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AltitudeLOWER = 200 km
AltitudeHIGHER = 8, 500 km
First, we need t o c alculate R 1 a nd R 2 .
R1 = AltitudeLOWER + RadiusEARTH
= 200 + 6378 = 6, 578 m
R2 = AltitudeHIGHER + RadiusEARTH
= 8500 + 6378 = 14, 878 m
Therefore,
√ √ΔvP ERIAP SIS = 2(14878)
398600 ( 21456 − 1)
6578
= 1, 383 mps
√ √ΔvAP OAP SIS = 2(6578)
398600 (1 − 21456 )
14878
= 1, 123 mps
ΔvBUDGET = 1383 + 1123
= 2, 506 mps
ΔvROUND−TRIP = 2(2506)
= 5, 011 mps
√T ransf er T imeSECONDS = π (6578 + 14878)3
8(398600)
= 5, 529 s
T ransf er T imeDAY S = T ransf er T imeSECONDS
86400
= 5529 = 0.064 days
86400
Round − T ripDAY S = 2(T ransf er T imeDAY S )
= 2(0.064) = 0.128 days
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M ission Duration = On − StationDAY S + Round − T ripDAY S
= 5 + 0.128
= 5.13 days
5.04 G uided Practice
You a re an spacecraft C aptain responsible t o transport p assengers t o a nother space s tation. U se
the H ohmann Transfer O rbit E quations to d etermine the orbital parameters of y our s paceflight.
Orbital S cenario # 1
Lower Orbital A ltitude: 2 85 k m
Higher Orbital A ltitude: 1,000 k m
On–Station Time: 4 days
Periapsis Δv Burn = __________ mps
Apoapsis Δ v B urn = __________ mps
Δv B udget = __________ mps
Transfer Time = _ _________ days
Round–Trip T ime = __________ days
Mission D uration = __________ d ays
Orbital Scenario # 2
Lower O rbital A ltitude: 4 00 km
Higher Orbital Altitude: 800 km
On–Station T ime: 1 0 d ays
Periapsis Δ v Burn = _ _________ m ps
Apoapsis Δv Burn = _ _________ mps
Δv B udget = _ _________ mps
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Transfer Time = _ _________ d ays
Round–Trip T ime = _ _________ d ays
Mission Duration = _ _________ d ays
5.05 Cross Curricular E xercises
ARTWORK
Find images o f the R .E.L. S kylon s paceplane on the Internet. U se t he i mages t hat you h ave
researched to d raw a picture o f the s paceplane rocketing into orbit.
R.A.F.T. W RITING
● Ro le: T eacher
● Au dience: Middle School students
● Fo rmat: F ive p aragraph essay
● T opic: The Gemini spacecraft. Who were the astronauts that flew the mission? What
spacecraft was used to boost the Gemini to a higher orbit? What was unique about the
missions? What was in common with all the missions? How does a Gemini change in
orbital altitude differ from the one presented in this textbook? How are they the same?
Why e ven b other to change a n orbit a nyway?
DISCUSSION TOPICS
● Was the mathematics i n this c hapter difficult to u nderstand?
● The authors c onclude t hat concept of c hanging t he s hape of an orbit is very c omplicated.
Do y ou agree with t he authors? Why o r Why n ot?
● What would it b e l ike to fly a board a s pacecraft that i s orbiting the Earth? Would y ou f ly
on such a spacecraft? W hy or w hy not?
5.06 Delta V S pace Mission D esign Website
We n ow p roceed to c reate the s uborbital website t hat includes t he engineering logs a nd t he a pp
embedded in a webpage.
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INSERT TEXT HERE
::
5.07 Delta V Space Mission D esign S preadsheet A pp
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space Mission Design App (SMDA).
The S.T.E.M. for t he Classroom/Google App i s broken down i nto f our ( 4) p arts:
1. Input/Output Interface
2. Graph
3. Constants
4. Calculations
The App can now be d eveloped.
Sample Google S heets A pp Design O pen S ource C ode
Once t he c ells have b een n amed referencing c ells i s e asy.
● CALCULATIONS
○ TotBA
INSERT O PEN S OURCE CODE
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Sample A pp Interface
Image 3 2: Delta V S pace M ission Design S preadsheet App
::
5.08 D elta V S pace M ission D esign Mobile App
Sample A ppSheet M obile App Design O pen Source C ode
Once t he G oogle Spreadsheet h as b een c ompleted, i t can be used t o help c reate the mobile a pp.
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INSERT C ODE H ERE
INSERT C ODE HERE
I NSERT C ODE HERE
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Sample A ppSheet Mobile App D esign
Image 33: Delta V Space M ission Design M obile A pp
5.09 Delta V Space Mission D esign P resentation D evelopment Page 9 9 o f 176
INSERT T EXT HERE
INSERT T EXT H ERE
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5.10 C hapter Test
I. V OCABULARY
Match the astronautics t erm with its d efinition.
1. Apoapsis A. T he l ower c ircular o rbital a ltitude o f a s pacecraft as
measured from the c enter o f a n orbiting b ody.
2 . Δ v B udget B. T he r ocket firing a t the lowest point o f a Transfer
Orbit.
3. Mission Duration C. The h ighest point i n a n e lliptical o rbit.
4. P eriapsis Δ v Burn D. T he total t ime necessary to accomplish a mission.
5 . Radius o f Lower O rbit E. T he t otal D elta V needed t o a ccomplish a m ission.
II. M ULTIPLE C HOICE
Circle the correct a nswer.
6 . The Apoapsis Δv rocket burn o ccurs a t the h ighest p oint of the Hohmann transfer o rbit.
B. FALSE
A. T RUE
7 . The Δ v Budget is t he total c hange i n v elocity needed to c onduct a roundtrip space mission.
B. FALSE
A. TRUE
8. A spacecraft is orbiting the Earth at an orbital altitude of 1,000 km. What is the orbital radius
of the s pacecraft?
A. 5,371 k m B. 6,371 k m C. 7 ,371 km D. C annot b e determined
9. What is the Hohmann transfer time of a spacecraft headed for the apoapsis ΔV rocket burn if
the RoundTrip T ransfer T ime is 7 hrs?
