THF-15 Satellite
Critical Design Review
Team Having Fun THF-15 Satellite
Matt Chapin1, Nick Wackel1, Olon Pierce1
The University of Alabama, Tuscaloosa, AL 35487
This report details a critical design proposal for replacing, on orbit, the Thermal
Infrared Sensor onboard Landsat 8 to extend its mission design life. Landsat 8 is an
American Earth observation satellite developed by NASA Goddard Space Flight
Center and the United States Geological Survey. The purpose of this report is to
present a feasible design of the propulsion, power, and thermal subsystems for
Critical Design Review.
I. Overview
Landsat 8 is an American Earth observation satellite launched on February 11, 2013. It is a collaboration
between NASA and the United States Geological Survey (USGS) with the underlying goal of “monitoring,
understanding, and managing the resources needed for human sustainment such as food, water and
forests” [1]. Landsat 8 collects multispectral images of Earth’s land surface and Polar Regions.
Instrumental in the collection of this data, the Thermal Infrared Sensor (TIRS) conducts thermal imaging
of two long-wavelength infrared bands. TIRS was a late addition to Landsat 8 and thus had a relaxed
design-life of three years. In order to extend the life of the Landsat 8 mission, NASA and USGS have
developed a robot capable of removing and replacing the sensor and request TIRS be retrofitted on orbit.
A. Mission Objective
The primary objective of the THF-15 satellite is to deliver the robot developed by NASA and USGS to
Landsat 8 and ensure successful completion of the TIRS repair. THF-15’s mission will be considered a
success if the following criteria are met:
1.
2.
3.
THF-15 intercepts Landsat 8 on orbit without severely altering its orbital trajectory and
causing structural or electronics damage.
THF-15 deploys the repair robot and installs the new TIRS on Landsat 8.
THF-15 detaches from Landsat 8 and performs a maneuver to enter a parking orbit.
Secondary objectives could be potential consequences of the THF-15 satellite project. For example,
successful completion of the primary objective will demonstrate lifespan-extension capabilities for the
Landsat project. The Landsat 8 satellite has a lifespan of five to ten years and therefore will require an
additional Thermal Infrared Sensor to remain fully operational for the remaining third of its lifespan.
B. Schedule
The existing TIRS on Landsat 8 will expire in early 2016. Launch of the THF-15 satellite must occur by
the end of 2016 to minimize the interruption in Landsat observations. Traditionally, the baseline for minor
satellite missions is an operational timeline of less than five years. THF-15 uses this model to estimate
time budgets for each phase of the operational timeline. The Conceptual Development Phase will focus
on securing government funding by conducting research and performing cost feasibility analysis. A
Preliminary Design Review will take place, and upon approval, THF-15 will proceed to the Detailed
Development Phase. This phase includes detailed mission design, technology development, and risk
mitigation. With most of the necessary technology (i.e. the repair robot and spare TIRS) already
developed by NASA and the USGS, THF-15 can reduce the amount of time spent in this phase. The
project will then undergo a Critical Design Review, and pending approval, will enter Production and
Deployment. This phase contains the manufacturing of the satellite, launch segment, and operational
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check once THF-15 reaches the target orbit. The THF-15 satellite will then be operated by the USGS until
its retirement.
Table 1. THF-15 Operational Timeline
Phase
Description
Time Budget
Conceptual
Development
Marketing
Research
2 months
4 months
Detailed Development
Production/Deployment
Tech Development/Risk
Mitigation
Detailed Design
Production
Launch
Ops Check on Orbit
4 months
8 months
5 months
1 month
10 days
Operation
USGS Control
5 years
Retirement
Orbit Transfer
1 month
As shown above in Table 1, THF-15 will have initial operating capability within two years. This fulfills the
requirement of replacing the Thermal Infrared Sensor by the end of 2016.
C. Payload
The payload of THF-15 is critical to mission success. It consists of two entities: the repair robot and spare
Thermal Infrared Sensor, both developed by NASA and the USGS. Each item has a mass and volume
associated with it, and these measurements will affect the design of the bus
The repair robot is an autonomous device that will remove the existing TIRS from Landsat 8 and install
the new one. It will deploy after THF-15 establishes a secure connection to Landsat 8. The robot is
designed to be send mission data continuously to the ground station until successful completion of the
mission is confirmed. Following completion, the robot with retract into the bus of THF-15 and await further
command. The mass of the repair robot given by NASA and the USGS is 100 kilograms. The volume is
assumed to be 0.5 cubic meters.
The Thermal Infrared Sensor (Fig. 1), one of two sensors utilized by Landsat 8, measures Earth’s surface
temperature in two thermal bands. The TIRS uses GaAs Quantum Well Infrared Photodetector arrays, a
lower-cost alternative to conventional infrared technology, to detect thermal infrared wavelengths of light.
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Figure 1. Thermal Infrared Sensor (TIRS)
The mass of TIRS is 225 kilograms, and its volume is 2.89 cubic meters. The dimensions are given as 2 x
0.76 x 1.9 meters.
D. Bus
The THF-15 satellite houses the mission payload, propulsion system, and communications structure. This
qualifies it as the bus of the mission architecture. Based on the combined volumes of both payload
components, THF-15 is projected to have a volume of 9 cubic meters. The dimensions are given as
2.2 x 1 x 2.1 meters.
In order to safely intercept Landsat 8 and attach to the satellite structure, the deployment face of THF-15
must be in the direction of motion. This requires THF-15 to have 3-axis attitude control, with a nadir-facing
communications antenna. Due to THF-15’s sun-synchronous orbit, the onboard solar panel will receive
constant solar energy to meet the power requirements. The propulsion system, in the form of two pivoting
thrusters, provides maneuverability and maintains attitude control. THF-15 also features a reaction wheel
that will provide additional attitude control by rotating the satellite by small amounts. This appendage will
assure proper alignment of THF-15 and may potentially reduce the amount of fuel needed to complete
the mission.
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II. Propulsion Subsystem
A. Delta V Budget
The first step to design the propulsion subsystem is developing a delta V budget, an accumulation of
orbital maneuvers that THF-15 will be required to complete for mission success. The budget is divided
into four phases: insertion, intercept, maintenance, and retirement. Insertion of THF-15 into its target orbit
is achieved by a two-stage launch vehicle coupled with a plane change maneuver by the satellite. The
intercept phase involves a delta V maneuver that will allow THF-15 to rendezvous with Landsat 8. Orbital
maintenance includes atmospheric drag makeup, attitude control, station keeping, and evasive
maneuvers. Finally, THF-15 will enter retirement by slowing down until it reaches an altitude of 350
kilometers.
