnetometer
Magnetometer by SSTL
Measurement range of ±60[𝜇𝑇] with an
accuracy of 0.016%.
Dimensions: 36[𝑚𝑚] × 90[𝑚𝑚] × 130[𝑚𝑚]
Mass: 0.19[𝑘𝑔]
Power consumption: 0.3[𝑊]
Operation life time: 7 years.
The selected option for both the former and current designs is Magnetometer by SSTL. It is
highly accurate and has a low power consumption while possessing acceptable dimensions,
mass and measurement range. Furthermore it is the only option found in which the
designed operational life time is noted and meets mission requirements.
While both make use of the same magnetometer, the former design included two
magnetometers for redundancy while the new design contains only one.
4.3.1.2 Sun Sensor
It was decided to include 5 sun sensors onboard to allow near full spherical coverage of the
spacecraft and also to provide redundancy.
SSoC-D60 by SOLARMEMS
2 axis sensor with a field of view of ±60° and an
accuracy of 0.5%
(*) Power consumption: ~0.15[𝑊]
* Estimated
The selected option for both the former and current designs is SSoC-D60 by SOLARMEMS. It
is highly accurate while also possessing a large field of view. It’s mass and dimensions are
very small and its power consumption is acceptable.

49
There was no need to reduce the size or mass of the sun sensors during the satellite
redesign. Maintaining maximum sun sensing coverage was seen as important and therefor
the choice of sun sensors was not changed.
4.3.1.3 Star Tracker
It was decided to include 2 star trackers onboard to ensure that when both are functioning,
at least one would provide bore-sight grade accuracy. This would also produce a larger
effective field of view and provide redundancy.
Nano Star Tracker by BCT
Field of view: 10° × 12° with 6[𝑎𝑟𝑐𝑠𝑒𝑐] bore-
sight and 40[𝑎𝑟𝑐𝑠𝑒𝑐] roll accuracies.
Power consumption: 1.5[𝑊]
The selected option for both the former and current designs is Nano Star Tracker by BCT. It
has small dimensions and a low mass along with high bore-sight and roll accuracies. It has an
acceptable field of view and a low power. Finally it is designed to be completely internal
with no need for a baffle to protrude from the satellite which greatly simplifies its
integration into the overall satellite design.
Here also, the former star tracker choice was seen fit to remain during the redesign. The
decision to use two star trackers was retained being that they are the main sensor used to
measure the satellite’s angular attitude and rate.
Actuators
All of the actuator selections were dictated firstly by a need for high maneuverability while
taking into account mass, dimension and power restrictions.
4.3.2.1 Magnetorquer
It was decided to include 3 perpendicular magnetorquers onboard to allow magnetic control
torques in all directions.
1. MT5-2 by ZARM Technik
Magnetic moment: 5[𝐴𝑚2]
Dimensions: ∅18[𝑚𝑚] × 240[𝑚𝑚]
Mass: 0.3[𝑘𝑔]
Power Consumption: 0.77[𝑊]

50
2. MTQ by NSS
Magnetic moment: 0.2[𝐴𝑚2]
Power Consumption: 0.2[𝑊]
The selected option for the former satellite design was MT5-2 by ZARM Technik. It has a
high magnetic moment along with a relatively low mass, small dimensions and a low power
consumption.
Following the redesign, a change was needed in the selection of the magnetorquers. The
new satellite’s dimensions would not allow three relatively large magnetorquers to be
placed inside perpendicular to one another. Also, following the reduction in both volume
and mass, the satellite could make due with magnetorquers with lower torque capabilities.
The new option chosen was MTQ by NSS. It has smaller dimensions, a lower mass and a
lower power consumption than the former option while still producing a satisfactory
magnetic dipole.
4.3.2.2 Reaction Wheels
RW1 Reaction Wheel by BCT
Max. torque: 0.04[𝑁𝑚]
Angular Momentum: 1.5[𝑁𝑚𝑠]
Mass: 1.6[𝑘𝑔]
Nominal Power Consumption: 5[𝑊]
Peak Power Consumption: 46[𝑊]
RWp015 Reaction Wheel by BCT
Angular Momentum: 0.5[𝑁𝑚𝑠]
Nominal Power Consumption: 0.2[𝑊]
The most extreme change in hardware was made to the reaction wheels.

