This document provides a summary of a satellite constellation design project to monitor the US-Mexico border. The constellation aims to provide near-continuous surveillance coverage of the border region using a minimum of 16 satellites. Key aspects of the design include: - Choosing a sun-synchronous low Earth orbit with 15.9 revolutions per day to provide adequate coverage. - Selecting a multi-spectral mid-IR imaging payload to achieve 1m ground resolution between 0.4-4μm wavelengths. - Designing a 373GB data storage and 424Mbps downlink capability to transmit imagery to a ground station. - Sizing solar panels and batteries to power the 541W system during

1.
Satellite Final Report
Team Rocket
Andy Bothun
Christian Knill
Cordarryl Solomon­Williams
Chengyu Perry Zhang
Yijie Wang

2. Background
Due to the existing threat of potential terrorists and drug traffickers crossing the
southern border of the United States, the Department of Homeland Security needs a capability
to monitor the southern border, specifically between Texas and Mexico. A task was generated
to develop a proposal on building and fielding a constellation of satellites providing near
continuous coverage of that region in order to accomplish surveillance of transiting entities
both day and night.
Introduction
The project has 2 missions. The main mission is to monitor the southern border of the
U.S. and alert the Department of Homeland Security of a potential threat in near real time. The
secondary mission is to collect data on transiting entities in order to assess the extent and
nature of relevant potential threat activities.
Requirements and Constraints
The mission need to meet several requirements and has a list of constraints.
Requirements:
● Resolution: 1.0 m
● Wavelength Range: 0.40­4.0 μm
● Orbit Size Range: 14­16 revs/day
● Constellation: min 16 Satellites
● Earth Latitude Coverage: +33⁰ to ­33⁰
● Swath Width: Min 100 km
● Point Stability: 0.5 km
● Mission Duration: 10 yrs.
Constraints:
● Total Fund <$500M (16 sats)
● Mission Ops: $16M/yr (16 sats)
● Facility Location: Schriever AFB
● Initial Op Capability > 50 months
● Downlink Freq.: 2.2 GHz, Uplink: 2.5 GHz
● Ground Station Receiver Gain: 3.0
● GS Receiver Band.: 200KHz, Temp.: 20⁰C
● Max Pass Time: 12 min
● Orbit Maintenance ΔV: 120 m/s/yr per sat
● Solar Panel Absorb: 0.3
● Solar Pane; Degrade: 3%/yr
● ITAR Regulated
The following paragraphs will cover the design of the constellation of satellites.
Orbit
The first thing to set up the constellations and orbit of the satellites is to identify the
target area needed to be surveyed. Sixteen locations were chosen on the border for any
location where the border changed directions. The list of target locations is displayed in Table 1.
The receiver station needs to be placed on the map to see if the orbit lets the satellite transmit

3. the data to the station. The Schriever Air Force base is at, latitude 38.8027 deg and longitude
­104.522 deg. The map can be seen in Figure 1 with both targets and receiver facility.
Target Latitude (deg) Longitude (deg)
1 25.7202 ­97.08
2 25.5 ­97.23
3 26.23 ­99.01
4 27.36 ­99.35
5 29.44 ­101.25
6 29.46 ­102.37
7 28.58 ­103.07
8 29.33 ­104.39
9 30.36 ­105.02
10 31.43 ­106.23
11 31.47 ­108.12
12 31.19 ­108.12
13 31.19 ­111.06
14 32.29 ­114.48
15 32.43 ­114.43
16 32.32 ­117.07
Table 1. Target Locations along Border
Figure 1. Targets and Facility Location
Next the initial orbit has to be made following the requirements set for the project;
inclination +33 deg to ­33 deg, and an orbit of 14 to 16 revs/day. The satellite will have a
TwoBody set­up in the STK program. This will give us a semi­axis of 6671 km and then the mean
motion will be 15.9337 rev/day, which will be a period of 5422.47 sec. The first orbit can be
seen in Figure 2.