1. Insertion
In order to rendezvous with Landsat 8, THF-15 will need to enter the sun synchronous orbit described by
Table 2.
Table 2. Orbital Parameters
Regime
Semi-major axis
Eccentricity
Perigee
Apogee
Inclination
Period
Sun-synchronous
7,080.49 kilometers
7.63E-05
708 kilometers
710 kilometers
98.20 degrees
98.83 minutes
The delta V requirement for orbital insertion was estimated using the Pythagorean Theorem to calculate
the velocity vector at an orbit of 710 km. Figure 1. The orbital speed, which is directed tangent to the orbit,
is given by Eq. 1.
𝑉𝑜 2 =
𝜇
𝑅𝑒 + ℎ
Eq. (1)
Equation 2 is the drop speed due to gravitational acceleration and is directed towards the earth. Taking
the sum of the squares gives Eq. 3, which is the estimated delta V requirement to achieve an orbit of 710
km.
𝑉𝑎 2 = 2𝑔ℎ
Eq. (2)
∆𝑉 = √𝑉𝑜 2 +𝑉𝑎 2
Eq. (3)
Equation 3 only accounts for reaching the altitude of the target orbit, not the inclination. To incorporate
this requirement into the delta V budget, a simple plane change is added to the model. To model for the
worst case scenario, the required plane change would be from 0 to 98.2 degrees. The delta V required is
given by Eq. 4.
𝜃
∆𝑉 = 2𝑉𝑜 sin⁡( )
2
Eq. (4)
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Table 3 gives the results for the orbital insertion model. The final value is the required delta V to reach the
target orbit.
Table 3. Orbital Insertion Estimate
Orbital Speed
Drop Speed
Altitude Delta V
Plane Change Delta V
Insertion Delta V
7.499 km/s
3.732 km/s
8.376 km/s
5.000 km/s
13.38 km/s
The launch vehicle chosen is the Atlas V 401, shown in Fig. 2, which contains the Common Core Booster
(CCB) and Centaur III (CIII) upper stage. The launch is scheduled for July 2016 from Vandenberg Air
Force Base SLC-3E. The CCB is a Pratt & Whitney/NPO Energomash RD-180 engine able to generate
3,827 kN of thrust and a specific impulse (ISP) of 311.1 seconds at sea level. It has an inert mass of
20,743 kg and can hold up to 284,089 kg of propellant. The second stage CIII is also a Pratt & Whitney
engine capable of 99.2 kN of thrust and an ISP of 450.5 seconds. It uses four 27 N hydrazine thrusters
and eight 40.5 N lateral hydrazine thrusters. The CII is 1,914 kg and carries 20,672 kg of propellant.
Figure 2. Atlas V 401 Configuration
To calculate the delta V that can be achieved by the Atlas V 401, both stages were considered. Shown in
Fig. 1 is the two-stage launch of the Atlas V 401. The CCB burns for 241 seconds and reaches an altitude
of 113 km before detaching. The Centaur upper stage will then ignite and reach an altitude of 710 km and
inclination of 98.2 degrees.
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Figure 3. Atlas V 401 Launch Segment
The delta V capability of the CCB and CIII were calculated using the Tsiolkovsky rocket equation given by
Eq. 5. For the CCB, the initial mass is the total mass at launch including the launch vehicle and satellite.
The initial mass for the CIII is the sum of the upper stage and satellite masses. The delta V calculated
assumes that all propellant is consumed for that stage.
∆𝑉 = 𝐼𝑠𝑝 𝑔0 ln
𝑚0
𝑚1
Eq. (5)
Table 4 gives the results for exhaust velocity, delta V, and propellant required. As shown below, the total
delta V achievable by the Atlas V 401 is 15.76 km/s. This value is greater than the delta V required of
13.38 km/s, so the launch vehicle chosen can achieve the target orbit.
Table 4. Orbital Insertion
Target
Exhaust Velocity
Delta V
Common Core Booster
113 km
3.054 km/s
6.132 km/s
Centaur III
710 km, 98.2 deg
4.419 km/s
9.628 km/s
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2. Intercept
Once THF-15 reaches the target orbit of 710 km and 98.2 degrees, it must rendezvous with Landsat 8 to
initiate the repair of TIRS. The delta V requirement accounts for the worst case scenario, where THF-15
and Landsat 8 are separated by a phase of 180 degrees. The intercept is accomplished by THF-15
entering an elliptical phasing orbit to change the time-position along its orbit. Figure 4 shows the concept
of an orbit phasing maneuver.
Figure 4. Orbital Phasing Maneuver
The first step to determining the delta V requirement is to calculate the mean motion, Eq. 6, of Landsat 8
in orbit. The mean motion is a measure of how fast a satellite progresses around its elliptical orbit. In an
elliptical orbit the angular velocity is not constant, so mean motion is used as the time-average angular
velocity over an orbit.
𝜇
𝑛𝑡 = √ 3
𝑎𝑡
Eq. (6)
Once the mean motion is found, the period of the phase maneuver is calculated by Eq. 7. It is dependent
on the number of orbits that the target will complete before rendezvous. The period is for the entire phase
orbit, not just one revolution around the Earth.
𝑃𝑝 =
𝑘𝑡 2𝜋 − ∆𝜃
𝑛𝑡
Eq. (7)
Equation 8 calculates the semi-major axis of the phase orbit using Kepler’s third law of planetary motion.
It is dependent on the number of orbits that the interceptor will complete before rendezvous.
𝑃𝑝 2 1
𝑎𝑝 = [𝜇(
) ]3
2𝜋𝑘𝑖
Eq. (8)
Finally, the delta V requirement is calculated as a two-impulse Hohman transfer where THF-15 will exit,
then reenter, its original orbit. The velocity of THF-15 before and after the maneuver is given by Eq. 1,
and the phase velocity can be calculated by Eq. 9. Therefore, the required engine impulses are given by
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Eqs. 10 & 11.The magnitude of each delta V requirement is equal, but the directions are opposite to
account for exiting and reentering the original orbit.
𝑉=√
2𝜇 𝜇
−
𝑟
𝑎𝑝
Eq. (9)
2𝜇 𝜇
𝜇
∆𝑉1 = √ −
−√
𝑟
𝑎𝑝
𝑟
Eq. (10)
𝜇
2𝜇 𝜇
∆𝑉2 = √ − √ −
𝑟
𝑟
𝑎
Eq. (11)
Table 5 gives the results for the intercept maneuver. The number of orbits that Landsat 8 and THF-15
complete before rendezvous were iterated to find an acceptable value, with respect to reducing delta V
while maintaining a reasonable elapsed time of the maneuver. The values used for calculation were
Landsat 8 completing 490 revolutions and THF-15 completing 520.