A. 3 .5 h rs B. 7.0 h rs C. 1 0.5 h rs D. Cannot b e d etermined
10. There are always two Δv rocket burns whenever a spacecraft needs to raise or lower its
orbital altitude. The second Δv rocket burn is used to change the shape of an orbiting spacecraft
into a ____________.
A. Ellipse B. Circle C. P arabola D. Cannot be determined
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III. C ALCULATIONS
A wayward satellite is need of repairs and to have some electronic parts replaced. The satellite is
in a stable orbit 1,250 km above the Earth. A crew inside a repair vehicle is also in a stable orbit,
but at an orbital altitude of 400 k m. T he crew will need 3 d ays t o c onduct a ll n ecessary r epairs.
11. W hat is t he L ower O rbital R adius?
12. What is the H igher O rbital R adius?
13. W hat is t he OnStation Time?
14. W hat i s the P eriapsis Δ v Rocket Burn?
15. W hat i s t he Apoapsis Δ v R ocket B urn?
16. What is t he Δ v B udget?
17. W hat i s t he R ound Trip Δ v Budget?
18. What is The T ransfer Time?
19. W hat i s R ound T rip Transfer T ime?
20. W hat i s t he M ission D uration?
IV. W RITING
Write a o ne p aragraph e ssay on the t opics below.
21. E xplain w hy a s pacecraft m ust first p ush off a nd t hen stop w hen it wants t o g o f rom one
point i n s pace t o another, such a s a h igher (or l ower) o rbital altitude.
22. E xplain how the O nStation T ime e ffects the Mission D uration.
23. E xplain how a spacecraft w ould r eturn b ack to its original orbital altitude i f t he A poapsis Δ V
rocket b urn w as n ot p erformed.
24. Explain w hy a s pacecraft m ust have a larger Round T rip Δv Budget if i t n eeds to g o t o a
higher orbital a ltitude.
25. Write a short story about what it would feel like to float weightlessly in space, while gazing
at t he c urvature o f the Earth a s i t t ransfers f rom a lower to a h igher o rbital a ltitude.
END O F C HAPTER 5 E XAM
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Chapter 6 : S pacecraft M ass
6.01 N arrative 9 9
6.02 V ocabulary 9 9
6.03 A nalysis 99
6.04 Guided Practice 99
6.05 Cross C urricula Activities 9 9
6.06 C rew Module Mission D esign W ebsite D evelopment 99
6.07 Crew Module Mission Design Spreadsheet App D evelopment 9 9
6.08 C rew M odule M ission D esign M obile A pp D evelopment 9 9
6.09 Crew M odule M ission D esign Presentation D evelopment 9 9
6.10 C hapter Test 99
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6. S pacecraft Mass
6.01 Narrative
In this, the second of a fourpart
interconnected astronauticsbased S.T.E.M.
project, students will calculate the total
mass of the Crew Module, a place where
astronauts live and work while operating in
the v acuum of space.
Time Frame
4.5 w eeks
Astronautics Problems
Crew Module Static M ass (kg)
Crew M odule Dynamic M ass ( kg)
Crew S ize (astronauts)
Mathematics U sed
Linear Equations
Basic Algebra
Science T opics
Physics, Astronautics
Activating Previous Learning
Basic M athematics
Image 3 4: B oeing Crew Module Cover
Essential Q uestions
● What is the relationship between the time it takes to complete a mission and the number
of a stronauts?
● Why i s i t i mportant t o determine t he m ass o f a spacecraft?
● How m any astronauts can fit i nto a s pacecraft?
● How d oes t he duration of a m ission e ffect t he number of c rew a s pacecraft can c arry?
● Who a re a re some of the p ioneers in s pacecraft d esign?
● Wait. I h ave to do science, t echnology, e ngineering, and m ath, a ll at t he same time?
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This l esson is p owered b y E8 :
1. Engage
○ Lesson Objectives
○ Lesson G oals
○ Lesson Organization
2. Explore
○ The B oeing Space Tug S tudy
○ The Crew Module ( CM)
○ The CM M ass
○ The C rew Size
○ Additional Terms and Definitions
3. Explain
○ Basic S pacecraft Systems
○ The CM S tatic Mass
○ The C M D ynamic M ass
4. Elaborate
○ Other Crew M odule E xamples
5. Exercise
○ CM Mass and Crew Size Parameters
○ CM Mass and Crew Size Scenario
6. Engineer
○ The E ngineering D esign Process
○ SMDA S pacecraft CM Mass a nd Crew S ize P lan
○ Designing a Prototype
○ SMDA Software
7. Express
○ Displaying the SMDA
○ Progress Report
8. Evaluate
○ Post Engineering A ssessment
::
Lesson Overview
Students first learn the basics of crew module design using pencil, paper, and scientific
calculator.
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Students then use what they have learned to create a space mission app designed according to
the Engineering Design Process, that will be used for realworld spacecraft. They will use
spreadsheet software to c reate the app.
The spreadsheet will be developed over the course of four S.T.E.M. projects, with each project
dealing w ith different a spects o f s pace m ission d esign.
The assigned space mission will include four space vehicles or satellites that that are named after
famous astronauts. Students will research and write a very short biography (one slide) about
these h eroic individuals, one for each of t he 4 p rojects.
Constants
● none
Input
● Mission Duration (Days)
● Spacecraft Systems M ass ( lbs)
Output
● Spacecraft C rew Systems M ass (kg)
● Spacecraft EC/LSS Mass ( kg)
● Spacecraft Expendables M ass ( kg)
● Spacecraft C ontingency Mass ( kg)
● Spacecraft Static M ass (kg)
● Spacecraft D ynamic Mass ( kg)
● Spacecraft Total M ass ( kg)
● Crew S ize (astronauts)
::
6.02 Vocabulary
CM C ommunications CM C ontingency CM C ontrols
CM Crew S ystems CM Dynamic Mass CM E C/LSS
CM E lectrical Power CM E xpendables CM Instrumentation
CM Misc. Equipment CM Static Mass CM Structure
CM Mass Crew Capsule Crew M odule (CM)
Crew Size
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Image 35: Boeing’s C ST–100 S tarliner C rew C apsule Docking t o the I SS
6.03 A nalysis
The b est t hing f or the s tudents to construct f or the E ngineering part of S.T.E.M. i s a n actual
spaceship. O bviously, s tudents c annot build a real s paceship not b ecause t hey d on't have the
smarts t o do it, b ut b ecause they don't h ave t he funding to d o it! H owever, w e c an do t he n ext
best thing: s imulate a space mission u sing a r eal spacecraft design using r eal s pacecraft numbers.
