S.T.E.M. F or the Classroom
Adventures i n Outer S pace
R.A.F.T. W RITING # 1
● Ro le: Teacher
● Au dience: M iddle S chool S tudents
● Fo rmat: Step–by–Step I nstructions
● T opic: D escribe t he R .E.L. S kylon P ayload E quation a nd h ow t he O rbital A ltitude i s the
independent v ariable a nd t he P ayload M ass is the dependent v ariable.
R.A.F.T. WRITING #2
● Ro le: T eacher
● Au dience: M iddle S chool students
● Fo rmat: F ive paragraph e ssay
● T opic: The Space Transportation System (Space Shuttle). Who were some of the
astronauts that flew the missions? What payload did they deposit in orbit? What was
unique about their missions? What was in common with all the missions? How does the
Space Shuttle differ from the spaceliner presented in this textbook? How are they the
same? Why e ven b other t o b uild a spaceliner a nyway?
DISCUSSION TOPICS
● Was t he m athematics in this c hapter difficult t o understand?
● The authors c onclude that expendable rockets should n o l onger b e used t o f ly i nto space.
Do y ou a gree with the authors? W hy or W hy not?
● What w ould it be l ike to f ly aboard a s paceship t hat takes off l ike a n ordinary airliner?
Would you fly o n the S kylon s paceliner? Why or why not?
2.06 L aunch Payload D esign Website
We n ow proceed to c reate t he suborbital website t hat includes the engineering l ogs a nd the a pp
embedded in a webpage.
INSERT T EXT HERE
::
Page 4 3 o f 176
S.T.E.M. For t he Classroom
Adventures i n Outer Space
2.07 L aunch P ayload Design S preadsheet App
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space M ission D esign App ( SMDA).
The S .T.E.M. for the C lassroom/Google A pp i s b roken down i nto four ( 4) p arts:
1. Input/Output Interface
2. Graph
3. Constants
4. Calculations
The A pp can now be d eveloped.
Sample G oogle Sheets App Design Open Source Code
Once the c ells have been n amed r eferencing c ells is easy.
● CALCULATIONS
○ AtLatitudePayload250=0.0011* DEG^2+15500
○ AtLatitudePayload800=0.0011* DEG^2+11000
● GRAPHING
○ m=(AtLatitudePayload800AtLatitudePayload250)/550
○ b=AtLatitudePayload250 m*250
○ AtLatitudePayload=m*ALT+b
INSERT OPEN S OURCE C ODE
Page 4 4 of 176
S.T.E.M. F or the C lassroom
Adventures i n O uter S pace
Sample App I nterface
Image 1 4: Launch P ayload Design Spreadsheet App
2.08 Launch P ayload D esign Mobile A pp
Sample AppSheet Mobile App Design O pen Source Code
Once the G oogle S preadsheet has b een completed, it c an b e used t o help c reate t he mobile app.
INSERT CODE HERE
Page 45 o f 1 76
S.T.E.M. F or t he C lassroom
Adventures in O uter S pace
I NSERT C ODE H ERE
INSERT C ODE H ERE
Sample A ppSheet M obile App Design
Image 1 5: Launch P ayload D esign Mobile App, P art I
Page 4 6 o f 176
S.T.E.M. F or t he C lassroom
Adventures i n Outer S pace
Image 1 6: Launch Payload Design Mobile App, Part I I
2.09 Launch Payload D esign P resentation D evelopment Page 4 7 o f 176
INSERT TEXT H ERE
INSERT TEXT HERE
::
S.T.E.M. F or t he Classroom
Adventures i n Outer S pace
2.10 Chapter T est
I. V OCABULARY
Match t he aerospace term w ith its definition.
1 . Launch S ite Latitude A. The height above Mean Sea Level (MSL) of a
spacecraft.
2. O rbital A ltitude B. The mass o f a p ayload effected b y E arth’s g ravity.
3. O rbital I nclination C. An orbit that flies above the North and South poles;
it has an Orbital Inclination of 9 8 d egrees.
4 . P ayload M ass D. T he l atitude ( measured in d egrees) o f t he launch s ite.
5. Polar Orbit E. The number of degrees that an orbit subtends relative
to t he e quator.
II. M ULTIPLE C HOICE
Circle t he c orrect answer.
6. The R.E.L. Skylon Payload Equation when graphed forms a parabola which can be describe
using a quadratic equation.
A. T rue B. False
7. The R.E.L. Skylon Payload Equation when graphed forms a straight line which can be
describe using a l inear e quation.
A. T rue B. False
8. The further north or south the R.E.L. Skylon launches from, the ____________ payload mass
it can carry into L ow E arth Orbit.
A. More B. Less C. Neither D. Cannot be d etermined
9. The higher the orbital altitude of the R.E.L. Skylon, the ____________ payload mass it can
carry i nto Low E arth Orbit.
A. M ore B. L ess C. N either D. C annot be d etermined
10. The more the R.E.L. Skylon carries into Low Earth Orbit, the ____________ the final orbital
altitude of the spaceliner.
A. H igher B. Lower C. Neither D. C annot b e determined
Page 4 8 o f 176
S.T.E.M. For t he Classroom
Adventures i n Outer S pace
III. C ALCULATIONS
An orbital s pacecraft l aunches f rom B aikonur C osmodrome t o t he I.S.S.
11. What i s t he L aunch S ite L atitude of t he cosmodrome?
12. What i s t he orbital i nclination that the spacecraft needs t o a ttain?
13. What i s t he Orbital Altitude o f the International S pace S tation?
14. W hat i s t he Baikonur CosmodromeI.S.S. g eneral Quadratic E quation?
15. W hat is the B aikonur C osmodromeI.S.S. 2 50 km g eneral Quadratic Equation?
16. What i s the B aikonur CosmodromeI.S.S. 800 k m general Q uadratic E quation?
17. W hat i s the s lope of t he B aikonur CosmodromeI.S.S. g eneral L inear Equation?
18. W hat i s the yintercept o f t he Baikonur C osmodrome–I.S.S. g eneral Linear E quation?
19. W hat i s t he Baikonur C osmodrome–I.S.S. general L inear Equation?
20. What is the maximum weight that the R.E.L. Skylon can lift to the International Space
Station from t he Baikonur Cosmodrome?
IV. WRITING
Write a one paragraph e ssay on t he topics below.
21. Explain how t o f ind the leading coefficient of the R .E.L. S kylon p ayload Q uadratic E quation.
22. E xplain w hy t he f urther n orth a launch site is located, the less p ayload t hat can be carried i nto
space.