Table 5. Orbital Intercept Delta V
Landsat 8 Mean Motion
Phase Period
Semi-major Axis
Delta V 1
Delta V 2
1.060E-3 rad/s
3.073E6 s
7068 km
-10.5 m/s
10.5 m/s
As shown in the table above, THF-15 will slow down at perigee to enter an elliptical orbit that has a
slightly shorter period than the original orbit. The difference between the periods of the original and
phasing orbit is 15.24 seconds, and the maneuver will take a little more than 35 days to complete.
3. Maintenance
THF-15 will need to be able to maintain its orbit to ensure complete mission success. The delta V budget
for orbital maintenance is divided into drag makeup, attitude control, station keeping, and evasive
maneuvers. These delta V requirements are typically very small and measured per year.
In a low-Earth orbit, frequent collisions of gas molecules with the satellite cause drag. If left unchecked,
the altitude of the satellite’s orbit will decay resulting in reentry. The delta V requirement for atmospheric
drag makeup is given by Eq. 12. The requirement is given per revolution around the Earth. The drag
coefficient is estimated to be 2.2, and the mass of the satellite is 575 kg. The cross-sectional area of THF15 is 5 m2. Atmospheric density at 710 km is 1.47E-13 kg/m3.
𝐶𝑑 𝐴
∆𝑉 = 𝜋(
)𝜌𝐴𝑉
𝑚
Eq. (12)
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To meet the THF-15 satellite’s attitude control requirements, low-impulse thrust bits will be used to
maintain the orientation. For a 3-axis stabilized spacecraft, such as THF-15, the delta V requirement per
year is estimated to be 10 m/s.
For Earth observation satellites in a sun-synchronous orbit, the gravitation of the Sun and Moon will affect
the orbit. This gravitation will cause inclination changes that need to be compensated for. Solar
gravitation is a significant factor for THF-15’s station keeping, and the delta V requirement per year is
estimated to be 6 m/s for East/West and 55 m/s for North/South.
In addition to orbital maintenance, the delta V budget needs to account for any evasive maneuvers that
THF-15 could potentially have. 100 m/s of the budget will be allocated for this.
Table 6 gives each delta V requirement for orbital maintenance.
Table 6. Orbital Maintenance Delta V
Drag Makeup
Attitude Control
East/West Station Keeping
North/South Station Keeping
Evasive Maneuvers
Delta V Requirement
1.105 m/s per year
10 m/s per year
6 m/s per year
55 m/s per year
100 m/s
4. Retirement
Once THF-15 has completed its mission, it will perform a maneuver to decrease its altitude to 350 km. At
this altitude, controlled reentry will occur after approximately 217 days. Equation 13 is used to calculate
the delta V requirement for this maneuver.
𝐻𝑖 − 𝐻𝑒
∆𝑉 = 𝑉𝑜 [
]
4(𝑅𝑒 − 𝐻𝑒 )
Eq. (13)
The calculated delta V requirement for retirement is 100 m/s.
B. Propulsion Subsystem Selection
The selection of the propulsion type is based on key performance requirements that impact operation,
weight, and cost. Those requirements are the delta V budget and thrust level constraints for orbital
insertion and maintenance. With these requirements in mind, reasonable options can be identified for
further analysis.
1. Requirements
From the delta V budget, the extreme conditions will be used as the initial criteria for selecting the
subsystem. The maximum delta V requirement for the onboard propulsion system is 100 m/s. The
minimum is 6 m/s per year for East/West station keeping.
2. Options
The principal propulsion options for orbit maintenance and attitude control are cold gas, monopropellant,
bipropellant, and dual mode. Cold gas systems are extremely simple, but have low performance and are
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the heaviest system for a given performance level. Monopropellant systems are simple, reliable, and low
cost, but also have low performance. Bipropellant and dual mode systems are high performance, but are
significantly more complicated than other systems.
The main drivers for the selection of the propulsion system are performance, complexity, and weight. Cold
gas thrusters would not be able to generate the thrust required to perform the intercept or evasive
maneuvers without large mass requirements. Bipropellant systems are complicated and generally used
for large thrust maneuvers. THF-15’s mission will not require high thrust levels, so a bipropellant system
would not be fully utilized. A monopropellant system would offer the most appropriate level of
performance while remaining simple and low-weight.
3. Selection
THF-15 will use a monopropellant system for onboard propulsion. One of the common monopropellants
used in the space industry is hydrazine, N2H4. Hydrazine is generally used as a low-power propellant for
spacecraft maneuvering thrusters. In hydrazine engines, the propellant is passed by a catalyst that
causes it to decompose into ammonia, nitrogen gas, and hydrogen gas. Equations 14-16 show the
reactions that occur in a hydrazine engine.
3𝑁2 𝐻4 → 4𝑁𝐻3 + 𝑁2
Eq. (14)
𝑁2 𝐻4 → 𝑁2 + 2𝐻2
Eq. (15)
4𝑁𝐻3 + 𝑁2 𝐻4 → 3𝑁2 + 8𝐻2
Eq. (15)
The first two reactions are exothermic, producing large volumes of hot gas from a small volume of liquid.
Thus, hydrazine is an efficient thruster propellant with a vacuum ISP of 225.
C. Propulsion Subsystem Architecture
1. Hydrazine Thrusters
For thrust operations, the flow of hydrazine is controlled by an electric-solenoid valve. Depending on the
thrust requirement, this action may be pulsed or long duration. The pressure in the propellant tank forces
hydrazine through the injection tube and into the injection head. The injection tube is bent in a coiled
shape that provides flexibility for the tube to handle stresses caused by the temperature disparity between
the inlet and injection head. The injection head has bores that uniformly distribute the hydrazine
propellant across the front of the upper catalyst bed. A screen between the injection head and the upper
catalyst bed prevents catalyst particles from entering the injection head and blocking the bores. The
catalyst beds consist of alumina pellets impregnated with iridium that cause the liquid hydrazine to heat to
its vaporization point upon contact. The upper and lower catalyst beds are separated by a screen and
distinguished by different grain sizes, with the upper having slightly larger grains. The upper bed
promotes the decomposition of the liquid or partially evaporated hydrazine, while the lower bed focuses
on the partial dissociation of ammonia for efficiency. For most thruster applications requiring high specific
impulse, the lowest percentage of ammonia dissociation that can be maintained reliably is between 3040%. Finally, the products of the hydrazine decomposition exit from the chamber through a high
expansion nozzle to produce thrust. Figure 5 shows an example of a hydrazine thruster.
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Figure 5. Hydrazine Thruster
THF-15 will have a total of twelve hydrazine thrusters, two per axis for redundancy.