And the B oeing S pace Tug Study w ritten i n 1 971 is that v ery s pacecraft! T he diameter o f t he
vehicle w as j ust u nder 1 5 f t. a nd would have f it p erfectly in t he S pace S huttle, w hich is what it
was designed t o d o. T he s tudy was f unded, b ut, a las, t he s pacecraft i tself w as n ot. H ence, i t w as
never built. But we c an t ake t heir misfortune (and ours, a s a s ociety) a nd m ake s omething good
out o f i t: we get t o design real s pace missions using a real s paceship!
This Space Tug was envisioned to have a Crew Module and an Engine Module, similar to the
Apollo Command/Service Module ( CSM).
We will extract information from the Boeing Study, and use it to create an equation that yields
the CM m ass, then t he number o f astronauts t hat c an b e safely c arried on a space mission.
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This chapter will use the piloted section, or Crew Module (CM) of the system, which is
displayed below (note the similarity with Boeing's current CST–100 design). Spacecraft system
weight information is given in the upper right corner of the image below and described at the
bottom p art o f t he i mage.
Image 3 6: Boeing Space T ug Study C rew M odule (CM) circa 1971
We c an s ee f rom t he d ata i n the image above t hat
● 15 C rew = 2 Day M ission
● 3 Crew = 5 0 Day Mission
Note that we m ake t he Mission Duration (MD) t he i ndependent variable in t he linear e quation.
If we make the first number x and the second number y , we get two points, namely (2, 15) and
(50, 3). We can use the formula for slope and the yintercept to write the linear equation in
slopeintercept (y=mx+b) f orm.
m = y2 − y1 = 3 − 15 = − 12 = − 0.25
x2 − x1 50 − 2 48
and
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b = y1 − mx1 = 15 − (− 0.25)(2) = 15 + 0.5 = 15.5
Therefore, y = mx + b b ecomes
CM CREW = mM D + b
and
CM CREW = − 0.25M D + 15.5
(Note: This calculation must be rounded down to the nearest crew. It is impolite to have a partial
crew member o n a spaceflight)
The CM habitable VolumetoCrew ratio is simply the total volume of the CM divided by the
Crew Size.
CMV OLUME = 1260
CM CRE W
The other spacecraft component's linear equations can be found in the same manner. For
example,
● 2 D ay M ission = 2,497 lbs Structure
● 50 D ay Mission = 2 ,497 lbs Structure
The points (2, 2497) and (50, 2497) yields a horizontal line, which means that this spacecraft
component remains the same (i.e., constant) weight regardless of t he MD.
Therefore,
CM STRUCTURE = 2497
Crew Systems yields (2, 3689) and (50, 1705), and so forth, until the entire list has been
converted.
The Static Weight is the sum of all the spacecraft components that are constant, and the Dynamic
Weight is the sum of all the spacecraft components that change when the MD changes. The total
Weight of the C M i s the s um of t he two weights.
M assSTATIC = CM STRU CTU RE + CM ELECTRIC + CM COM M + CM INSTR + CM CONTROL + CM M ISC
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M assDY NAMIC = CM SY STEMS + CM EC/LSS + CM EXP + CM CONTROL
M assCM = M assSTATIC + M assDY NAMIC
The weight needs to be converted to S.I. units; however, it is probably easier to keep the weight
in p ounds u ntil the end, and t hen c onvert the u nits.
M assCrewModule = M ass CM
2.2
Example
A wayward satellite requires repairs and to have some electronic parts replaced. The satellite is
in a stable orbit and a repair vehicle is ready to go to the satellite. The same orbital parameters
used in the previous chapter will be used here and it is estimated that the crew will need a total of
10 days to conduct all the necessary repairs and complete their mission. What is the size of the
crew n eeded f or t his space mission a nd what is the m ass o f the Crew Module?
The n umber of a stronauts needed i s
CM CREW = − 0.25M D + 15.5
= − 0.25(10) + 15.5
= − 2.5 + 15.5
= 13 Astronauts
Therefore, the Crew V olume R atio i s
CMV OLUME = 1260
CM CRE W
= 1260
13
= 96.92 f t3/Astronaut
That is, t here is almost 100 c ubic f eet of s pace f or e ach astronaut i nside the C rew M odule.
The Static Mass of the CM i s constant, and so
CM STATIC = CM STRU CTU RE + CM ELECTRIC + CM COM M + CM INSTR + CM CONTROL + CM M ISC
= 2497 + 130 + 327 + 188 + 60 + 80
= 3, 282 lbs
= 1, 489 kg
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The D ynamic Mass o f t he CM is f ound by p lugging i n 1 0 f or M D i n t he following equations
CM SY STEMS = − 41.33M D + 3772
= − 41.33(10) + 3772
= 3, 358 lbs
CM EC/LSS = 27.81M D + 1211
= 27.81(10) + 1211
= 1, 490 lbs
CM EXP = 20.50M D + 254
= 20.50(10) + 254
= 459 lbs
CM CONTINGENCY = 0.71M D + 852
= 0.71(10) + 852
= 859 lbs
and
M assDY NAMIC = CM SY STEMS + CM EC/LSS + CM EXP + CM CONTINGENCY
= 3358 + 1490 + 459 + 859
= 6, 166 lbs
= 2, 797 kg
The total mass of the C rew M odule thus becomes
M assCM = M assSTATIC + M assDY NAMIC
= 3282 + 6166
= 9, 448 lbs
= 4, 285 kg
::
6.04 G uided Practice
You a re an s pacecraft Captain responsible to t ransport passengers t o a nother s pace station. Use
the B oeing C rew M odule Equation t o d etermine t he parameters o f y our s paceflight.