23. E xplain why the h igher t he orbital altitude n eeded, t he l ess t he amount of p ayload t hat can b e
carried.
24. E xplain why the more the a mount o f payload i s needed to b e carried into space, the l ess the
orbital altitude t hat t he R .E.L. Skylon c an a ttain.
25. Write a short story about what it would feel like to float weightlessly inside of an R.E.L.
Skylon spaceplane while gazing at the curvature of the Earth as it flies an orbital spaceflight
profile.
END O F C HAPTER 2 E XAM
Page 49 o f 176
S.T.E.M. F or t he Classroom
Adventures i n Outer Space
Chapter 3: S pace S tation
3.01 N arrative 9 9
3.02 Vocabulary 99
3.03 Analysis 99
3.04 Guided Practice 9 9
3.05 C ross C urricula Activities 9 9
3.06 Space Station D esign Website D evelopment 9 9
3.07 S pace Station D esign S preadsheet A pp Development 9 9
3.08 Space S tation Design M obile App D evelopment 9 9
3.09 S pace Station Design Presentation Development 99
3.10 C hapter Test 99
::
Page 50 of 176
S.T.E.M. For t he C lassroom
Adventures in Outer Space
3. Space Station
3.01 Narrative
In this, the third of four aerospace–based
S.T.E.M. project, students will use the
Bigelow Aerospace B330 and BA–2100
pressurized modules to launch and assemble
a space station of their own design in Low
Earth Orbit ( LEO).
Time F rame
4.5 w eeks
Aerospace Problems
Space S tation C ost
Space Station Mass
Space S tation C rew S ize
Mathematics Used
Matrices
Science Topics
Physics, Aerospace
Activating P revious L earning
Basic M athematics
Image 1 7: Bigelow Aerospace Space S tation C over
Essential Questions
● Who a re the m any space station pioneers?
● What is a space station?
● Where can a B igelow s pace station b e spotted in the night s ky?
● When will t he f irst c ommercial Bigelow space s tation be flown?
● Why d o people want t o live o n a space s tations i n o rbit
● How m any people can l ive o n a space station?
● Wait. I have to do s cience, technology, engineering, and math, all a t t he same t ime?
Page 51 o f 1 76
S.T.E.M. F or the Classroom
Adventures i n Outer S pace
This l esson is powered b y E 8 :
1. Engage
○ Lesson O bjectives
○ Lesson Goals
○ Lesson Organization
2. Explore
○ The BA330 Habitat S pecifications
○ The BA2100 H abitat S pecifications
○ The Bigelow S pace Station a nd its C omponents a nd D efinitions
○ Additional T erms a nd D efinitions
3. Explain
○ Launch C onstraints
4. Elaborate
○ Other S pace Station Examples
5. Exercise
○ Space Station P arameters
○ Space Station D esign S cenario
6. Engineer
○ The Engineering D esign Process
○ SMDA S pace S tation Plan
○ Designing a P rototype
○ SMDA Software
7. Express
○ Displaying the SMDA
○ Progress R eport
8. Evaluate
○ Post E ngineering Assessment
::
Lesson Overview
Students first learn the basics of space station design using pencil, paper, and scientific
calculator. Students then use what they have learned to create a Space Mission Design App
(SMDA), designed according to the Engineering Design Process, that will be used for realworld
spacecraft.
We will be using the products from Bigelow Aerospace, which makes inflatable habitat modules
that once placed into orbit, well, i nflate. This allows for a greater volume of space inside for the
Page 5 2 o f 1 76
S.T.E.M. F or t he C lassroom
Adventures i n Outer S pace
crew. It has solar panels for electrical power and radiators to dispose of waste heat. It even has
windows!
Students will use spreadsheet software to create the app and will use slideshow software for
their presentations. They will also create a document of their experiences engineering the SMDA
and presenting t heir findings to t he rest o f t he class.
::
Constants
● None
Input
● Total BA 2 100 Modules
● Total B 330 Modules
● Total P B/DN M odules
Output
● Total B A–2100 S tacks
● Total B330 Stacks
● Total P B/DN S tacks
● Total S paceX F alcon H eavy
● Total N ASA S LS B lock I
● Total M ass of the s pace s tation
● Total C rew S ize
● Total C ost o f t he space s tation
::
3.02 Vocabulary
B330 M odule B300 S tack BA2100 Module BA2100 Stack
Crew Size Crew Volume Docking N ode (DN) Expendable Launch Vehicle
Falcon Heavy PB/DN PB/DN Stack Pressurized V olume
Propulsion Bus ( PB) SLS Block I Space Station
Page 5 3 o f 176
S.T.E.M. F or t he Classroom
Adventures i n O uter S pace
Image 18: Inside a mockup o f Space S tation Alpha
3.03 Analysis
To launch these excellent habitat modules into space, we obviously need a launch vehicle.
Shopping around for what’s available to use to launch our city, we find two Expendable Launch
Vehicles (ELV). These rockets haven’t been built yet, but so long as funding continues they will
be... one d ay. T he t wo ELVs are t he S LS I A a nd t he Falcon Heavy.
Since the SLS IA ELV can carry 105,000 kg into Low Earth Orbit (LEO), and one BA2100
weighs 1 00,000 k g, it c an c arry o nly one u nit a t a time. We will call this the “BA2100 Stack.”
The Falcon Heavy ELV can lift 53,000 kg to LEO. Each B330 weighs 25,000 kg, so it can carry
2 units at a time (assuming, of course, that it could fit in a payload shroud). We will call this the
“B330 Stack.”
Each PB/DN has a mass of 17,000 kg, so 3 units will fly on the Falcon Heavy ELV to LEO. This
will b e c alled t he “ PB/DN S tack.”
::
Page 5 4 o f 1 76
S.T.E.M. F or t he C lassroom
Adventures i n Outer Space
BA–2100 S tack:
● Cost: ( 1) SLS I A + (1) B A–2100 = $ 750M + $ 500M = $ 1,250M
● Mass: ( 1) B A2100 = ( 1) 100,000 kg = 1 00,000 kg
● Volume: ( 1) 2,100 m 3 = 2,100 m 3
● Crew: (1) 1 6 = 1 6 Astronauts
B330 Stack:
● Cost: ( 1) Falcon H eavy + ( 2) B 330 = $ 150M + (2) $125M = $400M
● Mass: (2) B330 = (2) 2 5,000 k g = 50,000 k g
● Volume: (2) 3 30 m 3 = 6 60 m 3
● Crew: (2) 6 = 12 Astronauts
PB/DN Stack:
● Cost: (1) Falcon Heavy + (3) P B/DN = $ 150M + (3) $ 75M = $375M
● Mass: (3) 1 7,000 k g = 51,000 kg
It now becomes an easy matter to compute the specifications of any space station design that we
choose. If a design calls for using four B330 modules, then two B300 Stacks are needed. Note,
however, that the space station design does have constraints. For instance, the number of B300
habitat m odules m ust b e e ven, a nd the number of P B/DNs must be a m ultiple o f 3 .