2. Propellant/Pressurant Tank
THF-15 is 3-axis stabilized, and therefore requires a propellant orientation method that operates under
zero gravity conditions. The simplest way to achieve this is to use high-pressure gas to displace the
propellant from its storage tank. Pressure-fed systems are reliable, light-weight, and deliver low to
moderate levels of thrust and total impulse. Alternative options are to use a pump or piston, but this
requires the use of a turbine or electric motor to drive the system. Pump-fed systems allow for higher
thrust and impulse levels, but are more complex and generally used for launch vehicles or upper stages.
THF-15 will use the blowdown system model, Fig. 6, with a positive expulsion tank to provide the engines
with fuel. Positive expulsion uses an active element, such as bladder or diaphragm, to serve as a barrier
between the pressurant gas and liquid propellant. This forces the liquid propellant, without any gas or
vapor, into the engine feed lines.
Figure 6. Blowdown System
There are several available options for positive expulsion tanks. The options that are typically used for
spacecraft applications are metal diaphragms, rubber diaphragms, rubber bladders, and metal bellows.
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Metal diaphragm and bellows tanks are high-weight, high-cost configurations. The metal diaphragm
requires a large pressure difference for expulsion, and the metal bellows has low volumetric efficiency.
The rubber diaphragm has a smaller pressure difference requirement during expulsion and high expulsion
efficiency. The only potential disadvantage of rubber diaphragm tanks is the compatibility with propellant.
ATK PSI Operations, the world’s largest manufacturer of propellant and pressurant tanks, has developed
a long-term hydrazine compatible diaphragm material, AF-E-332, that has over 30 years of demonstrated
use. The diaphragm configuration is preferred over the bladder because of its lighter weight and less
severe folding pattern during operation. On a side not, Landsat 8 currently uses a rubber diaphragm tank
developed by ATK PSI.
To size the propellant tank, the volume of the hydrazine propellant is needed. Using an alternate form of
the Tsiolkovsky rocket equation, Eq, 16, the mass of hydrazine required for each delta V maneuver can
be found.
𝑚𝑓 = 𝑚0 ∗ 𝑒
∆𝑉
−
𝑉𝑒
Eq. (16)
Table 7 lists the required propellant mass for each maneuver. The delta V requirements were calculated
over a five year period, which is the maximum lifespan of THF-15.
Table 7. Propellant Mass Required
Intercept 1
Intercept 2
Drag Makeup
Attitude Control
East/West Station Keeping
North/South Station Keeping
Evasive Maneuver
Deorbit
Propellant Required
3.962 kg
3.943 kg
11.12 kg
15.36 kg
11.12 kg
95.21 kg
31.78 kg
29.79 kg
The total mass of hydrazine required for the delta V budget is 194.4 kg. Using a 25% margin of error, the
mass of onboard propellant is 250 kg. To find the volume required for the propellant tank, the mass is
divided by the density of hydrazine at storage pressure and max operating temperature. The density of
hydrazine at these properties is 1021 kg/m 3. Therefore, the required volume is .2449 m3 or 244.9 L.
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Figure 7. ATK 80514-1 Blowdown Tank
The ATK 80514-1, Fig. 7, is a blowdown tank designed to hold 245.8 L of propellant at an operating
pressure of 28.41 bar. The pressurant volume for this tank configuration is 69.64 L of Helium. It is
constructed of 6A1-4V titanium and has a diameter of 66.04 cm. It has a dry mass of 28.12 kg, which is
approximately 8% of the total THF-15 bus mass. If estimating the fuel lines as 10% of the tank mass,
THF-15 fuel lines will have a combined mass of 3 kg.
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III. Power Subsystem
The purpose of the electrical power subsystem is to provide, store, distribute, and control spacecraft
electrical power.
Electrical Power
Subsystem
Power Source
Energy Storage
Power Distribution
Power Regulation
and Control
Figure 8. Functional Breakdown for the Satellite’s Power Subsystem
When designing the power subsystem, the most important sizing requirements are the demands for
average and peak electrical power and the inclination and altitude of the satellite.
A. Power Requirements
The electrical power loads for mission operations vary from beginning-of-life (BOL) to end-of-life (EOL).
For this mission, the end-of-life power demands may need to be reduced to compensate for solar array
performance degradation. Calculating the average electrical power needed at EOL will determine the
necessary size of the power source.
1. Payload
Our payload consists of both a replacement Thermal InfraRed Sensor and the robot that will replace the
old sensor with the new one. As both of these have been developed by NASA and the USGS, our
satellite does not need to provide power to either of the two payloads.
2. Propulsion
The THF-15 will need to be 3-axis stabilized, which will be accomplished with hydrazine thrusters. Each
one of these thrusters requires 5 W of power in order to operate. The satellite was designed with a total
of twelve thrusters to allow for redundancy. The maximum power budget for the propulsion system was
calculated to be 30 W as any maneuver would require at most six thrusters to be fired.
3. Attitude and Control
To maintain a 3-axis stabilization, an altitude and control system will be used in conjunction with the onboard propulsion system. The system will use reaction and momentum wheels to allow for pitch axis
torqueing and roll and yaw axis passive stability. Gyros and accelerometers will be implemented to
maintain a desired level of precision for the orbital profile. Tables 8-9 compare the various sensors and
actuators. From the tables, the power budget for the ADCD system is 310 W.
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Table 8. ADCS Actuators
Table 9. ADCS Sensors
4. Telemetry, Tracking, and Command
The THF-15 will use a typical X-band communications system. This system allows for necessary
redundancy and fulfills the mission requirements for a fixed ground station and a sun-synchronous orbit.
From Table 10, the power requirement is found to be 45.4 W.
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Table 10. Parameters for TT&C Subsystems
5. Command and Data Handling
The mission does not include collecting and transferring data and as such, the THF-15 requires only a
simple command and telemetry systems. A power budget of 12 W for this subsystem can be found using
Table 11.
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Table 11. C&DH Size, Weight, and Power
6. Thermal
The thermal subsystem will have no power requirement and will instead be used to dissipate heat.
7. Power
The power subsystem will require power in order to distribute and regulate power across the entire
satellite. For a satellite of this size, 5-25% of operating power is required for the power subsystem to
perform its functions. To allow for redundancy, the THF-15 has been designed with a power budget of
100 W for the power subsystem, which is 20% of the overall, power onboard the satellite.
8. Structure
The satellite structure will not have a power requirement.
The overall required power breakdown is shown in Table 12.