51
The selected option for the former satellite design was RW1 Reaction Wheel by BCT. It has
high torque, which is necessary for maneuverability, and also relatively low mass and an
acceptable power consumption.
Following the redesign a big cut in mass and volume was both needed and possible. The
former choice was replaced by RWp015 by BCT. It has a fraction of the mass, much smaller
dimensions, a lower power consumption while still producing a satisfactory torque and
angular momentum capacity.
4.3.2.3 Control Moment Gyroscope
A Control Moment Gyro system was also reviewed as a viable option for a torque inducing
component, instead of the reaction wheels. The specific reviewed model comes in a
compact package of four, does not require installation in a specific orientation and its
performance exceeds that of all of the reaction wheels of similar dimensions. Ultimately the
former option was chosen for the reason that Control Moment Gyros are not yet space
proven products and are still being developed.
Microsat CMG by HoneyBee Robotics
Nominal Wheel Rate: 8000[𝑅𝑃𝑀]
Mass: 0.6[𝑘𝑔]
Nominal Power Consumption: 1.5[𝑊]
Peak Power Consumption: 2[𝑊]
The idea was abandoned, however, because no CMGs
are currently being manufactured.
Flight Computer
A standard, flight proven flight computer was chosen in order to
supply the needed processing power onboard the satellite. The
selected component is the OBC750 by SSTL.
OBC750 by SSTL
Mass: 1.5[𝑘𝑔]
Power Consumption: 10[𝑊]

52
Hardware Location and Orientation
Several basic guidelines were used when placing and orienting the sensors and actuators
within the satellite. These guidelines ensure sufficient maneuverability of the satellite and
visual coverage by its sun sensors and star trackers.
3. Sun sensors were placed on each panel of the satellite apart from the one out of
which the payload points, because it would usually point toward the earth. This
would ensure near full coverage for sun detection.
4. The star trackers were placed on the panels which do not include solar panels or the
payload, thus ensuring that they would not need to point to the sun or the earth,
and could point towards the stars for the maximum amount of time possible.
5. The magnetorquers were placed within the satellite at right angles to each other in
order to allow a maximum magnetic torque range.
6. The reaction wheels were placed in a pyramid configuration, which allows for a full
torque vector range. The wheel tilt angle was set at 32° which optimizes power
consumption.
4.4 Simulation
As part of the work on the ADC system a full system simulation was developed. Due to the
fact that work on the constellation orbits took place with AGI's STK software, the simulation
was deemed as primarily intended for the ADCS team. This relaxed some of the necessity to
accurately model long term perturbations affecting the spacecraft's orbit in favor of smaller
integration times with high fidelity modelling of the attitude motion. In addition to the orbit
and attitude dynamics the simulation contains modules for the Power, Thermal dynamics,
Communication and Propulsion subsystems.
The simulation was written in MATLAB and has the following structure:
Figure 4.1: Simulation Block Diagram

53
A list of the major functions comprising the simulation is as follows:
Main- The main body of the simulation
Parameter change (init. Cond. Rew. Script)- This function allows to change values of system
parameters and initial conditions
Parameter_Init- This function contains all the physical parameters of the simulation such as
spacecraft component models, mass properties, control gains and initial conditions.
Main Sequence Block:
 Orbital_Dynamics- Integrates the orbital equations of motion using a 4th order
Runge-Kutta numerical solver to propagate the satellite's orbital motion in ECI
frame. The results are then transformed to (Lat/Long/Alt) coordinates.
 Environment- Calculates the sun vector in the body frame, determines if the satellite
is sunlight or eclipse, loads data for the atmospheric density and magnetic field from
output STK files and computes the environmental disturbing torques caused by the
gravity gradient, solar radiation pressure, aerodynamic drag and residual magnetic
dipole. This function also determines if ground stations and nearby satellites are
available and if sensors have view of their targets.
 Attitude_Determination- This function runs the error models for the sensors and
makes use of estimators and attitude determination algorithms to update the
spacecraft's states.
 Control Logic- Uses environmental data such as position, sunlight, ground command
and satellite command to decide which mode of operation the satellite should be in.
 Attitude Commander- Based on the mode of operation and data of position and
attitude, this function calculates the command quaternion and angular velocity that
the satellite should assume.
 Attitude Control- Based on the mode of operation and the received command
quaternion and angular velocity this function chooses the appropriate control law
and calculates the command torque. The command torque is then distributed to the
actuators using the Steering Logic function.
Attitude_Dynamics- This function integrates Euler's equations and the quaternion kinematic
equations using 4th order Runge-Kutta numerical solver to compute the ECI to body
quaternion and angular velocity.
Thermal_Simulation- This function receives sun and albedo fluxes and calculates the
temperature of the satellite using appoint mass model.
Power_Simulation- This function receives input power and consumption by components
and calculates all the performance criteria associated with the power subsystem.
Communication_simulation- This function receives distance to target and relative pointing
error and uses link budget calculations to return whether communication has been
established or not.