To summarize,
BA–2100 Stack
● COST: $1,250M
● MASS:100,000 kg
● VOLUME: 2,100 m3
● CREW: 16 Astronauts
B330 S tack
● COST : $400M
● MASS: 5 0,000 kg
● VOLUME: 660 m 3
● CREW: 12 A stronauts
PB/DN Stack
● COST: $ 375M
● MASS: 51,000 kg
Page 5 5 of 1 76
S.T.E.M. F or t he C lassroom
Adventures i n Outer Space
All t his information can be p ut i nto a matrix:
┌ ┐
⎸ $1,250M 100mt 2,100m3 16 C rew ⎸
Stack Information = ⎸ $400M 50mt 6 60m3 12 Crew ⎸
⎸ $375M 51mt – – ⎸
└ ┘
The n umber o f each stack that is needed c an a lso be w ritten as a m atrix:
N umber of Stacks = [BA − 2100 Stacks B330 Stacks P B/DN Stacks]
However, t he Number o f S tacks w ill h ave t o first b e calculated, since the number of B330s and
PB/DNs m ust be m ultiples o f 2 a nd 3 respectively.
Therefore, g iven:
● Number of B A–2100s
● Number of B 330s
● Number of P B/DNs
[ ]N umber of Stacks =
N umber of BA − 2100 N umber of B 330 N umber of P B/DN
2 3
Since the N umber o f Stacks is a [ 1 x 3 ] matrix, a nd t he Stack Information is a [ 3 x 4 ] matrix, we
can perform t he dot product of the 2 m atrices, w hich is r epresented a s:
[1 x 3 ] X [3 x 4] = [1 x 4]
[Number of Stacks] X [Stack Information] = T otal
where Total is represented a s:
T otal = [Cost M ass V olume Crew]
So let’s b uild us a c ity in space, shall w e?
::
Page 56 of 1 76
S.T.E.M. F or t he C lassroom
Adventures in O uter S pace
Example
The folks at Bigelow Aerospace have made it easy for us: they’ve already designed a very nice
space station! It’s called the “Hercules Resupply Depot,” but we’ll just call it “Home.” Thanks,
Bigelow!
Image 19: The Hercules Resupply D epot B igelow S pace Station
As you can see from the poster, we’ll need three BA–2100s, six B330s, and three PB/DNs to
complete the d esign. W e c an t herefore c alculate how many “ stacks” w e’ll need:
(3) B A–2100 = (3) BA–2100 Stacks
● (3) $ 1,250M = $3,750M
● (3) 1 00,000 kg = 300,000 k g
● (3) 2 ,100 m 3 = 6,300 m 3
● (3) 16 Crew = 4 8 Crew
(6) B330 = ( 3) B 330 Stacks
● (3) $ 400M = $1,200M
● (6) 25,000 k g = 150,000 kg
● (6) 330 m3 = 1 ,980 m 3
● (6) 6 C rew = 3 6 C rew
(3) PB/DN = (1) PB/DN Stack
● (1) $375M
● (3) 1 7,000 k g = 5 1,000 k g
::
Page 57 o f 1 76
S.T.E.M. F or the C lassroom
Adventures in O uter Space
Adding e verything u p w e g et:
● Total C ost: $ 5,325M
● Total Mass: 501,000 k g
● Total Volume: 8 ,280 m 3
● Total Crew: 84 A stronauts
The calculations, however, a re waaaaaay easier t o handle using M atrix Notation:
N umber of Stacks = [ 3 6 3 ] = [3 3 1]
2 3
and
┌ ┐
⎸ $ 1,250M 100mt 2,100m3 16 Crew ⎸
[3 3 1] X ⎸ $ 400M 5 0mt 6 60m3 12 Crew ⎸
⎸ $375M 51mt – – ⎸
└ ┘
┌ ┐
⎸ $ 1,250M 100mt 2,100m3 16 C rew ⎸
[3 3 1] = ⎸ $400M 5 0mt 660m3 12 C rew ⎸
⎸ $375M 5 1mt – – ⎸
└ ┘
Summing t he c olumns of t he m atrix t hat we just cross multiplied, we g et o ur f inal m atrix:
Space Station H ercules = [ $5,325M 501mt 8 ,280m3 84 Crew]
The a mount of s pace t hat each a stronaut gets c an n ow be calculated.
Crew V olume = T otal V olume
T otal Crew
= 8280
84
= 98.59m3 p er astronaut.
::
Page 5 8 of 176
S.T.E.M. F or the Classroom
Adventures in Outer Space
So this is a space station that has a mass of half a million kilograms, has over eight thousand
cubic meters of habitable space, can house 84 people, with almost one hundred cubic meters of
elbow room f or e ach person, can reboost i ts orbit, and costs a l ittle o ver f ive billion d ollars.
A c omparison of t he H ercules s pecifications with t he International S pace Station is below:
Hercules I.S.S.
Total C ost (USD) $5,325,000,000 $150,000,000,000
Total Mass (kg) 501,000 450,000
Total V olume ( m3 ) 8,280 837
Total Crew (Astronauts) 84 3
Total C rew Volume ( m3 / Astronaut) 99 279
The I.S.S. price tag eventually became $150B (USD), which makes the Hercules about one–third
the cost for roughly the same mass, and containing around 10 times the pressurized volume while
sustaining 28 times the crew size of the I.S.S. While the I.S.S. crew does enjoy almost 3 times
the i ndividual v olume, t he H ercules is c learly superior in v irtually e very c ategory.
::
3.04 Guided Practice
You a re an space s tation d esigner. Use t he B igelow Space Station Equation to c alculate t he
specifications for e ach s pace station.