4.
Figure 2. Initial Orbit
Once the initial orbit is chosen the constellation will be built to give max coverage.
Figure 3­5 show three different constellation set­ups. The chosen constellation in the end was
the one that had the least gap over a long period of time. Once that was set it was what gave
the best coverage, Constellation 1 was eventually the one chosen.
Figure 3. Constellation 1 Figure 2. Constellation 2
Figure 4. Constellation 3

5.
The details for the 16 satellites in the constellation can be seen in Table 2. This will show
the inclination, argument of perigee, RAAN, and the true anomaly.
Table 2. Satellite Information for Orbit
Figure 5 and 6 will show the constellation coverage over two of the targets. Since the
coverage is very similar for every target, only two graphs will need to be shown, the min and
max time. All the targets have a max time of not being seen of around 12 minutes. Since it is
very difficult for an individual or group to cross the border in that time it is an acceptable
constellation. Table 3 will then show the total coverage for the targets over a 24­hr period and
the max non coverage time.
Table 3. Coverage of Every Target

6.
Figure 5. Target 9 Coverage (Max)
Figure 6. Target 7 Coverage (Min)
Payload
To design the payload, the first thing is to size the payload from the requirements. The
requirements are the ground resolution of the sensor is 1m, wavelength is between 0.4 μm and
4 μm and the swath width is at least 100 km. The wavelength was assumed to be 2.1 μm to
have a good energy and atmospheric transmittance based on Figure 7 and Figure 8.
Figure 7. Energy Sources vs. wavelength

7.
Figure 8. Energy transmission vs. wavelength
The aperture diameter was calculated from:
.34mD = Res
2.44λ(SR)
= 1m
2.44×2.1×10 m×274.55×10 m−6 3
= 1
Then the size of the payload was calculated from the size of a Multi­spectral Mid­IR(Table 4).
Aperture Diameter 1m
Linear Dimension(Length) 1.5m
Linear Dimension(Diameter) 1m
Mass 800kg
Power 900W
Table 4.Multi­spectral Mid­IR Payload size
So the aperture ratio for the satellite in the project is calculated to be 1.34, and other size
properties can be calculated. The results are shown in Table 5.
Aperture Diameter 1.34m
Linear Dimension(Length) 2.01m
Linear
Dimension(Diameter)
1.34m
Mass 1191.8kg
Power 2165.49W
Table 5. Payload Size for the project(K=1)
Assume a 10% duty cycle, the average power is 216.549W. A scale drawing is in the Appendix.
From DMC project, the pixel diameter was assumed to be 7 μm. The focal length was
calculated :
.10mf = x
hd
= 1m
300×10 m×7×10 m3 −6
= 2
So the magnification is 7E­06 and number of pixel was calculated to be:

8. pixel SW 00, 00# = λ
magnification = 1 0
Then the image plane radius and angular field of view are calculated:
m .35mrd = 2
100,000
× 7 × 10−6
= 0
Include a 10% margin, rd=0.385m
°tan 0.662 θ = 2 −1
(f
rd
)= 2
To keep a 0.5kn stability, the angular field of view should be 20.662°±0.211°. The Muilt­spectral
Mid­IR payload has a pointing accuracy of 0.1 deg which satisfies the requirement of 0.211 deg.
Finally, the performance of the payload was decided: Ground speed and data
performance.
390.39m/sV g = P
2πRE
= 7
And based on the ground speed, the sensor should image 7390 swaths per sec. We assume the
data for a pixel is 8 bits. The data for a swath is 800,000 bits. The data per orbit is
00, 00bits/swath 390swath/s 422.47s .206 bits/orbit8 0 × 7 × 5 = 3 × 1013
By assuming the duty cycle to be 10%, the data per orbit is 3.206E12 bits. So the data storage
for one satellite should be 4E11 Bytes which is 373.2GBytes. Assume the average pass time over
the ground station is 15 minutes, the satellite requires a transmitting data rate of 424
MBytes/sec.
Electrical Power Subsystem Design
The EPS Design included the design of the solar plane based on the power consumption
and eclipse time analysis and the battery design.
For the power consumption and eclipse time analysis. The power budget is shown in Table 6
Payload 40% 216.55W
Structure 0 0
Thermal 0 0
Power 10% 54.138W
TT&C 20% 108.275W
ADCS 15% 181.206W
Propulsion 5% 27.069W
Total 100% 541.375W
Table 6. Power Budget