54
Propulsion Simulation- This function receives the required Delta-V and is activated upon
stabilization of the spacecraft in Orbit Control Mode. The function returns the thrust
generated and the resulting parasitic torques.
Equations of Motion
The spacecraft's orbital motion was modelled with the 2 body problem incorporating J2
perturbations.
Orbital Equation: 𝑟̅̈ = −
𝜇
𝑟3
⋅ 𝑟̅ + 𝐹̅𝑡𝑜𝑡𝑎𝑙
𝑟̅ [𝑚] − The satellite’ position vector from earth's center of mass in ECI frame
𝜇 [
𝑚3
𝑠2
] − Earth's gravitational constant
𝑟 [𝑚] − Magnitude of the distance from earth's center of mass
𝐹̅ [𝑁] – Sum of external forces on satellite
Earth's Oblateness Effect: 𝐹̅𝐽2
=
[
𝜇⋅𝑟 𝑥
𝑟3 [
3
2
𝐽2 (
𝑅 𝐸
𝑟
)
2
(
5𝑟𝑧
2
𝑟2 − 1)]
𝜇⋅𝑟 𝑦
𝑟3
[
3
2
𝐽2 (
𝑅 𝐸
𝑟
)
2
(
5𝑟𝑧
2
𝑟2
− 1)]
𝜇⋅𝑟𝑧
𝑟3 [
3
2
𝐽2 (
𝑅 𝐸
𝑟
)
2
(
5𝑟𝑧
2
𝑟2 − 3)]
]
𝑟𝑥 , 𝑟𝑦 , 𝑟𝑧 [𝑚] – The components of 𝑟̅
𝑅 𝐸 = 6378 [𝑘𝑚] – Earth’s mean radius
𝐽2 = 1.08262668 × 10−3
Other forces such as higher order zonal harmonics, aerodynamic drag and solar radiation
pressure were not introduced in to the orbital motion due to their mainly long term effect
which is negligible at the time scale of a few orbits.

55
Figure 4.2: J2 Perturbation Effects
Plot 4.1: Ground Track
In the above figures the effect of 𝐽2 perturbation on the orbit can be clearly seen.
The spacecraft's attitude dynamics are given by Euler's equations:
Euler's Equations: 𝜔̅̇ = 𝑱−1
⋅ [T̅total − 𝑱 𝑥
𝜔̅𝑱]