Space Station Delta:
● Number o f B A2100: 1
● Number o f B300: 4
● Number of PB/DN: 3
● Total C ost: $_______________
● Total Mass: _______________ kg
● Total Volume: _ ______________ m3
● Total C rew: _____ Astronauts
● Total Crew V olume: _ ____ m 3
Page 5 9 o f 176
S.T.E.M. F or t he C lassroom
Adventures i n O uter Space
Space S tation 2:
● Number of BA2100: 2
● Number of B300: 8
● Number of PB/DN: 6
● Total C ost: $ _______________
● Total M ass: _ ______________ k g
● Total V olume: _ ______________ m3
● Total C rew: _ ____ Astronauts
● Total Crew V olume: _____ m3
::
3.05 Cross Curricular E xercises
ARTWORK
Find i mages o f t he B igelow A erospace B 330 i nflatable s pace station module on t he I nternet. Use
the i mages that y ou have researched t o d raw a p icture o f t he s pace s tation in E arth orbit.
R.A.F.T. W RITING # 1
● Ro le: Teacher
● Au dience: Middle School s tudents
● Fo rmat: F ive p aragraph e ssay
● T opic: The Apollo Skylab. Who were the astronauts that flew the missions? How many
days did each crew stay? What was unique about their missions? What was in common
with all the missions? How does the Skylab differ from the space station presented in this
textbook? H ow a re they the same? W hy even bother t o b uild a s pace s tation anyway?
DISCUSSION TOPICS
● Was t he m athematics in this chapter difficult t o u nderstand?
● The authors conclude t hat t he Hercules space station i s s uperior t o the I .S.S. Do you
agree w ith t he a uthors? Why o r W hy n ot?
● What would i t be like t o stay aboard a B igelow space station? W ould y ou l ike t o b e a
guest a t a s pace h otel? Why o r why not?
::
Page 60 o f 176
S.T.E.M. F or the C lassroom
Adventures in O uter S pace
3.06 S pace S tation Design W ebsite
We n ow proceed t o create the s uborbital w ebsite that includes the engineering l ogs a nd the a pp
embedded i n a w ebpage.
INSERT TEXT HERE
3.07 S pace S tation D esign Spreadsheet App
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space M ission Design App (SMDA).
The S .T.E.M. for the Classroom/Google App i s broken down into four (4) p arts:
Input/Output Interface
Graph
Constants
Calculations
The A pp c an now b e developed.
Sample G oogle Sheets A pp Design O pen S ource Code
Once t he c ells have b een named r eferencing cells is e asy.
● CALCULATIONS
○ TotBA2100Wt=InputNumBA2100*BA2100Wt
○ TotBA2100Vol=InputNumBA2100*BA2100Vol
○ TotBA2100Crew=InputNumBA2100*BA2100Crew
○ TotBA2100Cost=InputNumBA2100*BA2100Cost
○ TotBA330Wt=InputNumBA330*BA330Wt
○ TotBA330Vol=InputNumBA330*BA330Vol
○ TotBA330Crew=InputNumBA330*BA330Crew
○ TotBA330Cost=InputNumBA330*BA330Cost
Page 61 o f 1 76
S.T.E.M. F or the Classroom
Adventures i n Outer Space
○ SpaceStationVol=TotBA2100Vol+TotBA330Vol
○ SpaceStationCrew=TotBA2100Crew+TotBA330Crew
○ SpaceStationCrewVol=SpaceStationVol/SpaceStationCrew
INSERT OPEN S OURCE C ODE
INSERT O PEN S OURCE CODE
INSERT OPEN SOURCE CODE
Page 62 of 176
S.T.E.M. For the Classroom
Adventures in Outer S pace
Sample A pp Interface
Image 2 0: Space S tation Design Spreadsheet App
3.08 Space Station Design Mobile A pp
Sample A ppSheet Mobile A pp D esign O pen S ource C ode
Once t he Google Spreadsheet h as been completed, i t c an be used to help c reate the mobile a pp.
INSERT C ODE H ERE
Page 6 3 of 1 76
S.T.E.M. For t he Classroom
Adventures in Outer S pace
INSERT C ODE HERE
Sample AppSheet Mobile App D esign
Image 21: S pace Station Design Mobile A pp
Page 64 of 176
S.T.E.M. For the C lassroom
Adventures in Outer S pace
3.09 O rbital M ission Design P resentation D evelopment
INSERT T EXT HERE
INSERT T EXT HERE
INSERT TEXT HERE
Page 65 of 176
S.T.E.M. F or the C lassroom
Adventures i n Outer S pace
3.10 C hapter Test
I. VOCABULARY
Match the a erospace t erm w ith its d efinition.
1. B330 M odule A. T he n umber of a stronauts a board a s pace s tation.
2 . Crew Size B. A Bigelow habitat module that has a pressurized
volume o f 330 c ubic meters
3. Crew Volume C. The unit used to reboost the space station due to
orbital d ecay
4. Falcon Heavy D. T he total p ressurized v olume for each crew m ember
5. P ropulsion B us (PB) E. A n ELV from S paceX that c an l ift 53,000 kg
II. M ULTIPLE C HOICE
Circle the correct answer.
6. The name of the Bigelow habitat module is also the volume (in cubic feet) of the habitable
interior o f t he module.
A. TRUE B. F ALSE
7. Bigelow habitat modules come complete with docking ports, solar panels, radiators, and a
breathable a tmosphere.
A. T RUE B. F ALSE
8. What is the habitable volume of a space station design that consists of one BA–2100 module
and two B330 modules?
A. 2,760 i n3 B. 2,760 ft3 C. 2 ,760 m3 D. C annot be determined
9. A space station design calls for eight BA330 habitat modules. How many B330 Stacks will
be n eeded?
A. Two B. F our C. S ix D. C annot be d etermined
10. The Crew Volume can be found by dividing the space station ______________ into the total
number of s pace station c rew
A. Volume B. M ass C. C rew Size D. Cannot b e d etermined
Page 6 6 o f 176
S.T.E.M. For t he C lassroom
Adventures in O uter S pace
III. CALCULATIONS
A space s tation design calls for 6 B330 m odules a nd 3 P B/DNs.
11. How m any SLS IA E LVs w ill b e r equired?
12. H ow m any F alcon H eavy ELVs will be required?
13. How many BA–2100 S tacks will b e required?
14. H ow many B 330 Stacks w ill be r equired?
15. H ow many P B/DN Stacks w ill be r equired?
16. W hat is the weight of this s pace station?
17. W hat i s the habitable v olume of this s pace s tation?
18. What is t he n umber of crew of t his space station?
19. What is the C rew Volume o f this space station?
20. W hat i s the total cost of this s pace station?
IV. WRITING
Write a one paragraph e ssay on t he t opics below.
21. Explain how to f ind t he total h abitable volume o f a Bigelow space s tation s imply b y k nowing
how m any of each module it h as.
