presents
a High School S.T.E.M. Laboratory Textbook
Joe Maness
and
Richard Kerry Holtzin, Ph.D.
S.T.E.M. F or t he Classroom
presents
ADVENTURES I N O UTER SPACE
A High School S .T.E.M. L aboratory Textbook
_____________
Joe Maness
and
Richard Kerry H oltzin, P h.D.
On t he Front Cover:
An image that encapsulates all the concepts in this textbook. A Bigelow space station is depicted in Low Earth
Orbit with several Boeing crew capsules docked. Behind the space station is a Reaction Engines, Ltd. Skylon that
had departed Spaceport America and is now arriving to drop off cargo. Below the Skylon is the Virgin Galactic
SpaceShipTwo conducting a suborbital spaceflight. In the background is the immediate goal of any spacefaring
civilization: the Moon.
Image: Re–NewSpace Media
Copyright © 2 017 b y J OE M ANESS and R ICHARD KERRY H OLTZIN, P H.D.
Text c opyright b y J OE M ANESS and RICHARD KERRY HOLTZIN, P H.D.
All illustrations (where used) are the property of their respective artists and are protected by
copyright law.
First e dition p ublished January, 2017.
All R ights Reserved.
No portion of this book may be reproduced in whole or in part, by any means (with the exception
of short quotes for the purpose of review), without permission of the publisher. The author would
also a ppreciate citing this t ext i f s ome of the material i s u sed f or s uch a p urpose.
Cover: Adventures i n Outer S pace
Re–NewSpace Media ( labeled for reuse)
Printed in the United States o f A merica
Library of Congress C ataloging–in–Publication Data
JOE MANESS A ND R ICHARD KERRY HOLTZIN, P H.D.
S.T.E.M. F or t he Classroom p resents
Adventures i n O uter S pace
A High School S.T.E.M. L aboratory T extbook
First edition
Includes Table o f Contents
ISBN 9 –99–999999–9
TABLE O F C ONTENTS
PREFACE 1
S.T.E.M. E DUCATION 99
FALL S EMESTER – A EROSPACE 99
Unit 1: V ehicles
Chapter 1 : S uborbital Spaceflight – V irgin G alactic 99
Chapter 2 : Orbital Spaceflight – R eaction Engines, L td. 9 9
Unit 2: Destinations
Chapter 3 : Space S tation – B igelow A erospace 99
Chapter 4 : S paceport – S paceport America 99
SPRING SEMESTER – ASTRONAUTICS 99
Unit 3: Basic Astronautics
Chapter 5 : D elta V a nd T ransfer T ime – T he B oeing C ompany 99
Chapter 6 : S pacecraft Mass – T he B oeing Company 9 9
Unit 4: Advanced A stronautics
Chapter 7 : The Rocket E quation – T he B oeing Company 99
Chapter 8 : L unar Landing – T he B oeing Company 9 9
APPENDIX
Admin: G oogle Blogger Website D esign 99
Posts and Comments 99
Layout a nd Gadgets 99
Customizing 9 9
Captain’s Log: G oogle D ocs Engineering J ournal
Creating and u pdating the E ngineering J ournal 9 9
Embedding a P DF Engineering Journal 9 9
The A pp: G oogle S heets Spreadsheet Design 9 9
Open Source C ode 9 9
Layout 9 9
Embedding a G oogle S heets A pp 9 9
The App: A ppSheet M obile A pp Design
Open Source Code 9 9
Layout 9 9
Embedding a G oogle S heets A pp 99
Express Y ourself: G oogle Y ouTube V ideos
Creating a Video 99
Uploading a V ideo 9 9
Embedding a G oogle YouTube Video 9 9
Data C ollection: G oogle F orms F orm Design 99
Creating a Google F orm 9 9
Embedding a Google F orm 9 9
Stage F right: G oogle S lides P resentation o f S tudent W ork 9 9
The S cience Fair Setting 99
Videotaping a nd Uploading the P resentation 9 9
Embedding a Google Slides Presentation 99
FOR THE EDUCATOR
Lesson P lans 9 9
Teacher Presentations 9 9
Student Handouts 9 9
ANSWERS TO P ROBLEM S ETS 9 9
GLOSSARY 9 9
EQUATIONS A ND C ONSTANTS 99
IMAGE ATTRIBUTIONS 9 9
INDEX 99
The c hapters in t his textbook feature the innovative p roducts o f these
aerospace/astronautics/technology companies
S.T.E.M. F or the C lassroom
“Do not repeat the tactics which have gained you one victory, but let your methods be regulated
by the i nfinite variety o f circumstances.”