Table 12. Power Consumption by Subsystem
Satellite Subsystem
Power Requirement [W]
Payload
0
Propulsion
30
Attitude and Control
310
Telemetry, Tracking, and Command
45.4
Command and Data Handling
12
Thermal
0
Power
100
Structure
0
Overall Power
497.4
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B. Power Sources
The power source generates electrical power within the satellite. In general, there are four possible types
of power sources that could be used. Photovoltaic solar cells convert incident solar radiation directly to
electrical energy. Static power sources use a heat source for direct thermal-to-electrical conversion.
Dynamic power systems also use a heat source to produce electrical power using the Brayton, Stirling, or
Rankine cycles. Fuel cells convert the chemical energy of an oxidation reaction to electricity. Table 13
compares the various power source options.
Table 13. Comparing Power Sources
This mission requires an Earth-orbiting satellite, which does not allow for a nuclear reactor power source
due to the threat of nuclear radiation. The satellite requires a relatively constant power consumption
rather than large peaks throughout its orbit. Fuel fells could be used to fulfill the mission, but the required
fuel tanks would add unnecessary weight. Fuel cells also have a finite amount of potential power
production. Solar panels allow for continuous power production in a sun-synchronous orbit, and are
known for being rather reliable.
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C. Solar Array Design
Mission life and the average power requirement are the two key design considerations in sizing the solar
array for the satellite. The solar system must be sized to meet the power requirements at EOL, due to
degradation over life. In order to calculate the solar-array needed for the satellite, the power provided by
the solar array during daylight must first be determined.
𝑃𝑠𝑎 =
𝑃𝑒 𝑇𝑒 𝑃𝑑 𝑇𝑑
+
𝑋𝑒
𝑋𝑑
𝑇𝑑
Eq. (17)
𝑃𝑠𝑎 ⁡: power provided by solar array
𝑃𝑒 , 𝑃𝑑 ∶⁡ satellite’s power requirements during eclipse and daylight
𝑇𝑒 , 𝑇𝑑 ∶⁡lengths of eclipse and daylight per orbit
𝑋𝑒 = 0.65 , 𝑋𝑑 = 0.85 ∶ efficiency values for eclipse and daylight for direct energy transfer
As this satellite will be in a sun-synchronous orbit, there will not be an eclipse period. Using Eq. 17, the
Psa is found to be 585.176 W.
Table 14 shows the efficiencies of the three main types of solar cells: silicon, gallium arsenide, and
indium phosphide.
Table 14. Performance for Solar Cells
Gallium arsenide has the highest efficiency and indium phosphide reduces the degrading effects of
radiation, but both cost about three times more than silicon. Because cost is a driving factor for
completing the mission, silicon will be used as the technology is more reliable and has a lower cost per
𝑊
watt. Solar panels have a known solar-illumination intensity value of 1367⁡ 2 if the solar radiation is
𝑚
normal to the surface, which can be used along with a material’s BOL efficiency to calculate the ideal
solar cell output performance per unit area, P0. Silicon solar cells have an efficiency of 14% which gives
𝑊
a P0 value of 202⁡ 2. As this is the ideal value, the realistic power production capability of the
𝑚
manufactured solar array is needed. An assembled solar array is less efficient than single cells due to
design inefficiencies, collectively referred to as inherent degradation, I d. Table 15 shows the inherent
degradation values.
19
Table 15. Elements of Inherent Solar Array Degradation
At beginning-of-life, a solar array’s power per unit area can be calculated using Eq. 18.
𝑃𝐵𝑂𝐿 = 𝑃0 𝐼𝑑 𝑐𝑜𝑠𝜃
Eq. (18)
𝑃𝐵𝑂𝐿 ∶⁡power at beginning-of-life
𝑃0 ∶ solar cell output performance per unit area
𝐼𝑑 ∶ inherent degradation
𝜃 ∶ Sun incidence angle between the vector normal to the surface and the Sun line
Using an inherent degradation of 0.77 and a worst case Sun incidence angle of 23.5 °, the PBOL is
𝑊
calculated to be⁡142.64⁡ 2 . As the mission progresses, the solar array’s performance will degrade. The
𝑚
life degradation, Ld, for a silicon solar array is as much as 3.75% per year. The actual lifetime
degradation can be found using Eq. 19.
𝐿𝑑 = (1 −
𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒⁡𝑙𝑖𝑓𝑒
)
𝑦𝑒𝑎𝑟
Eq. (19)
This gives a lifetime degradation value of 0.826 for the five year mission. Now that the lifetime
degradation and power production capability at beginning-of-life are known, the power at end-of-life can
be calculated using Eq. 20.
𝑃𝐸𝑂𝐿 = 𝑃𝐵𝑂𝐿 𝐿𝑑
Eq. (20)
𝑊
The power production capability at end-of-life was found to be⁡117.821⁡ 2. Finally, the required solar
𝑚
array area to produce the necessary power can be sized. The solar-array area is calculated using Eq. 21.
𝐴𝑠𝑎 =
𝑃𝑠𝑎
Eq. (21)
𝑃𝐸𝑂𝐿
The resulting Asa for the THF-15 is 4.967⁡𝑚2 . Assuming the worst possible specific power value for solar
𝑊
panels from Table 13,⁡25⁡ , the mass of the solar array was found to be⁡23.407⁡𝑘𝑔. The worst case cost
𝑘𝑔
of these solar panels is found to be about $1,760,000 using the specific cost of 3000⁡
$
𝑊
from the table.
D. Energy Storage
As the solar panels aboard the THF-15 will be producing power continuously throughout the entire
mission, a way to store the power is required. A secondary battery will be used as this class of battery
sacrifices a lower specific energy density for the ability to be recharged. The battery will also work as a
backup power source in the event the satellite changes to an undesired attitude. Secondary batteries are
shown in Table 16.
20
Table 16. Characteristics of Secondary Batteries
The nickel-cadmium secondary battery was chosen as it will fulfill the mission requirements as a backup
power source and has a favorable specific energy density. This is also a well-tested and space-qualified
battery which is essential for a backup power source.
21
IV. Thermal Subsystem
THF-15 will require a thermal subsystem to ensure all onboard components will remain functional
throughout the mission and guaranteed mission success. Due to limits on time full thermal analysis will be
unavailable, but in discussion with the contractor it has been agreed upon that steady state conditions will
be satisfactory for this mission segment. In order to achieve this steady state condition the following
formula must be satisfied.
𝑄𝑖𝑛 + 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 − 𝑄𝑜𝑢𝑡 = 0
Eq. (22)
𝑄𝑖𝑛 + 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑄𝑜𝑢𝑡
Eq. (23)
Which can easily be simplified to.
By using the energy absorbed by the space craft as well as the energy created by the internal parts in the
space craft, the overall minimum and maximum temperature of the body of THF-15 can be calculated at a
steady state condition.