56
𝜔̅ [
𝑟𝑎𝑑
𝑠
] – Inertial angular velocity in body frame
𝑱 [𝑘𝑔 ⋅ 𝑚2] – Inertia Tensor in body frame
𝑇̅𝑡𝑜𝑡𝑎𝑙 [𝑁𝑚] – The sum of all external and internal torques
The kinematics of the attitude Quaternion are given by Poisson's equations:
Poisson's Equations: [
𝑞̇1
𝑞̇2
𝑞̇3
𝑞̇ 𝑟
] =
1
2
⋅ [
𝑞 𝑟 ⋅ 𝜔1 − 𝑞3 ⋅ 𝜔2 + 𝑞2 ⋅ 𝜔3
𝑞3 ⋅ 𝜔1 + 𝑞 𝑟 ⋅ 𝜔2 − 𝑞1 ⋅ 𝜔3
−𝑞2 ⋅ 𝜔1 + 𝑞1 ⋅ 𝜔2 + 𝑞 𝑟 ⋅ 𝜔3
−𝑞1 ⋅ 𝜔1 − 𝑞2 ⋅ 𝜔2
]
𝑞1, 𝑞2, 𝑞3 – The vector part of the inertial to body Quaternion
𝑞 𝑟 – The scalar part of the inertial to body Quaternion
Physical Models
4.4.2.1 Geomagnetic Field Model:
At first, an approximate dipole model was used as earth's magnetic field. However, due to
relatively large inaccuracies compared to the standard IGRF model and in order to avoid
heavy computation penalties it was opted to use magnetic field data produced by STK and
load it to the simulation. This figure shows the IGRF data received from STK simulations:
Plot 4.2: Magnetic Field [STK]

57
4.4.2.2 Atmospheric Density Model:
Following the successful implementation of the STK geomagnetic data a similar approach
was used for the atmospheric density.
4.4.2.3 Eclipse Determination Model:
A simple cylinder was used to model the eclipse. We define the axes of an eclipse frame:
𝑌̂𝑒𝑐𝑙𝑖𝑝𝑠𝑒 =
𝑍̂ 𝐸𝐶𝐼 × 𝑆̂ 𝐸𝐶𝐼
|𝑍̂ 𝐸𝐶𝐼 × 𝑆̂ 𝐸𝐶𝐼|
𝑍̂ 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 =
𝑆̂ 𝐸𝐶𝐼 × 𝑌̂𝑒𝑐𝑙𝑖𝑝𝑠𝑒
|𝑆̂ 𝐸𝐶𝐼 × 𝑌̂𝑒𝑐𝑙𝑖𝑝𝑠𝑒|
𝐶 𝐸𝐶𝐼→𝑒𝑐𝑙𝑖𝑝𝑠𝑒 = [
𝑌̂𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑋̂ 𝐸𝐶𝐼 𝑆̂ 𝐸𝐶𝐼 ⋅ 𝑋̂ 𝐸𝐶𝐼 𝑍̂ 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑋̂ 𝐸𝐶𝐼
𝑌̂𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑌̂𝐸𝐶𝐼 𝑆̂ 𝐸𝐶𝐼 ⋅ 𝑌̂𝐸𝐶𝐼 𝑍̂ 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑌̂𝐸𝐶𝐼
𝑌̂𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑍̂ 𝐸𝐶𝐼 𝑆̂ 𝐸𝐶𝐼 ⋅ 𝑍̂ 𝐸𝐶𝐼 𝑍̂ 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑍̂ 𝐸𝐶𝐼
]
𝑇
𝑅̅ 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 = 𝐶 𝐸𝐶𝐼→𝑒𝑐𝑙𝑖𝑝𝑠𝑒 ⋅ 𝑟̅𝐸 𝐶𝐼
𝑖𝑓 (√𝑅 𝑒𝑐𝑙𝑖𝑝𝑠𝑒(1)2 + 𝑅 𝑒𝑐𝑙𝑖𝑝𝑠𝑒(3)2 < 𝑅 𝑒𝑎𝑟𝑡ℎ) && (𝑟̅𝐸 𝐶𝐼 ⋅ 𝑆̂ 𝐸𝐶𝐼 < 0)
𝑇ℎ𝑎𝑛 𝑡ℎ𝑒 𝑠𝑝𝑎𝑐𝑒𝑐𝑟𝑎𝑓𝑡 𝑖𝑠 𝑖𝑛 𝑒𝑐𝑙𝑖𝑝𝑠𝑒. 𝑇ℎ𝑖𝑠 𝑓𝑖𝑔𝑢𝑟𝑒 𝑑𝑒𝑚𝑜𝑛𝑠𝑡𝑟𝑎𝑡𝑒𝑠 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 𝑓𝑜𝑟 𝑎 𝑡𝑦𝑝𝑖𝑐𝑎𝑙 𝑜𝑟𝑏𝑖𝑡:
Plot 4.3: Sunlight Flag