– S un Tzu
S.T.E.M. F or the Classroom
Adventures i n O uter S pace
PREFACE
Mathematics can be rather dull, especially in a classroom where students cannot tie together the
mathematics that they are learning to problems that involve the real world. Even if the students
do get to be exposed to real world problems, it is often something that students cannot really
relate to.
A train leaves NY traveling west at 100 mph. At the same time another train is traveling east
from LA g oing a t 8 0 mph. W hat is the c olor of the second t rain?
Students will often read word problems, and not really get the what the underlying mathematics
is all about. Students need to have something that they can get excited about so that they can
learn mathematics a t a deeper level.
Shortly after the creation of this S.T.E.M. ideal, a radical new thought began to emerge. The
story g oes something like t his:
...you take a biology class, you get a biology lab. You take chemistry? Here’s your chemistry lab.
Got S.T.E.M.? Then here you go with your S.T.E.M. lab. Got physics? Then you got a physics lab
too. Got a stronomy? w ell, t hen, h ere’s your astro...
Wait. You mean to tell me that there is no such thing as a S.T.E.M. lab? What? Really? Wouldn’t
modeling realworld data on realworld spacecraft get students to be a l ittle m ore interested in
learning S.T.E.M.? Why not? It’s not like there’s existing spacecraft designs that students can use
to model the realworld, right? Go tell that to Virgin Galactic, Reaction Engines, Ltd., Bigelow
Aerospace, Spaceport America, Boeing, S paceX, e t a l.
Of course, the choice of aerospace and astronautics for this lab textbook was purely arbitrary.
Other textbooks will focus on, say, an underwater adventure, complete with the science and
technology and engineering and mathematics used for submarines and undersea habitats. The
idea is t hat t he s tudent learns the same S.T.E.M. s kill set no matter w hich class i s taken.
That being said, this class is the lab that accompanies all seniorlevel classes. It allows students
to use S.T.E.M. in a fun and realworld fashion. The idea is that students l earn the theory in their
science and math classes and they a pply the theory in a S.T.E.M. lab. It really is that simple and
interesting!
Given the above, students will learn basic aerospace and astronautics as a way to delve deeper
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into mathematics, as well as science and technology and engineering. They will demonstrate
what they have learned by displaying their embedded slideshow presentations, embedded
spreadsheet space mission apps, embedded PDF Engineering Reports, and embedded YouTube
videos o f t heir p resentations o n a w ebsite t hat t hey c reate.
All of this sounds rather expensive. For instance, embedding frames in a website requires higher
level HTML and PHP programming. So what is the price of admission for all of this? The
answer is twofold: A) computers hooked to the Internet, and B) a free Google GMail account.
That’s it! Since most high schools already have a computer lab, Part A is really no problemo.
Since Google i s f ree, w ell...
All the software tools necessary to embed these slideshows, spreadsheets, PDF files, and
streaming video come free from Google Technology. Even the mobile app software is free,
provided that a Google GMail account exists. Therefore, our product is accessible to any student
at a ny S.E.S. l evel, which m eans the affluent a nd t he non–affluent h ave e qual a ccess. Nice!
Once the two parts have been met, students can then take virtual trips to any place their
imaginations will allow. The best part is that their journey (of the imagination) will be realistic
and doable, which makes things way more fun and interesting. With this textbook, and a little
determination, it allows students to fly realistic space missions, from suborbital flights, all the
way to a landing on the M oon!
Another plus for this class is that the student has created a Portfolio o f what they have learned in
their final year of high school in the form of a website. Moreover, they can put the link to their
website on t heir resume.
There are probably more advantages that I have failed to list within these pages. Still, I think you
get the point. Mathematics, especially higher math, like Algebra 2 and PreCalculus, can be
daunting to a high school student. But tell them that they’re going to outer space, and here’s the
science, technology, engineering, and the mathematics to get there, then watch what happens.
You’ll see it in their e yes.
So, there is no such t hing a s a S.T.E.M. l ab, huh?
Well, there is one n ow...
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ACKNOWLEDGEMENTS
We both met on a fine morning back in August 2012 when Dr. Rich (as his students
affectionately call him) was a substitute teacher for my high school. Dr. Rich had noticed my
flight jacket, and mentioned that he too was an enlisted AntiSubmarine Warfare (ASW) swabbie
(Navy enlisted personnel) like me, and that he once flew commercial airplanes for a living. I told
him about my background flying backseat ASW jets off of carriers, and the ultralight aircraft that
I once owned and piloted. But the most intriguing of all our common interests was our love for
human exploration of space and the society that it could spawn, and our belief in education as the
absolute backbone of our s ociety.