A. Target Temperature
Differing components on board the THF-15 will require different temperature ranges to remain
operational. Below in Table 17 are the reasonable estimates for both the operational as well as survival
temperatures for many of the crucial components.
Table 17. Typical Temperature Ranges
Component placement within the satellite is crucial, as the elements that can operate in colder conditions
can be placed along the colder deep space facing walls, and the components that require more heat can
be centralized around others that are generating that heat. As stated a full thermal analyses will be
unavailable and we will only be looking at the overall body temperature of the satellite. As seen from the
Table 17 above the batteries will be the restricting factor for our satellite with an operational temperature
22
range of 273 – 288 Kelvin. In discussion with the contractor a differing temperature range of 5 degrees
higher was settled upon, 278-293 Kelvin, due to the steady state calculations vs. a full thermal analysis.
B. Satellite Configuration
THF-15 has been designed to carry the replacement TIRS as well as the robot designed for installation,
both provided by NASA and the USGS. The dimensions for the THF-15 are 2.2 x 1 x 2.1 m tall, this will
provide room for the TIRS (2 x .76 x .19 m) as well as an additional 1.74 m 3 for the replacement robot.
The THF-15 will be in sun-synchronous orbit and will always have one nadir facing side as well as one
side always facing the sun. Both of these faces will be the larger sides (2.2 x 2.1 m) of the satellite with
the goal of absorbing as much heat as possible. The other four sides, with a combined total surface area
of 8.6 m2, will always be facing out into deep space radiating off the excess heat. A simple drawing is
shown below in Figure 9.
Figure 9. Satellite Configuration Diagram
23
C. Thermal Control Options
In general there are two different types of ways to control the onboard temperature of a space craft. This
first is having an active thermal control system, or ATCS, and the second is a passive control thermal
system, PCTS. For this project we will utilized a PCTS to save weight, time, as well as money. Passive
control thermal systems are comprised of different insulations as well as coatings that are applied to the
outside of the space craft. Different coatings and materials have differing absorptivity, α, and emissivity, ε,
properties that can be combined to find the optimal temperature range. Below in Table 18 are the different
coatings and their properties we tested for the THF-15.
Table 18. Thermal Material Properties
α min
α max
ε
S13G-LO
.2
.25
.85
Z93
.17
.2
.92
ZOT
.18
.2
.91
Chemglaze A276
.22
.28
.88
Chemglaze Z306
.92
.98
.89
3M Black Velvet
.97
.97
.84
8 mil Quartz Mirror
.05
.08
.8
2 mil Silvered Teflon
.05
.09
.66
5 mil Silvered Teflon
.05
.09
.78
2 mil Aluminized Teflon
.1
.16
.66
5 mil Aluminized Teflon
.1
.16
.78
½ mil
.34
.34
.55
1 mil
.38
.38
.67
2 mil
.41
.41
.75
5 mil
.46
.46
.86
.08
.17
.04
Material
White Paints
Black Paints
Optical Solar Reflectors
Aluminized Kapton
Metallic
Vapor Deposited
Aluminum
24
Bare Aluminum
.09
.17
.07
Vaporized Deposited Gold
.19
.3
.03
Anodized Aluminum
.25
.86
.45
¼ mil Mylar
Deteriorates
Deteriorates
.34
Beta Cloth
.32
.32
.86
Astro Quartz
.22
.22
.8
MAXORB
.9
.9
.1
Miscellaneous
D. Thermal Calculations
In this section the formulas for all calculations will be discussed along with associated values found for
the different materials. As stated earlier the driving equation for these calculations is shown below.
𝑄𝑖𝑛 + 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑄𝑜𝑢𝑡
Eq. (24)
1. Energy In From Sun
The first step in designing the thermal system was to determine the amount of heat that was being taken
in by THF-15. There are multiple different sources that contribute heat to the satellite while in orbit. The
first, being the most obvious, is the direct heat taken in from the sun. One side of THF-15 will always be
facing the sun and must be able to absorb the energy without over heating the entire satellite. The
equation for energy absorbed from the sun is shown below.
𝑄𝑠𝑢𝑛 = 1367⁡
𝑤
𝑚2
∗ 𝐴𝑠𝑢𝑛 ∗ ⁡ 𝛼𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
Eq. (25)
Where
𝐴𝑠𝑢𝑛 = 𝐴𝑟𝑒𝑎⁡𝑜𝑓⁡𝑆𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒⁡𝐹𝑎𝑐𝑖𝑛𝑔⁡𝑆𝑢𝑛
Eq. (26)
𝛼𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔⁡𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙⁡𝐴𝑏𝑠𝑜𝑝𝑡𝑖𝑣𝑖𝑡𝑦
Eq. (27)
This equation was run with all materials using both the minimum and maximum absorptivity, α, to
calculate the worst case scenarios. These values can be seen below in Table 19.
Table 19. Material Absorptivity
Material
Minimum (W)
Maximum (W)
S13G-LO
1271.42
1589.28
Z93
1080.71
1271.42
White Paints
25
ZOT
1144.28
1271.42
Chemglaze A276
1398.57
1778.00
Chemglaze Z306
5848.55
6229.98
3M Black Velvet
6166.41
6166.41
8 mil Quartz Mirror
317.86
508.57
2 mil Silvered Teflon
317.86
572.14
5 mil Silvered Teflon
317.86
572.14
2 mil Aluminized Teflon
635.71
1017.14
5 mil Aluminized Teflon
635.71
1017.14
½ mil
2161.42
2161.42
1 mil
2415.71
2415.71
2 mil
2606.42
2606.42
5 mil
2924.28
2924.28
Vapor Deposited
Aluminum
508.57
1080.71
Bare Aluminum
572.14
1080.71
Vaporized Deposited
Gold
1207.85
1907.14
Anodized Aluminum
1589.28
5467.12
¼ mil Mylar
N/A
N/A
Beta Cloth
2034.28
2034.28
Astro Quartz
1398.57
1398.57
MAXORB
5721.41
5721.41
Black Paints
Optical Solar Reflectors
Aluminized Kapton
Metallic
Miscellaneous
26
2. Energy In From Earth
The energy taken in from the Earth is divided into two separate categories. There is the heat that is
reflected from the earth, albedo, as well as the heat that is naturally given off by the earth. The amount of
heat naturally given off as well as the amount of heat reflected by the earth is dependent on the orbit of
the satellite. Emitted radiation values as well as the albedo percentage are represented in the figure
below.
Table 20. Radiation for Orbit Inclination
The THF-15 will be at in inclination of around 90 degrees so only the bottom row applies to our
calculations. Throughout its period the satellite we receive between 218 and 244 W/m 2 directly radiated
from the earth, qradiation. It can also be seen from the above figure that it will receive an albedo of 23-57%
of the total reflected heat. The formulas for calculating the energy taken in by the satellite are given
below.