22. E xplain w hy (or why not) three P B/DNs can be launched using a F alcon Heavy ELV.
23. Explain why (or why n ot) two BA–2100 habitat modules c an be launched using t he S LS I A
ELV.
24. Explain how to calculate the t otal pressurized volume for each crew m ember (Crew V olume).
25. Write a short story about what it would feel like to float weightlessly inside of a Bigelow
space s tation, w hile g azing at t he curvature o f the E arth as i t flies around the world.
END OF CHAPTER 3 E XAM
Page 6 7 of 176
S.T.E.M. F or t he C lassroom
Adventures in Outer Space
Chapter 4 : Spaceport
4.01 N arrative 9 9
4.02 Vocabulary 9 9
4.03 Analysis 99
4.04 G uided P ractice 99
4.05 Cross C urricula A ctivities 99
4.06 Unpowered Glide Landing W ebsite Development 99
4.07 Unpowered Glide L anding S preadsheet App Development 9 9
4.08 Unpowered G lide Landing Mobile A pp D evelopment 9 9
4.09 Unpowered G lide L anding Presentation Development 9 9
4.10 C hapter T est 99
Page 68 o f 176
S.T.E.M. F or the Classroom
Adventures in Outer S pace
4. S paceport
4.01 N arrative
In this, the fourth and final aerospacebased
S.T.E.M. project, students will track the
position and speed of a spacecraft that is
landing at S paceport America.
Time F rame
4.5 weeks
Aerospace P roblems
Glide S lope
Altitude
Distance F rom Runway
Descent R ate
Ground Speed
Mathematics U sed
Trigonometry
Vector A nalysis
Science Topics
Physics, Aerospace
Activating P revious Learning
Geometry
I mage 22: Spaceport A merica C over
Essential Questions
● Who a re the p ioneers o f spaceports?
● What i s t he C omplement o f an angle?
● Where can a s paceport b e located?
● When was Spaceport America open for business?
● Why would people prefer to l and at a s paceport a s opposed t o an airport?
● How do I u se T rigonometry to calculate t he distance and a ltitude of a s pacecraft?
● How do I c alculate how far away a s paceliner is from the spaceport?
● Wait. I have to d o science, t echnology, e ngineering, and m ath, a ll at the s ame t ime?
Page 69 o f 176
S.T.E.M. For the C lassroom
Adventures i n O uter S pace
This lesson i s p owered b y E 8 :
1. Engage
○ Lesson O bjectives
○ Lesson G oals
○ Lesson Organization
2. Explore
○ The R ight Triangle
○ The T rigonometric Identities
○ Basic Vector A nalysis
○ Additional T erms and Definitions
3. Explain
○ Glide S lope
4. Elaborate
○ Other Spaceport Examples
5. Exercise
○ Spacecraft landing P arameters
○ Spacecraft landing Scenario
6. Engineer
○ The Engineering D esign Process
○ SMDA Spacecraft L anding Plan
○ Designing a P rototype
○ SMDA Software
7. Express
○ Displaying the S MDA
○ Progress R eport
8. Evaluate
○ Post E ngineering A ssessment
::
Lesson Overview
Students first learn the basics of spaceflight unpowered glide landing using pencil, paper, and
scientific calculator. Students then use what they have learned to create a Space Mission Design
App (SMDA), designed according to the Engineering Design Process, that will be used for
realworld s pacecraft.
Page 7 0 o f 176
S.T.E.M. For the C lassroom
Adventures i n Outer Space
We will be using Spaceport America (33 o N, 107 o W), located just north of Las Cruces, NM.
Typical spacecraft that could land at this facility are the Virgin Galactic SpaceShipTwo and the
R.E.L. S kylon.
Students will use spreadsheet software to create the app, and will use slideshow software for
their presentations. They will also create a document of their experiences engineering the SMDA
and p resenting t heir findings to t he rest o f the class.
Constants
● None
Input
● Glide A ngle ( deg)
● Glide D istance 1 ( ft)
● Glide D istance 2 ( ft)
Output
● Altitude ( m AGL)
● Distance f rom Spaceport (m)
● Glide S lope ( deg)
● Glide S peed ( mps)
● Descent R ate ( mps)
● Ground Speed (mps)
● Time to T ouchdown (min)
::
4.02 Vocabulary
Adjacent S ide Altitude Above G round Level (AGL)
Descent Rate Distance From Spaceport Glide A ngle
Glide D istance Glide S lope Glide Speed
Ground Speed Hypotenuse Landing L aser
Landing P rofile LineOfSight Opposite S ide
Right T riangle Time T o T ouchdown Touchdown
Page 71 o f 1 76
S.T.E.M. For the Classroom
Adventures i n Outer Space
Image 2 3: The unique b uilding that houses s pacecraft at t he s paceport
4.03 A nalysis
Any spacecraft returning from space is always out of propellant. This is because all the
propellant is used during the trip into space. Consequently, there is none available for the return
trip. All machines that have wings can glide, that is, fly with the engine turned off. Some glide
better than others, b ut s till, t hey a ll glide.
This is why spacecraft come in with their nose down; they are maintaining required airspeed. As
they cross over the edge of the runway, the nose is pulled up and the spacecraft flattens out its
glide as air is packed underneath the wings. It’s then just a simple matter of letting the spacecraft
sink t o a gentle touchdown.
Once on the ground the nose is kept in the air “wheelie” fashion, so that speed can be bled off
without using brakes, because they can get very hot extremely quickly. After the nose comes
down on its own the brakes can then be (sparingly) applied. Eventually, the spacecraft rolls to a
full stop.
Back h ome o nce again!
Page 7 2 of 1 76
S.T.E.M. For t he C lassroom
Adventures i n Outer Space
Image 2 4: G lide path of a v ehicle returning f rom space
We will be tracking a hypothetical spacecraft returning from space (such as the Virgin Galactic
SpaceShipTwo) as the pilots on board perform an unpowered glide landing back to the
Spaceport.
A Landing Laser located at the edge of the Spaceport runway will be used to track the landing
spacecraft. T he laser w ill determine the Glide A ngle a nd the G lide D istance:
Image 2 5: D iagram of L anding Configuration
Page 7 3 o f 1 76
S.T.E.M. For the C lassroom
Adventures i n O uter Space
This laser will measure the Glide Angle from the vertical, since the ground may or may not be
level. The laser itself when triggered will perform two bursts over a one second period. This
gives us Glide D istance 1 and G lide D istance 2.