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Mission Scenario #1
Mission Duration: 10 d ays
Spacecraft S ystems Mass: 3 ,500 l bs
Spacecraft Crew Systems Mass = __________ kg
Spacecraft E C/LSS M ass = _ _________ kg
Spacecraft E xpendables M ass = _ _________ kg
Spacecraft Contingency M ass = __________ k g
Spacecraft Static Mass = __________ k g
Spacecraft D ynamic M ass = __________ k g
Spacecraft T otal Mass = _ _________ k g
Crew Size = _ _________ astronauts
Mission S cenario # 2
Mission D uration: 8 days
Spacecraft S ystems M ass: 1,000 lbs
Spacecraft Crew Systems Mass = _ _________ kg
Spacecraft E C/LSS Mass = __________ k g
Spacecraft Expendables Mass = _ _________ k g
Spacecraft C ontingency M ass = __________ kg
Spacecraft Static Mass = _ _________ k g
Spacecraft Dynamic M ass = __________ k g
Spacecraft Total Mass = __________ kg
Crew S ize = _ _________ astronauts
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6.05 C ross C urricular E xercises
ARTWORK
Find images of a crew capsule such as the Boeing CST–100 or the SpaceX Dragon on the
Internet. Use the images that you have researched to draw a picture of the spaceplane rocketing
into orbit.
R.A.F.T. WRITING
● Ro le: T eacher
● Au dience: Middle S chool s tudents
● Fo rmat: Five paragraph essay
● T opic: The Apollo Crew Module (CM). Did any astronaut ever fly in the CM alone?
Which CMs never traveled to the Moon? What was unique about the missions? What was
in common with all the missions? How does an Apollo CM differ from the CM presented
in this textbook? How are they the same? Why even bother to build a Crew Module
anyway?
DISCUSSION TOPICS
● Was the m athematics in this c hapter difficult t o understand?
● The a uthors conclude that t he Space Tug could b e b uilt t oday. Do you a gree with the
authors? Why or W hy not?
● What w ould i t be l ike t o fly aboard a Crew M odule headed to a nother l ocation i n space?
Would you f ly o n the Boeing C rew Module? Why or why n ot?
6.06 Crew M odule Space Mission Design Website
We now proceed to create the suborbital w ebsite that includes t he e ngineering l ogs a nd t he app
embedded i n a w ebpage.
INSERT TEXT HERE
::
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6.07 C rew Module Space Mission Design Spreadsheet App
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space Mission Design A pp (SMDA).
The S .T.E.M. for the Classroom/Google App is broken d own i nto f our ( 4) p arts:
1. Input/Output Interface
2. Graph
3. Constants
4. Calculations
The A pp c an n ow b e developed.
Sample Open S ource C ode
Once the c ells have b een n amed r eferencing cells is e asy.
● CALCULATIONS
○ TotBA
INSERT CODE HERE
INSERT C ODE HERE
INSERT CODE HERE
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INSERT CODE H ERE
I NSERT CODE H ERE
INSERT CODE H ERE
::
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Sample A pp I nterface
S.T.E.M. For t he C lassroom
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Image 37: Crew M odule S pace M ission Design S preadsheet A pp
::
6.08 Crew Module S pace Mission D esign Mobile App
Sample AppSheet Mobile A pp Design O pen Source Code
Once t he G oogle Spreadsheet h as been completed, it c an be used to h elp c reate the mobile app.
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INSERT CODE HERE
I NSERT C ODE H ERE
Sample A ppSheet Mobile A pp Design
Image 38: Crew Module Space Mission Design Mobile App
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6.09 C rew M odule Space M ission Design P resentation Development
INSERT TEXT HERE
INSERT T EXT HERE
::
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6.10 C hapter Test
I. VOCABULARY
Match the a stronautics t erm w ith its definition.
1 . CM EC/LSS A. The number of astronauts aboard a spacecraft or
space station.
2 . CM Static W eight B. A spacecraft, such as the Boeing CST100, that is
used t o ferry crew to a nd f rom a space station.
3. C M Structure C. The C M s hell, insulation, r adiators, etc.
4. C rew Capsule D. The mass of the CM components that does not vary
with t he Mission D uration.
5. Crew S ize E. The CM Environmental Control/Life Support
Systems. Cabin pressure, a tmosphere, water, etc.
II. M ULTIPLE CHOICE
Circle the correct answer.
6. The Dynamic Mass of a spacecraft Crew Module changes depending upon the number of
days needed f or astronauts t o p erform a s pace mission.
B. F ALSE
A. TRUE
7 . T he size o f t hat c rew that a m ission can c arry is d etermined by the S tatic Mass of t he CM.
B. F ALSE
A. TRUE
8. What is the m aximum number of a stronauts that can fit i nto t he B oeing S pace T ug C M?
A. 3 B. 10 C. 1 5 D. Cannot b e determined
9. The mass of the Electrical Power component of the CM will __________ as the mission
duration increases.
A. I ncrease B. D ecrease C. Stay the S ame D. Cannot be d etermined
10. The mass of the EC/LSS component of the Crew Module will __________ as the mission
duration increases.
A. Increase B. D ecrease C. S tay t he Same D. C annot be determined
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III. C ALCULATIONS
A wayward satellite is need of repairs and to have some electronic parts replaced. The satellite is
in a stable orbit, and a repair vehicle is ready to go to the satellite. It is estimated that the crew
will need a t otal of n ine d ays to conduct a ll t he n ecessary repairs and complete their m ission.
11. What i s number o f Astronauts needed?
12. W hat i s the h abitable v olume f or one astronaut?
13. W hat is the m ass o f t he C rew Systems component?
14 . W hat i s the m ass o f t he E C/LSS c omponent?
15. What i s t he m ass o f the E xpendables c omponent?
16. W hat i s the m ass o f t he C ontingency c omponent?
17. What i s Dynamic M ass o f t he CM?
18. What i s Static Mass of the CM?
19. What is t he T otal M ass of the CM?
20. What is the Total M ass of t he CM i n kilograms?
IV. W RITING
Write a o ne paragraph essay on t he topics below.
21. Explain w hy the w eight o f some Crew M odule components, s uch a s Instrumentation and
Control, d o n ot d epend on t he duration of the space m ission.