9. From STK simulation, the eclipse time is 2193.06s and daylight time is 3229.41s. Assume the
power loads during eclipse and daylight are the same. The daylight and eclipse efficiency
and which are the same as DMC electrical power subsystem..8Xd = 0 .6Xe = 0
67.95W Psa = Td
+Xd
P Td d
Xe
P Te e
= 7
At the beginning of the life, the power density solar array generated is
Flux)(ξ)(I )cosθ PBOL = ( d
Assume the input solar density is 1367 , efficiency of solar cell is 28% and inherent/mW 2
degradation is 0.77 as DMC used. The satellite used sun­tracking solar panel so the sunlight
incidence angle is 0. The power density output at the beginning of life is calculated as 294.724
. The satellite required a 10 years life and 1% degradation per year was assumed. The/mW 2
power density output at the end of life was calculated:
(1 %) 66.54W/mPEOL = PBOL − 1 10
= 2 2
So the area of solar panel is 2.881 .m2
Then for the battery design, NiH battery was used. In 10 years life, the battery need to charge
and discharge for and0years 65.25days 4hours 600sec/5422.37sec 8198cycles1 × 3 × 2 × 3 = 5
from Figure 9, the depth of discharge should be 35%.
Figure 9. Depth of discharge vs. cycle life
Assume one battery is used and the transmission efficiency between battery and load n is 0.9
which is a typical used value, the battery capacity should be:

10. 046.973W r Cr = P Te e
(DOD)Nn = 1 ∙ h
Use the same kind of battery as DMC, the energy density is 50 Whr/kg. The battery mass is
20.939kg.
Communication
Communications satellites allow telephone and data conversations to be relayed
through the satellite.The most important feature of a communications satellite is the
transponder ­­ a radio that receives a conversation at one frequency and then amplifies it and
retransmits it back to Earth on another frequency. A satellite normally contains hundreds or
thousands of transponders.
Communication satellites are all in geosynchronous orbit, meaning that they stay in one place
in the sky relative to the Earth. “The signal transmitted between the spacecraft and the ground
station, or between two spacecraft, must arrive at the receiver with enough strength to be
detected. The strength of the received signal depends upon: Strength of the signal transmitted
(power density in the desired direction) Amount of attenuation due to the medium
(atmospheric attenuation, path loss, etc) Sensitivity of the receiver (ability to focus received
signal and detect information)”.
Each satellite is launched into space at about 300 km above the Earth. At this speed and
altitude, the satellite will revolve around the planet approximately 15 times every 24 hours.
Constraints that had been set for the communication design approved to operate at RF
frequencies 2.2 GHz downlink and 2.5 GHz uplink, ground Station (GS) receiver gain 3.0,
receiver bandwidth 200 KHz, and a receiver temperature: 20°C.
Uplink is the frequency at which ground control is communicating with the satellite and
downlink is when the satellite transponder convert the signal and send it down to the second
earth station.

11. Equations for Communication
Frii’s Transmission
Effective Isotropic
Radiated Power
Antenna Gain
Free Space
Pointing Loss
Link Budget

12.
Costs Estimation
Mass Budget
Percent Mass
payload 42% 1191.8Kg
Structure 18.1% 513.6Kg
Thermal 2.3% 65.26Kg
Power 22.7% 644.1Kg
TT&C 4.4% 124.9Kg
ADCS 6% 170.34Kg
Propulsion 4.5% 127.69Kg
Table 7. Mass Budget

13. Table 8 Launch Vehicles Consideration
For Launch costs, We need to look to minimize the amount of launches as well as fully utilizing
the maximum payload space available in each launch.
With a satellite mass of 1191.8 kg, the Athena 3 would have the capability of bringing 3
satellites to our designed orbit, which is quite close to LEO, for $31M per launch. Therefore
with 5 launches of Athena 3, we’d deliver 15 satellites. Another one left we could use one
Taurus for launching, which would be $20M. Therefore, the total cost of launch vehicles would
be 31*5+20=$175M
Testing and Theoretical First Unit Cost
Component Value RDE&T and TFU(FY00$K) TFU(FY00$K)
Payload 0.45 15064

14. structure 85.5 6937.16542 1935.1654651
thermal 15.6 750.41657 353.1654
Electrical power 135 11679.60983 4863.36463
TT&C 15 1823.465673 515.3465459
TT&C 15 1823.465673 515.3465459
C&DH
ADCS 22.3 5740.3208 3643.32457
Propulsion 32.6 262.46543 144.62321
Grand Total 27033.456
To calculate the unit cost, we used the equation as follows:
And the unit costs of all the parts of the satellite are calculated as: (with the conversion into
FY00$)
Unit number Production cost Unit cost (FY00$K)
1 27033.456 27033.456
2 51567.1564 25359.37655
3 69534.67448 23546.67234
4 82467.6461 20925.0431
5 116732.9431 20345.7793
6 136476.9235 20245.71601
7 159985.4315 23576.6725
8 163449.983 19573.37697