Note: Ideally, the laser would be firing every second so that a more accurate plot of the
spacecraft can be made as it comes in for the landing. This constraint to the project means that
we are basically taking a snapshot of the position and speed of the spacecraft with each laser
firing.
The resulting Landing Profile can be represented as a Right Triangle, and can then be labeled
appropriately. The G lide Slope is simply t he C omplement o f the G lide Angle.
Glide Slope = Complement(Glide Angle) = 90o − Glide Angle
Image 2 6: Pythagorean T riangle used to calculate s pacecraft landing data
The Right Triangle can be solved by using the Trigonometric functions of Sine and Cosine. For
the purposes of t his exercise, t he a ngles will not h ave t o first b e converted to radians.
cos(θ) = Adj acent S ide
H y potenuse
sin(θ) = Opposite S ide
H y potenuse
Writing t he t rigonometry in aerospace f orm, the g eneral e quation b ecomes:
cos(Glide Slope) = Distance T o Spaceport
Line−Of −S ig ht Distance
sin(Glide Slope) = Line−Of Altitude
−S ig ht− Distance
Page 74 o f 1 76
S.T.E.M. F or t he Classroom
Adventures in O uter Space
Rearranging the e quation, w e get,
Distance T o Spaceport = Line − Of − Sight Distance · cos(Glide Slope)
Altitude (AGL) = Line − Of − Sight Distance · sin(Glide Slope)
To graph the Landing Profile, simply graph the t wo p oints:
(0, 0) & ( Distance to Spaceport, Altitude)
The linear equation can e asily b e d erived from t hese t wo points.
The two laser bursts one second apart gives us two distances with t=1. Thus we get two different
distances, LineOfSight Distance 1 and LineOfSight Distance 2. Using d=rt and rearranging,
we g et,
Glide Speed = Line − Of − Sight Distance 2 − Line − Of − Sight Distance 1
Using the s ame trigonometric functions a s b efore, the o ther rates c an be c alculated.
Ground Speed = Glide Speed · cos(Glide Slope)
Descent Rate = Glide Speed · sin(Glide Slope)
and
T ime T o T ouchdown = Line−Of −S ig ht Distance
Glide S peed
::
Example
An R.E.L. Skylon is returning to Spaceport America from space after dropping off some
passengers and picking up more that are homeward bound. The Landing Laser bounces a laser
off of t he s paceplane t o determining t he following i nformation:
● Glide Angle = 55 degrees
● Glide Distance 1 = 19.80 mi
● Glide D istance 2 = 1 9.75 m i
Page 75 of 176
S.T.E.M. F or t he C lassroom
Adventures in O uter Space
Find the following information a bout t he landing s pacecraft a t this m oment i n t ime.
● Altitude AGL
● Distance to S paceport
● Glide Slope
● Glide Speed
● Descent R ate
● Ground Speed
● Time To Touchdown
First, w e m ust change our i nputs t o S.I. u nits:
Line − Of − Sight Distance 1 = Glide Distance 1 = 31, 865 m
1609
Line − Of − Sight Distance 2 = Glide Distance 2 = 31, 785 m
1609
So,
Glide Slope = 90o − 55o = 35o
Altitude (AGL) = Line − Of − Sight Distance 2 · sin(Glide Slope)
= 31785(0.57) = 18, 277 m
Distance T o Spaceport = Line − Of − Sight Distance 2 · cos(Glide Slope)
= 31785(0.82) = 26, 102 m
Glide Speed = Line − Of − Sight Distance 1 − Line − Of − Sight Distance 2
= 31865 − 31785 = 81 mps
Descent Rate = Glide Speed · sin(Glide Slope)
= 81(0.57) = 46 mps
Ground Speed = Glide Speed · cos(Glide Slope)
= 81(0.82) = 46 mps
T ime T o T ouchdown = Line−Of −S ig ht Distance 2 = 690 s = 11.5 min
Glide S peed
S.T.E.M. E ducation. D on’t come home without it...
Page 76 of 176
S.T.E.M. For t he C lassroom
Adventures in O uter S pace
4.04 G uided Practice
You a re a n s paceliner C aptain r eturning f rom a m ission i n s pace. U se the S paceport A merica
Equation to keep t rack of y our landing parameters.
Landing S cenario
● Glide A ngle = 4 5 d egrees
● Glide D istance 1 = 15.05 m i
● Glide D istance 2 = 1 5.00 mi
Altitude AGL = _ _________ m
Distance to S paceport = __________ m
Glide Slope = _ _________ o
Glide Speed = _ _________ m ps
Descent R ate = __________ m ps
Ground Speed = _ _________ m ps
Time To Touchdown = _ _________ s
::
4.05 Cross Curricular Exercises
ARTWORK
Find images of S paceport America on the I nternet. U se t he i mages t hat you have r esearched to
draw a picture of spaceliners flying in a nd o ut of the spaceport.
R.A.F.T. WRITING
● Ro le: Teacher
● Au dience: Middle School students
● Fo rmat: Five p aragraph e ssay
● T opic: The Kennedy Space Center (KSC). What spacecraft were launched from there?
Did any of the space launches go to the Moon? What was unique about their missions?
Page 77 o f 1 76
S.T.E.M. F or the C lassroom
Adventures i n Outer Space
What was in common with all the missions? How does KSC differ from the spaceport
presented in this textbook? How are they the same? Why even bother to build a spaceport
anyway?
DISCUSSION T OPICS
● Was t he mathematics in t his chapter difficult t o u nderstand?
● The authors conclude that is a n e xcellent l ocation t o use as a s paceport. D o y ou agree
with the authors? Why or Why n ot?
● What would it be like t o f ly i nto space from Spaceport A merica? W ould y ou fly on either
SpaceShipTwo or t he S kylon spaceliner? Why o r w hy not?
4.06 Spaceport Unpowered Glide L anding Website
We now proceed t o c reate the suborbital w ebsite t hat i ncludes t he e ngineering logs and the a pp
embedded in a w ebpage.
INSERT T EXT HERE
::
4.07 Spaceport Unpowered Glide L anding Spreadsheet App
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space M ission Design App ( SMDA).
The S .T.E.M. f or t he C lassroom/Google App is broken d own i nto four (4) parts:
1. Input/Output Interface
2. Graph
3. Constants
4. Calculations
The A pp c an n ow b e d eveloped.
Page 78 of 1 76
S.T.E.M. F or the Classroom
Adventures i n Outer S pace
Sample O pen S ource Code
Once the c ells have been named referencing cells is e asy.