𝑄𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑛 = ⁡ 𝑞𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 ∗ 𝐴𝑒𝑎𝑟𝑡ℎ ∗ 𝛼𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
Eq. (28)
𝑄𝑎𝑙𝑏𝑒𝑑𝑜 = 𝑞𝑎𝑙𝑏𝑒𝑑𝑜 ∗ 𝑎𝑙𝑏𝑒𝑑𝑜 ∗ 𝐴𝑒𝑎𝑟𝑡ℎ ∗ ⁡ 𝛼𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
Eq. (29)
Where
𝑞𝑟𝑎𝑑𝑖𝑡𝑖𝑜𝑛 = 𝐸𝑚𝑖𝑡𝑡𝑒𝑑⁡𝑅𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
𝑞𝑎𝑙𝑏𝑒𝑑𝑜 = 1000⁡
𝑊
𝑚2
Eq. (30)
Eq. (31)
𝐴𝑒𝑎𝑟𝑡ℎ = 𝐴𝑒𝑟𝑎⁡𝑜𝑓⁡𝑆𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒⁡𝐹𝑎𝑐𝑖𝑛𝑔⁡𝐸𝑎𝑟𝑡ℎ
Eq. (32)
𝛼𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔⁡𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙⁡𝐴𝑏𝑠𝑜𝑝𝑡𝑖𝑣𝑖𝑡𝑦
Eq. (33)
Because Aearth and αmaterial are the same in both cases, a simplified formula for total Q earth is given below.
𝑄𝑒𝑎𝑟𝑡ℎ = (𝑞𝑟𝑎𝑑𝑖𝑡𝑖𝑜𝑛 + (𝑞𝑎𝑙𝑏𝑒𝑑𝑜 ∗ 𝑎𝑙𝑏𝑒𝑑𝑜)) ∗ 𝐴𝑒𝑎𝑟𝑡ℎ ∗ 𝛼𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
Eq. (34)
27
This was calculated for all materials using the minimum and maximum values for emitted radiation,
albedo, and absorptivity to find the worst case scenarios. The values are given in Table 21 below.
Table 21. Material Radiation
Material
Minimum (W)
Maximum (W)
S13G-LO
413.95
940.17
Z93
351.56
752.14
ZOT
372.56
752.14
Chemglaze A276
455.35
1052.99
Chemglaze Z306
1904.18
3685.47
3M Black Velvet
2007.67
3647.86
8 mil Quartz Mirror
103.49
300.85
2 mil Silvered
Teflon
103.49
338.46
5 mil Silvered
Teflon
103.49
338.46
2 mil Aluminized
Teflon
206.98
601.71
5 mil Aluminized
Teflon
206.98
601.71
½ mil
703.72
1278.63
1 mil
786.51
1429.06
2 mil
848.60
1541.88
5 mil
952.09
1729.91
165.58
639.32
White Paints
Black Paints
Optical Solar
Reflectors
Aluminized Kapton
Metallic
Vapor Deposited
Aluminum
28
Bare Aluminum
186.28
639.32
Vaporized
Deposited Gold
393.25
1128.20
Anodized
Aluminum
517.44
3234.48
¼ mil Mylar
N/A
N/A
Beta Cloth
662.32
1203.42
Astro Quartz
455.35
827.35
MAXORB
1862.78
3384.61
Miscellaneous
3. Energy Generated
The last component that makes up the total energy taken in by THF-15 is the actual energy generated on
board by the components. The power subsystem lead, Matt Chapin, was consulted with to estimate the
energy needed for THF-15 to have a successful mission. For our calculations it was estimated about
497.4 watts of power would be generated, and of that 75% would be given off as heat. This gives us a
value of 373.05 watts that needs to be accounted for in the thermal system.
4. Total Energy In
The formula for totally energy in is given below, followed by the resulting values for all materials in Table
22.
𝑄𝑖𝑛 + 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑄𝑒𝑎𝑟𝑡ℎ + 𝑄𝑠𝑢𝑛 + ⁡ 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑
Eq. (35)
𝑄𝑖𝑛 + 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = ((𝑞𝑟𝑎𝑑𝑖𝑡𝑖𝑜𝑛 + (𝑞𝑎𝑙𝑏𝑒𝑑𝑜 ∗ 𝑎𝑙𝑏𝑒𝑑𝑜)) ∗ 𝐴𝑒𝑎𝑟𝑡ℎ ∗ 𝛼𝑒𝑎𝑟𝑡ℎ⁡𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ) + (1367⁡
⁡𝛼𝑠𝑢𝑛⁡𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ) + (375)
𝑤
𝑚2
∗ 𝐴𝑠𝑢𝑛 ∗
Eq. (36)
Table 22. Material Total Energy
Material
Minimum (W)
Maximum (W)
S13G-LO
2060.38
2904.45
Z93
1807.57
2398.56
ZOT
1891.84
2398.56
White Paints
29
Chemglaze A276
2228.91
3207.98
Chemglaze Z306
8127.73
10290.44
3M Black Velvet
8549.07
10189.27
8 mil Quartz Mirror
796.34
1184.42
2 mil Silvered Teflon
796.34
1285.60
5 mil Silvered Teflon
796.34
1285.60
2 mil Aluminized Teflon
1217.69
1993.85
5 mil Aluminized Teflon
1217.69
1993.85
½ mil
3240.14
3815.05
1 mil
3577.21
4219.76
2 mil
3830.02
4523.30
5 mil
4251.36
5029.19
Vapor Deposited Aluminum
1049.15
2095.03
Bare Aluminum
1133.42
2095.03
Vaporized Deposited Gold
1976.11
3410.34
Anodized Aluminum
2481.72
9076.31
¼ mil Mylar
N/A
N/A
Beta Cloth
3071.60
3612.70
Astro Quartz
2228.91
2600.92
MAXORB
7959.19
9481.02
Black Paints
Optical Solar Reflectors
Aluminized Kapton
Metallic
Miscellaneous
5. Energy Out
With four out of the six sides of THF-15 always facing deep space there is a worry that all heat radiating
out of the satellite will leave components on board frozen or below survival temperatures when the
satellite reaches its equilibrium. The equation below will yield a Tsatellite based on the radiation formula for
a black body.