22. Explain w hy the weight of some C rew Module components, such as Environmental Control
and L ife S upport, depend on t he d uration of t he space mission.
23. Explain why taking m ore a stronauts than what was c alculated f or the Crew S ize d ecreases
the Mission D uration for t he space m ission.
24. E xplain why taking l ess astronauts than w hat was calculated f or the Crew S ize i ncreases the
Mission Duration for the space m ission.
25. Write a short story about what it would feel like to float weightlessly inside a Crew Capsule
as i t orbits the E arth.
END OF CHAPTER 6 E XAM
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Chapter 7: T he R ocket E quation
7.01 Narrative 9 9
7.02 V ocabulary 99
7.03 Analysis 99
7.04 Guided Practice 9 9
7.05 C ross Curricula A ctivities 99
7.06 O rbital Mission Design Website D evelopment 99
7.07 O rbital M ission D esign Spreadsheet App Development 9 9
7.08 Orbital M ission Design Mobile App D evelopment 9 9
7.09 O rbital M ission Design Presentation Development 9 9
7.10 C hapter T est 99
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The Rocket E quation
7.01 Narrative
In this, the third of a fourpart
interconnected astronauticsbased S.T.E.M.
project, students will calculate the mass of
the rocket propellant (both the fuel and the
oxidizer) needed to conduct an orbital
space m ission.
Time F rame
4.5 weeks
Astronautics P roblems
Rocket Exhaust Velocity
Rocket Empty M ass
Rocket P ropellant Mass
Mathematics Used
Exponential Equations
Basic A lgebra
Science Topics
Physics, A stronautics
Activating P revious L earning
Basic Algebra
I mage 39: Boeing Engine M odule P ulp
Essential Questions
● What is the S pecific Impulse of rocket e ngine?
● Why i s i t i mportant t o d etermine t he e xhaust v elocity of a rocket e ngine?
● How does the m ass r atio o f a rocket effect its f inal v elocity?
● Who are some o f t he p ioneers i n r ocket engine design?
● Wait. I have to do s cience, t echnology, engineering, and m ath, a ll at t he same t ime?
::
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This lesson is powered b y E 8 :
1. Engage
○ Lesson O bjectives
○ Lesson G oals
○ Lesson Organization
2. Explore
○ The Boeing Space T ug S tudy
○ The E ngine Module ( EM)
○ The E M Propellant
■ EM Fuel (LH2 )
■ EM Oxidizer ( LO2 )
○ Additional Terms a nd D efinitions
3. Explain
○ Basic Spacecraft Systems
○ The E M Specific Impulse
4. Elaborate
○ Other Engine Module Examples
5. Exercise
○ EM L H2 and L O2 Parameters
○ EM LH2 and LO2 S cenario
6. Engineer
○ The E ngineering D esign Process
○ SMDA S pacecraft EM P ropellant P lan
○ Designing a P rototype
○ SMDA S oftware
7. Express
○ Displaying t he S MDA
○ Progress Report
8. Evaluate
○ Post E ngineering Assessment
::
Lesson O verview
Students first learn the basics of engine module design using pencil, paper, and scientific
calculator.
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Students then use what they have learned to create a space mission app designed according to the
Engineering Design Process, that will be used for realworld spacecraft. They will use
spreadsheet software t o c reate the a pp.
The spreadsheet will be developed over the course of four S.T.E.M. projects, with each project
dealing with d ifferent aspects o f s pace m ission d esign.
The assigned space mission will include four space vehicles or satellites that are named after
famous astronauts. Students will research and write a very short biography (one slide) about
these heroic individuals, o ne f or e ach of t he 4 projects.
Constants
● Standard Gravity ( m/s2 )
● RL10 R ocket Engine I sp ( sec)
Input
● Rocket I nert Mass ( lbs)
● Propellant Mixture R atio
Output
● Rocket E xhaust Velocity ( kps)
● Rocket Empty Mass ( kg)
● Rocket G ross M ass (kg)
● Total A mount o f P ropellant (kg)
● Total Amount o f L H2 (kg)
● Total A mount o f LO2 (kg)
::
7.02 Vocabulary
EM E mpty M ass (m1 ) EM Gross M ass (m 0) EM Inert M ass
Engine M odule ( EM) Exhaust V elocity ( V EXH)
Nozzle–Extended Liquid H ydrogen (LH2 )
Liquid Oxygen (LO2 ) Nozzle–Retracted
Propellant Propellant R atio
Propellant M ass
Propellant R eserve RL10 Rocket Engine Specific Impulse ( IS P )
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Image 4 0: The Boeing C ST100 s howing o ff its Engine M odule
7.3 A nalysis
We will be using data from a s pacecraft design t hat w as completed b ut never constructed. The
Boeing S pace Tug study was f inished i n 1 971. It c alled for a p iloted r ocket s ystem t hat w ould
operate i n L ow E arth O rbit ( LEO). A n unpiloted version of t he r ocket system w ould h ave
carried satellites a nd other sensors to h igher earth orbits.
::
This project will use t he unpiloted s ection, o r Engine Module (EM) of t he s ystem, which i s
displayed below.
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Image 4 1: Boeing S pace Tug Study E ngine M odule (EM) circa 1971
Electrical power w as to b e d erived f rom b atteries, and t he R eaction Control Systems ( RCS) u sed
gaseous hydrogen a nd o xygen, instead o f an hypergolic propellant.
Combining t he E ngine M odule w ith t he C rew Module f rom C hapter Six, this i s what t he
spacecraft looks l ike:
This is a lso the spacecraft that w ould h ave flown as d esigned i n 1971. Notice t he s imilarity w ith
the A pollo C SM spacecraft. Just l ike the f ormer, this spaceship h as a c rew s ection and a rocket
engine section.
This chapter w ill a llow this great d esign t o f inally fly in s pace!
::
We w ill b e using the R ocket E quation to c alculate t he propellant n eeded t o go from o ne o rbit to
another.
( )Δv = vEXH ln
m0
m1
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where
● Δv = Change in o rbital v elocity
● v EXH = E xhaust V elocity o f t he r ocket engine
● m0 = Gross M ass of t he r ocket
● m1 = Empty M ass o f t he r ocket, including propellant r eserve
The r ocket E xhaust Velocity (VE XH ) is found by multiplying t he Rocket Engine S pecific Impulse
(Isp) by the S tandard G ravity ( g0 ) .
vEXH = ISP · g0
The P ayload Mass i s the m ass of t he c argo p lus t he m ass o f the Crew Module (see Chapter S ix).