● CALCULATIONS
○ LOSDist1=GlideDist1/1609
○ LOSDist2=GlideDist2/1609
○ GlideSlope=90GlideAngle
○ Alt=LOSDist2*sin(GlideSlope)
○ DistToSpaceport=LOSDist2*cos(GlideSlope)
INSERT O PEN S OURCE C ODE
INSERT O PEN S OURCE C ODE
Page 79 of 176
S.T.E.M. For the C lassroom
Adventures in Outer Space
Sample App Interface
Image 27: S paceport U npowered Glide L anding Spreadsheet A pp
::
4.08 S uborbital S pace M ission D esign M obile A pp
Sample AppSheet M obile App Design O pen Source C ode
Once t he G oogle S preadsheet h as been c ompleted, i t can b e u sed to help create t he mobile app.
I NSERT CODE H ERE
Page 8 0 o f 1 76
S.T.E.M. F or t he C lassroom
Adventures in Outer Space
Sample A ppSheet Mobile App D esign
Image 2 8: Unpowered G lide Landing Mobile A pp
4.09 Orbital Mission D esign Presentation D evelopment
INSERT TEXT HERE
INSERT T EXT HERE
Page 81 of 176
S.T.E.M. For t he Classroom
Adventures i n O uter S pace
4.10 C hapter T est
I. V OCABULARY
Match t he aerospace term w ith its d efinition.
1 . A djacent S ide o f a Right A. A triangle with one of the angles equal to exactly 90
Triangle degrees.
2 . D escent R ate B. The side next t o t he given angle ( not t he
Hypotenuse).
3 . G lide S lope C. The distance a spacecraft descends over a certain
4 . Hypotenuse period o f time.
D. T he angle a s pacecraft m akes to the h orizontal.
5 . R ight T riangle E. The l ongest side of a right t riangle.
II. MULTIPLE CHOICE
Circle t he c orrect a nswer.
6. A spacecraft is returning from space for a landing back at Spaceport America. It is required
for t he s pacecraft t o have t he engines turned on in order to land s afely.
A. T RUE B. F ALSE
7. Given a Right Triangle, the sine of an angle (that is not the Right Angle) is defined as the
Hypotenuse d ivided b y t he Adjacent s ide.
A. T RUE B. F ALSE
8. W hat i s the G lide Slope o f a l anding s pacecraft i f t he Glide A ngle is 6 0o ?
A. 60o B. 30 o C. 1 5 o D. C annot be d etermined
9. The Landing Laser is malfunctioning and is giving the Glide Angle of a landing spacecraft.
What is t he d istance to t he Spaceport of the spacecraft?
A. 8 .3 k m B. 1 6.6 k m C. 3 3.2 km D . C annot be determined
10. If the measurement of the Adjacent Side of an angle is increased, then the measurement of
that angle ____________.
A. Increases B. D ecreases C. Unchanged D . C annot b e determined
Page 82 o f 176
S.T.E.M. F or the C lassroom
Adventures in O uter S pace
III. C ALCULATIONS
An R.E.L. S kylon is in a n u npowered glide l anding returning t o S paceport America. The
Landing Laser p aints the spacecraft with a 61o Glide A ngle and a 19.70 m iles Glide Distance.
Exactly one second later, the s pacecraft i s holding s teady at 61 o, b ut i s n ow a t 19.65 miles.
11. What is Glide Distance 1 ? G lide Distance 2 ?
12. W hat is L ineofSight D istance 1 ?
13. W hat i s LineofSight D istance 2?
14. W hat is t he Glide S lope?
15. What is t he D istance t o t he Spaceport?
16 . What i s t he A ltitude (AGL)?
17. W hat is the Glide S peed?
18. What i s the G round Speed?
19. W hat i s the D escent R ate?
20. What is t he T ime T o T ouchdown?
IV. W RITING
Write a o ne paragraph e ssay on the topics b elow.
21. Explain why a t riangle c an never have t wo right a ngles.
22. Explain w hy if in a R ight Triangle, increasing the Opposite S ide o f an angle i ncreases t he
measurement o f t hat a ngle.
23. Explain how to convert G lide D istance i nto LineOfSight Distance, t hat i s, c onvert Glide
Distance t o S .I. u nits.
24. Explain h ow t o find the D escent Rate of a s pacecraft r eturning from space.
25. Write a short story about what it would be like to feel the adrenaline after an unpowered glide
back to S paceport America from Low Earth Orbit aboard any s pacecraft that y ou desire.
END OF C HAPTER 4 E XAM
Page 83 of 176
S.T.E.M. For the Classroom
Adventures in Outer Space
END FALL SEMESTER
Page 84 of 176
S.T.E.M. For the C lassroom
Adventures i n Outer S pace
SPRING SEMESTER
ASTRONAUTICS
Unit 3: B asic A stronautics
Chapter 5 : Delta V and Transfer Time 99
Chapter 6 : Spacecraft M ass 99
Unit 4 : A dvanced Astronautics
Chapter 7 : T he R ocket Equation 99
Chapter 8 : Lunar Landing 99
Page 85 of 176
S.T.E.M. For the C lassroom
Adventures i n O uter Space
Chapter 5 : D elta V a nd T ransfer Time
5.01 N arrative 99
5.02 Vocabulary 9 9
5.03 Analysis 99
5.04 Guided Practice 99
5.05 C ross Curricula Activities 9 9
5.06 D elta V Mission D esign W ebsite D evelopment 99
5.07 D elta V Mission D esign Spreadsheet A pp Development 99
5.08 Delta V Mission Design M obile App D evelopment 9 9
5.09 Delta V M ission Design Presentation Development 9 9
5.10 Chapter T est 9 9
Page 8 6 o f 176
S.T.E.M. F or t he Classroom
Adventures in Outer Space
5. D elta V a nd T ransfer T ime
5.01 N arrative
In this, the first of four interconnected
astronautics–based S.T.E.M. projects,
students will calculate the change in orbital
velocity D elta V (Δv) needed to change the
orbital altitude of a spacecraft.
Time F rame
4.5 weeks
Astronautics P roblems
Periapsis Δv
Apoapsis Δ v
Δv Budget
Transfer T ime
Mission D uration
Mathematics U sed
Square Root F unctions
Science T opics
Physics, A stronautics
Activating P revious Learning
Basic Mathematics
I mage 2 9: Boeing Delta V Cover
Essential Q uestions
● What i s the relationship b etween t he change i n v elocity a nd the orbital a ltitude?
● Why do I n eed to raise o r l ower m y orbital altitude?