58
4.4.2.4 Disturbance Torques:
Gravity Gradient Torque: 𝑇̅𝑔𝑔 =
3𝜇
𝑟3
⋅ (𝑅̂ 𝑛𝑎𝑑𝑖𝑟)
𝑥
⋅ 𝑱 ⋅ 𝑅̂ 𝑛𝑎𝑑𝑖𝑟
𝑅̂ 𝑛𝑎𝑑𝑖𝑟 – The nadir vector in body frame
This figure shows the evolution of the Gravity gradient torque when the minimum inertia
axis was placed 45° to nadir direction (Axisymmetric spacecraft):
Plot 4.4: Gravity Gradient Torque
Residual Magnetic Dipole Torque: 𝑇̅ 𝑚𝑎𝑔
𝑑𝑖𝑠𝑡𝑢𝑟𝑏
= 𝑚̅ × 𝐵̅
𝑚̅ [𝐴𝑚2] – The residual magnetic dipole. This vector was modelled as a random direction
that slowly rotates with a magnitude of 0.1 [𝐴𝑚2]
𝐵̅ [𝑇𝑒𝑠𝑙𝑎] – Earth’s magnetic field vector in body frame
Solar Radiation Pressure Torque: 𝑇̅𝑠𝑜𝑙𝑎𝑟
= ∑ 𝛿̅𝑖 × (𝑊𝑓𝑙𝑢𝑥
𝑘
𝑖=1 (1 + 𝑅𝑖)
𝐴 𝑖
𝐶
𝑛̂ 𝑖 ⋅ 𝑆̂)
𝑊𝑓𝑙𝑢𝑥 = 1366 [
𝑤
𝑚2
] − 𝑇ℎ𝑒 𝑠𝑢𝑛′
𝑠 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 𝑓𝑙𝑢𝑥 𝑑𝑒𝑛𝑠𝑖𝑡𝑦
𝑅𝑖 − 𝑇ℎ𝑒 𝑖 𝑡ℎ 𝑠𝑖𝑑𝑒 𝑝𝑎𝑛𝑒𝑙′
𝑠 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐴𝑖 [𝑚2] − 𝑇ℎ𝑒 𝑖 𝑡ℎ 𝑠𝑖𝑑𝑒 𝑝𝑎𝑛𝑒𝑙′
𝑠 𝑎𝑟𝑒𝑎
𝐶 = 3 ⋅ 108
[
𝑚
𝑠𝑒𝑐
] − 𝑇ℎ𝑒 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡
𝑛̂ 𝑖 − 𝑇ℎ𝑒 𝑖 𝑡ℎ 𝑠𝑖𝑑𝑒 𝑝𝑎𝑛𝑒𝑙′
𝑠 𝑛𝑜𝑟𝑚𝑎𝑙 𝑣𝑒𝑐𝑡𝑜𝑟
𝑆̂ − 𝑇ℎ𝑒 𝑠𝑢𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝑖𝑛 𝑏𝑜𝑑𝑦 𝑓𝑟𝑎𝑚𝑒
𝛿̅𝑖 [𝑚] − 𝑇ℎ𝑒 𝑖 𝑡ℎ 𝑝𝑎𝑛𝑒𝑙 𝑡𝑜 𝑆 𝐶⁄ 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑚𝑎𝑠𝑠 𝑣𝑒𝑐𝑡𝑜𝑟
𝑘 − 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑖𝑑𝑒 𝑝𝑎𝑛𝑒𝑙𝑠 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑡𝑜 𝑡ℎ𝑒 𝑠𝑢𝑛
Calculated only for panels in which 𝑛̂ 𝑖 ⋅ 𝑆̂ > 0, otherwise the 𝑖 𝑡ℎ torque was set to 0.
Aerodynamic Torque: 𝑇̅ 𝑎𝑒𝑟𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐
= ∑ 𝛿̅𝑖 × (𝑘
𝑖=1 −
1
2
𝜌𝑉𝑟𝑒𝑙
2
𝐴𝑖 𝑛̂ 𝑖 ⋅ 𝑉̂𝑟𝑒𝑙)

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