𝑄𝑜𝑢𝑡 = 𝐴𝑠𝑝𝑎𝑐𝑒 ∗ ⁡𝜎 ∗ ⁡ 𝜀𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ∗ (𝑇𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 4 − 𝑇𝑠𝑝𝑎𝑐𝑒 4 )
Eq. (37)
30
Where
𝐴𝑠𝑝𝑎𝑐𝑒 = 𝑇𝑜𝑎𝑙⁡𝐴𝑟𝑒𝑎⁡𝐹𝑎𝑐𝑖𝑛𝑔⁡𝑆𝑝𝑎𝑐𝑒
𝜎 = 5.76 ∗ 10−8 ⁡(
𝑊
𝑚2 𝐾 4
Eq. (38)
)
Eq. (39)
𝜀 = 𝑒𝑚𝑖𝑠𝑠𝑖𝑣𝑖𝑡𝑦⁡𝑜𝑓⁡𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙⁡𝑓𝑎𝑐𝑖𝑛𝑔⁡𝑠𝑝𝑎𝑐𝑒
Eq. (40)
𝑇𝑠𝑝𝑎𝑐𝑒 = 3⁡(𝐾)
Eq. (41)
Because not all sides facing deep space have to be the same material the equation above was expanded
to allow for more customization to narrow down the temperature in which THF-15 would be subject to.
𝑄𝑜𝑢𝑡 = (𝐴𝑠1 ∗ 𝜎 ∗ ⁡ 𝜀𝑠1 ∗ (𝑇𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 4 − 𝑇𝑠𝑝𝑎𝑐𝑒 4 )) + (𝐴𝑠2 ∗ 𝜎 ∗ ⁡ 𝜀𝑠2 ∗ (𝑇𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 4 − 𝑇𝑠𝑝𝑎𝑐𝑒 4 )) + (𝐴𝑠3 ∗ 𝜎 ∗ ⁡ 𝜀𝑠3 ∗
(𝑇𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 4 − 𝑇𝑠𝑝𝑎𝑐𝑒 4 )) + (𝐴𝑠4 ∗ 𝜎 ∗ ⁡ 𝜀𝑠4 ∗ (𝑇𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 4 − 𝑇𝑠𝑝𝑎𝑐𝑒 4 ))
Eq. (42)
Solving the equation for the temperate of the satellite yields the following.
𝑇𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 =
4 𝑄𝑜𝑢𝑡 +(𝐴𝑠1 ∗𝜎∗𝜀𝑠1 ∗𝑇𝑠𝑝𝑎𝑐𝑒 4 )+(𝐴𝑠2 ∗𝜎∗𝜀𝑠2 ∗𝑇𝑠𝑝𝑎𝑐𝑒4 )+(𝐴𝑠3 ∗𝜎∗𝜀𝑠3 ∗𝑇𝑠𝑝𝑎𝑐𝑒 4 )+(𝐴𝑠4 ∗𝜎∗𝜀𝑠4 ∗𝑇𝑠𝑝𝑎𝑐𝑒 4 )
√
(𝐴𝑠1 ∗𝜎∗𝜀𝑠1 )+(𝐴𝑠2 ∗𝜎∗𝜀𝑠2 )+(𝐴𝑠3 ∗𝜎∗𝜀𝑠3 )+𝐴𝑠4 ∗𝜎∗𝜀𝑠4 )
Eq. (43)
And from our stead state condition we know
𝑄𝑖𝑛 + 𝑞𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑄𝑜𝑢𝑡
Eq. (44)
So
𝑄𝑜𝑢𝑡 = ((𝑞𝑟𝑎𝑑𝑖𝑡𝑖𝑜𝑛 + (𝑞𝑎𝑙𝑏𝑒𝑑𝑜 ∗ 𝑎𝑙𝑏𝑒𝑑𝑜)) ∗ 𝐴𝑒𝑎𝑟𝑡ℎ ∗ 𝛼𝑒𝑎𝑟𝑡ℎ⁡𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ) + (1367⁡
𝑤
𝑚2
∗ 𝐴𝑠𝑢𝑛 ∗ ⁡ 𝛼𝑠𝑢𝑛⁡𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ) + (375)
Eq. (45)
Which can then be substituted into the equation for the temperature of the satellite to solve for the
minimum and maximum temperatures of THF-15 based on the differing materials and coatings used on
all the sides
E. Final Design
1. Properties
By following the above equations the thermal design team was able to put together a system that will
keep the THF-15 between 279.3 and 290.4 Kelvin. This not only fits perfectly within the goal temperature
range of 278 to 293 Kelvin, but also was accomplished using only materials for outer coatings and will not
require any extra power and add minimal weight. The design will feature Astro Quartz on both the side
facing the earth as well as the side facing the sun, and 2 mil aluminized kapton on all four sides facing
deep space.
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2. Absorbing Sides
Astro Quartz was decided on for the two walls that will be absorbing energy because of its constant
absorptivity. The difference between worse case hot and worse case cold can only vary by 15 degrees so
the amount of energy absorbed by the material, no matter the condition, being constant was a positive
quality of all the miscellaneous materials tested. Initial testing was done with the Beta Cloth material but
even with all other sides painted white, for maximum emissivity, that spacecraft was reaching about 300
kelvin. With 300 kelvin being directly out of our target range we looked into the next lowest constant
absorptivity, which was Astro Quartz. Table 23 below shows all properties and calculated values for the
Astro Quartz material.
Table 23. Astro Quartz Properties
Material
α MIN
α MAX
ε
Qearth MIN
Qearth MAX
Qsun MIN
Qsun MAX
Qgen
Qin MIN
Qin MAX
Astro Quartz
.22
.22
.8
455.35
827.35
1398.57
1398.57
373.05
2226.96
2598.97
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V. Concept Drawing
Figure 10. THF-15 Satellite
33
VI. References
A. Atlas V Launch Services User’s Guide
http://www.ulalaunch.com/uploads/docs/AtlasVUsersGuide2010.pdf
B. Falcon 9 Launch Vehicle Payload User’s Guide
http://decadal.gsfc.nasa.gov/pace-201206mdl/Launch%20Vehicle%20Information/Falcon9UsersGuide_2009.pdf
C. NASA – Landsat 8
http://www.nasa.gov/mission_pages/landsat/main/#.VDznD_ldXyA
D. USGS – Landsat 8
http://landsat.usgs.gov/landsat8.php
E. Space Mission Analysis and Design, Third Edition
F. Orbital Decay Calculator
http://www.lizard-tail.com/isana/lab/orbital_decay/
G. Orbital Mechanics Handout
http://ccar.colorado.edu/asen5050/projects/projects_2012/bartkowicz/website/orbital_mechanics_4.html
H. ATK PSI Blowdown Tank Data Sheet
http://www.psi-pci.com/Data_Sheets_Library/DS514.pdf
I.
Physical and Chemical Properties of Hydrazine
http://webbook.nist.gov/cgi/cbook.cgi?ID=C302012&Units
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