● How long d oes i t take to r each m y d estination?
● How long c an I s tay a t m y d estination?
● How d oes t he r adius o f the earth d etermine Δ v?
● Who are are s ome of the pioneers i n s pace exploration?
● Wait. I h ave t o do science, technology, e ngineering, a nd m ath, all at t he s ame time?
Page 8 7 of 1 76
S.T.E.M. For the C lassroom
Adventures in Outer S pace
This lesson i s powered b y E 8 :
1. Engage
○ Lesson O bjectives
○ Lesson G oals
○ Lesson Organization
2. Explore
○ The Circular O rbit
○ The Elliptical Orbit
○ Delta V (Δv)
○ Additional Terms and D efinitions
3. Explain
○ Change in Velocity
4. Elaborate
○ Other Orbital E xamples
5. Exercise
○ Δv a nd T ransfer Time P arameters
○ Δv and Transfer T ime S cenario
6. Engineer
○ The Engineering D esign P rocess
○ SMDA S pacecraft ΔV Plan
○ Designing a P rototype
○ SMDA S oftware
7. Express
○ Displaying the S MDA
○ Progress R eport
8. Evaluate
○ Post Engineering Assessment
Lesson O verview
Students first learn the basics of astronautics involving the Hohmann Transfer Orbit Equations
using pencil, paper, and scientific calculator. Students then use what they have learned to create a
Space Mission Design App (SMDA), designed according to the Engineering Design Process, that
will b e used for real–world s pacecraft.
Students will learn about circular and elliptical orbits and how orbital altitude can be changed
using rocket burns. Students will be using the Periapsis and Apoapsis Δv equations, as well as
the T ransfer Time equation.
Page 88 of 1 76
S.T.E.M. F or t he Classroom
Adventures in Outer Space
Students will use spreadsheet software to create the app and will use slideshow software for
their presentations. They will also create a document of their experiences engineering the SMDA
and presenting t heir findings to t he rest o f the class.
Constants
● Standard Gravitational P arameter μ ( m3 / s 2 )
● Earth Radius ( equatorial) (m)
Input
● Lower O rbital A ltitude ( m)
● Higher O rbital Altitude ( m)
● On–Station T ime (days)
Output
● Periapsis Δv Burn ( mps)
● Apoapsis Δ v Burn ( mps)
● Δv Budget (mps)
● Transfer T ime ( days)
● Round–Trip T ime (days)
● Mission D uration (days)
::
5.02 Vocabulary
Apoapsis Apoapsis Δv B urn Circular O rbit
Delta V ( Δv) Δv Budget Elliptical Orbit
Gravity Parameter ( μ) Hohmann Transfer O rbit Higher O rbital Altitude
Lower O rbital A ltitude Mission Duration On–Station Time
Orbital A ltitude Periapsis Periapsis Δv B urn
Radius of H igher O rbit Radius of Lower Orbit Round–Trip T ime
Round–Trip Δ v Standard G ravity ( g 0 ) Transfer O rbit # 1
Transfer O rbit #2 Transfer Time
::
Page 89 of 176
S.T.E.M. F or t he C lassroom
Adventures i n O uter Space
Image 30: O rbital mechanics c an be very complicated
::
5.03 Analysis
In order to raise or lower a spacecraft that is in orbit around a body, such as the Earth, the
Hohmann equations are used. These equations determine the change in orbital velocity (Δv)
needed to go t o different orbital altitudes.
√ √ΔvP ERIAP SIS = μ ( 2R2 − 1)
R1 R1 + R2
√ √ΔvAP OAP SIS = μ (1 − 2R1 )
R2 R1 + R2
Page 9 0 of 1 76
S.T.E.M. F or t he Classroom
Adventures i n Outer S pace
where
● μ = S tandard Gravitational Parameter, equal t o 398,600.44189 km3 /s 2
● R 1 = R adius of the i nner (smaller) o rbit
● R 2 = R adius o f t he o uter (larger) orbit
The Δ v B udget is s imply t he t wo Δ v r ocket burns a dded together.
ΔvBUDGET = ΔvP ERIAP SIS + ΔvAP OAP SIS
Using the p rinciple of R eversibility o f Orbits, the t otal Δv n eeded t o g et t o the destination and
back is
ΔvROUND−T RIP = 2(ΔvBUDGET )
The t ransfer t ime i s calculated in s econds.
√T ransf er T imeSECONDS = π (R1 + R2)3
8μ
There a re 8 6,400 seconds p er day, so t he n umber of days it t akes t o c hange t he o rbital altitude of
a s pacecraft b ecomes:
T ransf er T imeDAY S = T ransf er T imeSECONDS
86400
And the R ound–Trip Time is double t he T ransfer Time:
Round − T ripDAY S = 2(T ransf er T imeDAY S )
The Mission Duration is the R ound–Trip T ime added t o t he OnStation T ime.
M ission Duration = On − StationDAY S + Round − T ripDAY S
::
Page 91 of 176
S.T.E.M. F or the Classroom
Adventures i n O uter S pace
Orbits are circular a nd the transfer o rbit is an ellipse:
Image 3 1: Hohmann T ransfer Orbit D iagram
In the diagram above, green represents the lower circular orbital altitude and red represents the
higher circular orbital altitude. Yellow represents the elliptical transfer orbit from green to red (or
dashed yellow representing from red to green).
The first Δv rocket engine firing is done at the lowest point in the elliptical transfer orbit
(periapsis). This puts the spacecraft on the path in yellow. At the highest point in the elliptical
orbit (apoapsis), another rocket engine firing occurs, this time circularizing the orbit (in red). To
go h ome, simply r everse the p rocedure, u sing the p rinciple of reversibility of o rbits.
We will use as inputs the lower and higher orbital altitudes, as well as the OnStation Time,
which is the number of days the astronauts spend at the mission destination. To review, the Δv
Budget is found by adding the two Δv numbers together. The Round–Trip Time is twice the
Transfer t ime, and the M ission Duration is the O nStation T ime plus the R ound–Trip T ime.
Example
You are the Captain of a spacecraft that is currently in a Low Earth Orbit (LEO) at an orbital
altitude of 200 km. You need to increase your orbital altitude to 8,500 km so that you can deposit
a new satellite and bring back the old one. Your On–Station Time is 5 days. Find the change in
velocity, t ransfer time, R ound–Trip T ime, and the M ission Duration f or t his space m ission.
Page 92 o f 176
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
Downloadable PDF STEM Textbook
Discover the best professional documents and content resources in AnyFlip Document Base.
Search