EM P AY LOAD = W eightCARGO + W eightCrewModule
The Empty Mass ( m1 ) of t he r ocket i ncludes the Inert M ass a nd t he Payload Mass.
m1 = EM INERT + EM RESERV E + EM P AY LOAD
The S pace Tug diagram shows t hat the Inert M ass i s 5 ,610 lbs, w hich equals to 2,545 kg.
So,
m1 = 2, 545 + EM P AY LOAD
The Gross Mass ( m 0 ) of the rocket i s t he weight o f t he p ropellant p lus m 1 . Referencing t he
diagram, the m ass of the t he propellant is 3 9,800 lbs which equals 1 8,053 kg. However, some
missions w ill n ot r equire less than t he c apacity o f t he s pacecraft, s o t he mass o f the propellant
will v ary f rom mission t o mission.
m0 = m1 + EM P ROP ELLANT
Solving t he r ocket e quation for p ropellant, t he a mount of fuel a nd oxidizer n eeded for any s pace
mission can b e c alculated.
( )Δv = vEXH ln
m0
m1
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( )Δv = ln m0
m1
vEXH
( ) = ln Δv
vEXH
m1 + EMP ROP ELLANT
m1
( )Δv
vEXH
= ln 1 + EMP ROP ELLANT
m1
1 + EMP ROP ELLANT = e ΔV
V EXH
m1
EMP ROP ELLANT = e ΔV − 1
V EXH
m1
( )EM P ROP ELLANT = m1
eV ΔV − 1
EXH
ExcessP ROP ELLANT = P ropellant − EM P ROP ELLANT
Finally, the E M p ropellant breakdown i s t he weight o f the Liquid H ydrogen ( LH2 ) fuel and the
Liquid O xygen ( LO2 ) o xidizer.
LH 2 = EMP ROP ELLANT
M ixureRatio + 1
LO2 = LH2 · M ixureRatio
The e xcess p ropellant i s t he capacity o f t he rocket m inus w hat w e a ctually carry.
::
Example
You are the Mission Commander of a spacecraft that is tasked to repair a satellite in Low Earth
Orbit. Your vehicle is a Boeing Space Tug outfitted with a Crew Module (CM) that weighs in at
4,345 kg, a nd a r epair kit that w eighs 4,761 k g. T he Δ v B udget + Reserve i s 4 ,133 m ps.
Calculate the amount of propellant needed, the propellant, the propellant breakdown, the excess
propellant, and the G ross Weight of y our spacecraft.
vEXH = ISP · g0
= (460)(9.80665) = 4, 511 mps
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EM P AY LOAD = M assCARGO + CM
= 4761 + 4345
= 9, 106 kg
m1 = 2545 + EM P AY LOAD
= 2545 + 9106
= 11, 650 kg
( )EM P ROP ELLANT = m1
eV ΔV − 1
EXH
= (11650)(e 4133 − 1)
4511
= 17, 475 kg
The excess p ropellant b ecomes:
ExcessP ROP ELLANT = P ropellant − EM P ROP ELLANT
= 18053 − 17475
= 578 kg
The propellant breakdown i s:
LH 2 = EMP ROP ELLANT
M ixureRatio + 1
= 17457
6.85
= 2, 551 kg
LO2 = LH2 · M ixureRatio
= 2485 · 5.85
= 14, 924 kg
Finally, t he Gross W eight of t he spacecraft i s,
m0 = m1 + EM P ROP ELLANT
= 11, 650 + 17, 475
= 29, 126 kg
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7.04 G uided Practice
You are an s pacecraft Captain r esponsible to transport p assengers t o another space station. U se
the Boeing Engine M odule Equation t o d etermine the p arameters of your spaceflight.
Mission S cenario # 1
Rocket Inert Mass: 8,000 lbs
Propellant Mixture Ratio: 5.85:1
Rocket Exhaust Velocity = _ _________ k ps
Rocket E mpty M ass = _ _________ k g
Rocket G ross M ass = _ _________ kg
Total A mount o f Propellant = __________ k g
Total Amount of L H 2 = _ _________ k g
Total Amount o f LO 2 = _ _________ kg
Mission S cenario #2
Rocket Inert Mass: 7 ,500 l bs
Propellant M ixture Ratio: 5 .50:1
Rocket Exhaust Velocity = __________ k ps
Rocket E mpty M ass = _ _________ kg
Rocket G ross M ass = _ _________ kg
Total Amount of P ropellant = __________ k g
Total Amount o f L H 2 = __________ k g
Total Amount of LO2 = __________ kg
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7.05 Cross Curricular E xercises
ARTWORK
Find images of a crew capsule with an Engine Module attached such as the Boeing CST–100 or
the SpaceX Dragon on the Internet. Use the images that you have researched to draw a picture of
the s paceplane rocketing i nto orbit.
R.A.F.T. WRITING
● Ro le: T eacher
● Au dience: M iddle S chool students
● Fo rmat: F ive paragraph e ssay
● T opic: The Apollo Service Module (SM). What Launch Vehicles were used? Which SM
traveled to the Moon? What was unique about the missions? What was in common with
all the missions? How does an Apollo SM differ from the EM presented in this textbook?
How a re they t he same? W hy e ven b other to b uild a Service M odule anyway?
DISCUSSION TOPICS
● Was the m athematics in this chapter d ifficult to u nderstand?
● The authors c onclude that the S pace Tug c ould be built t oday. D o y ou a gree with t he
authors? Why o r W hy n ot?
● What would it b e l ike t o fly a board a r ocket h eaded to a nother l ocation in s pace? W ould
you fly on the Boeing Engine M odule? W hy o r w hy not?
7.06 E ngine Module S pace Mission D esign W ebsite
We now proceed to create t he s uborbital website that i ncludes t he e ngineering l ogs a nd the app
embedded i n a w ebpage.