15. 9 189822.354 19437.35595
10 203978.359 19234.4622
11 229460.357 16542.802
12 242591.7496 19345.432
13 256347.3243 18231.32465
14 282364.3457 19254.2545
15 301972.3784 18348.4256
16 315753.3541 18346.95234
Total Cost 323.7 Million
Therefore, the total cost would be the total operation cost(Launch vehicle cost) plus the Cost of
16 satellites, which is 353.7M+ 175M= 498.7M
So our design is right under the budget, which met the constraint and requirement of the
mission.

16.
Reliability
In determining the reliability of the system it is important to make use of the reliability
equation:
R=e^(­t/MTBF)
Since this mission needs to last 10 years, we will use 10 years as the time for the calculations.
The MTBF values were determined from satellite systems websites such as: Ferrotec.com, and
archive.erricssin.net
Reliability of each system over 10 years
Payload Structure Thermal Power TT&C ADCS Propulsion Comms
R(10 yr) .557 .916 .645 .803 .803 .606 .864 .803
MTBF(yr) 17.1 114.1 22.8 45.6 45.6 20.0 68.4 45.6
t(yr) 10 10 10 10 10 10 10 10
To combine together reliabilities of individual systems it is important to use the following
generic equations:

17.
Redundancies Rsystem [1 1 A) n] 1 1 B) n] .. n − 1 = − ( − R ˆ * [ − ( − R ˆ * .
System Reliabilities with various redundancies of systems:
# of
Redundancies
Rsystem
(10 yr)
P(16/16)
(%)
16/R
P(16/{16/R})
(%)
Nadj
P(16/Nadj)
(%)
0 .0892 1.6*10^­15 180 N/A N/A N/A
1 .5136 2.3*10^­3 32 62.98 41 95.91
2 .7977 2.69 21 76.08 24 96.13
3 .9189 25.84 18 82.48 20 98.06
4 .9672 59.14 17 89.43 18 98.01
5 .9866 80.59 17 97.86 17 97.86
As you increase the number of redundancies, the system noticeably becomes more reliable.
Then I adjust the number of satellites to be the minimum number needed to have a probability
of 95% or higher that at least 16 satellites will survive the mission. This results in our ideal case
of 4 redundancies and 18 satellites.

18.
This is the bathtub curve describing our mission failure. As you can see, our satellite array is
very survivable during the required lifetime and can last many years after.
Disturbance Torques
Cp ­ Cg = .3 m
Residual Dipole = 1.0 A m^2
Cd = 2.5
Ro atm = 1.47 *10^­13 kg/m^3
Me = 7.96*10^15 T m^3
q = .6
Fs = 1376 W/m^2
Inertia of the satellite is:
Ixx = 536 kg m^2 Iyy = 536 kg m^2 Izz = 270 kg m^2
Gravity Disturbance Torque:
Tg max = (1.5μe/R^3)*(Imax ­ Imin)*(1)
= 5.360*10^­4 N m
Magnetic Torque:
Tm max = [dipole]*Me*(1)/R^3
= 2.673*10^­5 N m

19. Aerodynamic Drag Torque:
v = [μe/R]^.5 = 7.73 km/s
Ta max = .5*Roatm*Cd*SA *(Cp ­ Cg)*v^2
=1.000*10^­5 N m
Solar Pressure Torque:
As ≈ (15 m)*(3 m) = 45 m^2
Tsrp = Fs*As*(1 + q)*(1)*(Cp ­ Cg)/c
=.990*10^­4 N m
System will accommodate Total Disturbance Torque:
Td = ∑(Tx^2)^.5
= 5.460*10^­4 N m
Conclusion
The design met all the requirements and the budget for 16 satellites is just under $500M. The
longest break of the coverage is 12 minutes which is believed to be an accepted value.
However, the budget is not sufficient for 18 satellites which is the ideal case for a high
reliability. The potential solution is to use another existing payload characteristics for scaling to
decrease the payload of the project satellite. Decreasing the payload to under 800kg will allow to
launch 18 satellites under the budget requirements.
Appendix
Scale drawing of the satellite