INSERT T EXT HERE
::
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7.07 E ngine M odule Space Mission D esign Spreadsheet A pp
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space Mission D esign App ( SMDA).
The S.T.E.M. f or the Classroom/Google App is b roken d own i nto four (4) parts:
1. Input/Output I nterface
2. Graph
3. Constants
4. Calculations
The App c an now b e developed.
Sample O pen Source Code
Once t he cells have been named referencing cells is easy.
● CALCULATIONS
○ TotBA
I NSERT CODE HERE
I NSERT C ODE H ERE
::
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Sample App Interface
Image 42: Space M ission Design S preadsheet App
7.08 E ngine M odule S pace M ission Design M obile A pp
Sample A ppSheet Mobile A pp Design O pen S ource Code
Once t he G oogle S preadsheet has been completed, it c an be used to h elp c reate t he mobile app.
INSERT C ODE H ERE
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I NSERT C ODE HERE
Sample AppSheet M obile A pp D esign
Image 4 3: E ngine Module Space M ission Design Mobile A pp
7.09 Engine M odule S pace Mission Design Presentation D evelopment
INSERT T EXT HERE
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7.10 C hapter T est
I. V OCABULARY
Match t he a stronautics term w ith its d efinition.
1 . E M I nert W eight A. The force with respect to the amount of propellant
used per u nit o f t ime.
2 . L iquid O xygen (LO2 ) B. The weight of the Engine Module without propellant
and payload.
3. NozzleRetracted C. The rocket engine nozzle which is pulled back to its
original s hape.
4. P ropellant Ratio D. W hat a rocket e ngine u ses a s a n o xidizer.
5 . Specific Impulse ( IS P ) E. The rocket engine nozzle which is pulled back to its
original shape.
II. M ULTIPLE C HOICE
Circle t he correct answer.
6. The p ropellant of a rocket is t he rocket fuel needed to m ake t he rocket fly.
B. FALSE
A. T RUE
7 . The m ore a rocket carries, the m ore ΔV t he rocket can generate.
B. FALSE
A. T RUE
8. A propellant ratio o f 5:1 means that there i s five t imes a s much ________ a s there i s fuel.
A. L H2 B. L O2 C. P ropellant D. C annot b e d etermined
9. As the Specific Impulse (IS P ) of a rocket engine _____________, the ΔV capability of the
rocket engine i ncreases.
A. Increases B. D ecreases C. Stay t he the Same D. Cannot b e d etermined
10. By extending the nozzle of the RL10 rocket engine, the Specific Impulse (IS P) of the engine
increase b y a pproximately _________ s econds.
A. Two ( 2) B. Three (3) C. Stay the S ame D. Cannot b e determined
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III. CALCULATIONS
A Boeing Space Tug is on a satellite repair mission. The RoundTrip ΔV Budget is 5,216 mps.
The Specific Impulse is 460s, and the Inert Mass is 5,610 lbs. The payload is a standard 10Crew
CM, which w eighs 9 ,540 lbs, and a standard satellite repair k it, which w eighs 12,000 lbs.
11. W hat i s the Exhaust V elocity ( VE XH) of the rocket e ngine?
12. W hat i s the C rew M odule (CM) w eight i n S.I. u nits?
13. What is t he w eight o f t he P ropellant Reserve i n S.I. u nits?
14. W hat is t he mission p ayload in S.I. units?
15. What i s t he Empty W eight ( m1 ) o f t he r ocket?
16. W hat is t he Gross Weight ( m0 ) of the r ocket?
17. W hat i s t he amount o f propellant n eeded for t his space mission?
18. W hat i s t he amount o f LH 2 fuel needed f or the s pace m ission?
19. What i s the amount o f L O 2 o xidizer needed f or the s pace m ission?
20. W hat is the a mount of p ropellant that w ill be l eft over a t t he end o f the s pace mission?
IV. W RITING
Write a one p aragraph e ssay o n t he t opics b elow.
21. Explain why one of the most common misconceptions in rocketry is that the propellant of a
rocket is n ot just t he r ocket f uel o nly.
22. Explain why the payload weight of space mission is critical to the performance (i.e., the ΔV
requirements) of a rocket engine.
23. Explain why the greater the rocket engine Specific Impulse (IS P) , the greater the rocket
Exhaust V elocity.
24. Explain why the greater the rocket Exhaust Velocity, the greater the change in velocity that
the r ocket e ngine can p erform.
25. Write a short story about what it would be like to feel the power of a rocket engine as it
accelerates you u p to a destination in space.
END O F CHAPTER 7 E XAM
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Chapter 8 : L unar L anding
8.01 N arrative 9 9
8.02 Vocabulary 99
8.03 Analysis 99
8.04 G uided P ractice 99
8.05 Cross Curricula Activities 99
8.06 L unar Lander Mission D esign W ebsite D evelopment 99
8.07 Lunar L ander M ission Design Spreadsheet App Development 9 9
8.08 Lunar Lander Mission Design Mobile A pp Development 9 9
8.09 L unar Lander Mission Design P resentation D evelopment 9 9
8.10 C hapter Test 9 9
::
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Lunar Landing
8.01 Narrative
In this, the fourth and final part of a
fourpart interconnected astronauticsbased
S.T.E.M. project, students will design a
mission that will l and on t he moon!
Time F rame
4.5 w eeks
Astronautics P roblems
Lunar L ander E xhaust V elocity
Lunar L ander Empty M ass
Lunar Lander G ross Mass
Lunar L ander Propellant Mass
Return On I nvestment ( R.O.I.)
Mathematics Used
Finance, B asic A lgebra
Science Topics
Physics, A stronautics
Activating P revious L earning
Linear E quations
Exponential Equations
Image 4 4: B oeing Lunar Lander Pulp
Essential Q uestions
● What i s the ΔV r equirement f or a l anding on the l unar s urface from lunar orbit?
● What i s t he Δ V requirement for a taking o ff f rom the l unar s urface back to l unar orbit?
● Why is it important to have a R eturn On Investment (R.O.I.)?
● How d oes t he the amount of lunar material available for s ale on t he o pen market effect
the s elling p rice of the l unar material?
● Who are are s ome of t he pioneers in l unar l anding design?
● Wait. I h ave t o d o science, technology, engineering, and math, all a t the same time?
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This l esson i s p owered by E 8 :
1. Engage
○ Lesson O bjectives
○ Lesson G oals
○ Lesson Organization
2. Explore
○ The B oeing Space Tug S tudy
○ The L unar L ander K it
■ Landing L egs
■ Payload T ray
○ Additional T erms and Definitions
3. Explain
○ Basic Spacecraft Systems
○ The Rocket Nozzle
■ Extended
■ Retracted
4. Elaborate
○ Other Lunar L ander Examples
5. Exercise
○ Lander Lander P ayload and Payback Example
○ Lander Lander Payload a nd P ayback Scenario
6. Engineer
○ The Engineering Design P rocess
○ SMDA Spacecraft EM P ropellant Plan
○ Designing a P rototype
○ SMDA Software
7. Express
○ Displaying the SMDA
○ Progress Report
8. Evaluate
○ Post Engineering Assessment
::
Lesson Overview
Students first learn the basics of lunar landing mission design using pencil, paper, and scientific
calculator. Students then use what they have learned to create a space mission app designed
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according to the Engineering Design Process, that will be used for realworld spacecraft. They
will u se s preadsheet s oftware t o c reate the a pp.
The spreadsheet will be developed over the course of four (4) S.T.E.M. projects, with each
project d ealing with different a spects o f space m ission design.
The assigned space mission will include four (4) space vehicles or satellites that are named after
famous astronauts. Students will research and write a very short biography (one slide) about
these h eroic i ndividuals, one f or e ach o f t he 4 projects.
Constants
● Unit Conversion (carats/lbs)
● Lunar Investment (USD)
● PDI delta V (kps)
● PAI d elta V ( kps)
● Lander Kit M ass ( lbs)
● Lunar Tray Mass ( lbs)
Input
● TEI Orbital A ltitude ( km)
● EOI O rbital A ltitude ( km)
● Average Selling Price ( USD)
Output
● Lander Gross Mass ( lbs)
● Propellant Mass ( lbs)
● Excess Propellant (lbs)
● LH 2 Mass (lbs)
● LO2 Mass ( lbs)
● Lunar M aterial Mass (lbs)
● Gross Income (USD)
● Net I ncome (USD)
● Return On I nvestment (%)
8.2 V ocabulary
Lunar Lander K it Lunar Investment Lunar Material
Lunar Payload T ray Powered A scent Initiation (PAI) Powered D escent I nitiation (PDI)
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Image 4 5: The A pollo 1 6 Lunar M odule o n the lunar surface, 1972
8.03 A nalysis
We will be using data from a spacecraft design that was completed but never constructed. The
Boeing Space Tug study was finished in 1971. It called for a piloted rocket system that would
operate in Low Earth Orbit (LEO). An unpiloted version of the rocket system would have
carried s atellites a nd other sensors to h igher earth orbits.
A C M/EM i s brought u p t o t he space s tation a nd a Lunar L ander K it i s a ttached to i t.
The L unar Lander Kit c ontains t he following items:
● Landing L egs K it
● Landing R ADAR Kit
● Auxiliary Power Supply Kit
● RCS B ooster Kit
● Extra I nsulation
● Extra Micrometeoroid S hielding
Total M ass ( estimated): 8 96 l bs.
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In addition, a tray resembling a doughnut is attached around the bottom part of the vehicle below
the l anding legs. T otal W eight: 1,500 l bs.
::
We will again be using the Rocket Equation (Chapter 6), solved for propellant, to calculate the
rocket f uel a nd o xidizer n eeded t o go f rom o ne orbit t o another.
( )EM P ROP ELLANT = m1
eV ΔV − 1
EXH
Instead of going from one orbit to another, we will be going from lunar orbit down to the lunar
surface.
::
We will be using the Reaction Engines, Ltd., Skylon spacecraft (Chapter 2) to shuttle back and
forth between Earth and Space Station Alpha (Chapter 3) in Low Earth Orbit LEO. The Skylons
are o perated out of Spaceport A merica ( Chapter 4) in N ew M exico, U SA.
The lander is transported to the Moon, where it proceeds down to the lunar surface. The crew
fills the Tray with lunar material. After the containers have been filled, the crew lifts off from the
lunar surface and connects to another transport. The Lander with its lunar material combination
heads h ome.
Once the crew returns to Space Station Alpha, a Skylon transports the containers back to Earth.
A passenger S kylon returns the t riumphant lunar c rew home.
::
Example
A consortium of astronautics companies have raised $27.14B USD to invest in a space mission
comprising of a Lunar Lander that is tasked to bring back Lunar Material from the surface of the
Moon.
You a re the Mission C ommander.
Your vehicle is a Boeing Space Tug, outfitted with a Lunar Lander Kit and a Payload Tray. The
Command Module (CM) weighs in at 4,345 kg, and the science mission payload is 4,761 kg,
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Adventures in O uter S pace
including the Payload Tray. The science payload will be left on the lunar surface, and the
equivalent weight in lunar material will be brought back. This material has an estimated value at
$1,500 USD per carat.
Calculate the propellant needed to land on the Moon and liftoff back into lunar orbit, the excess
propellant, the amount of Lunar Material brought back, the Gross Weight of the Lander, the
Gross Income after all the Lunar Material has been sold, the taxable income from the sale, and
finally, t he Return on I nvestment.
Using the the equations from Chapter 7, we see that we need to use the Rocket Equation to
calculate the needed propellant. Also, since the rocket nozzle needs to be retracted in order to
make room f or t he l anding, t he Specific I mpulse o f t he r ocket d rops by 3 seconds.
::
Assigning l abels to the i nputs, and c onverting e verything t o S .I. u nits, w e g et:
Lunar Investment = $24, 000, 000, 000 U SD
P ropellant = 39, 800 lbs = 18, 053 kg
CM = 4, 327 kg
P DI = 2, 181 mps
P AI = 1, 890 mps
g0 = 9.80665 m/s2
Science P ayload = 4, 761 kg
P ayload T ray = 1, 500 lbs = 680 kg
Lander Kit = 896 lbs = 406 kg
Selling P rice = $1, 500/carat = $7, 500, 000/kg
The o utput b ecomes:
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