Another mutual advantage we shared was the fact that we weren’t in this for the money. Thus, it
became a labor of love for both of us. The idea of students receiving this type of education at the
high school level is what motivated us through the tough times. Indeed, here is proof that we
could live in a Star Trek society where people work for growth and learning and not for personal
wealth a nd gain.
So it was the case that we would meet for breakfast on a Saturday or a Sunday, discussing the
countless different aspects of the journey that we were on. Dr. Rich always kept the process
moving forward; always steering a true heading. It was certainly a long and winding road to get
to this point, but I think that it was well worth the slings and arrows that we both had to endure
to get here. Education can be a tough business, especially when the goal is exciting young people
enough t o d isplay even a m ild interest i n S .T.E.M.
I believe that w e have produced a f ine piece o f educational m aterial.
Thanks, Dr. Rich!
::
Of course, this entire textbook could not have truly been called “real–world” unless it was
flight–tested first. So my eternal gratitude to the classes at The Learning Community Charter
School (TLCCS) A lgebra 2 and P recalculus classes.
The students used their knowledge of high school math to try and understand complicated
aerospace and astronautics concepts.
So three cheers for the students of TLCCS. Without all of your courage and dedication in the
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face of everchanging space projects from your (slightly) deranged teacher, you endured and
persevered. We salute y ou in t his, your finest hour.
Thanks, y ou w onderful t est p ilots e r s tudents!
::
Finally, thanks to all my friends and family who had to endure my ups and downs during the
course of developing this book (4 years! Yikes!). I humbly apologize, and I hope that we’re all
still c ool.
Thanks!
Joe M aness
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SCIENCE T ECHNOLOGY
ENGINEERING MATHEMATICS
...but m y friends c all me S.T.E.M.
Prerequisites
There are only two minimum conditions that must be met before a student is able to handle this
lab. T he student m ust:
1. be a High S chool Junior (HSJ)
2. have p assed high school Algebra 1 and G eometry.
Of course, it is always left up to the professionalism of the teacher to grant any waivers on a
one–to–one basis.
Image 01: S tudents a nd t heir t eacher taking the S .T.E.M. Lab waaaaaay t oo s eriously...
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Narrative
This textbook deals with various aspects of space mission design. It is used as cover to expose
HSS to applied mathematics disguised as fun projects they complete over the course of two
semesters. Unwittingly, these students then become stronger in other fields of study as their
selfconfidence g rows. Students w ill b e r equired t o u se the f ollowing f ree s oftware in t his class:
● Research Google S earch
● Email a nd Contacts: Google G Mail
● Time Management: Google C alendar
● Website Admin: Google B logger
● Word P rocessor: Google D ocs converted t o P DF f ormat
● Spreadsheet: Google S heets
● Mobile A pp D evelopment: AppSheet A pp
● Slideshow P resentation: Google S lides
● Images: Google D rawing
● Information Collection: Google F orms
● Streaming V ideo: Google Y ouTube
● Laptop Computer (optional): Google C hromebook
Since most, if not all, HSS already know most of the other version of these software tools, the
learning curve should be fairly flat. Students will also use Social Media in their effort to show off
what they have u ploaded to the I nternet.
::
Organization a nd Pacing
It is recommended that t eachers follow the s chedule below f or each chapter:
CHAPTER
New Material 5 days
Website Development 4 days
Spreadsheet A pp D evelopment 3 d ays
Mobile A pp Development 5 d ays
Presentation Development 3 days
Chapter Exam 1 day
P resentations 1 d ay .
Total duration for each c hapter 22 d ays (4.5 w eeks)
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Lesson Overview
Students first learn the basics of aerospace and astronautics using pencil, paper, and scientific
calculator. They then use what they have learned to create a space mission app designed
according to t he E ngineering D esign P rocess that will b e used for r ealworld s pacecraft.
They will use spreadsheet software to create their apps. Eight apps will be developed over the
course of eight S.T.E.M. projects, with each project dealing with different aspects of space
mission design.
Students then advance to developing mobile apps that they can install on their smart phones.
Eight m obile apps w ill b e d esigned corresponding t o t he eight chapters of this t extbook.
The assigned space mission will include eight (8) space vehicles or satellites that are named after
famous astronauts. Students will research and write a short biography (one slide) about these
heroic i ndividuals, one for e ach o f t he eight projects.
::
Learning O bjectives
Evaluation
● Interpret data r elated to a erospace a nd astronautics.
● Select an o ptimum d esign from many d esign options t o solve t echnological p roblems.
Synthesis
● Explain the principles of spaceflight i n mathematical a nd p hysical terms.
● Integrate m athematics and astronautics in t he engineering design process.
Analysis
● Analyze the physical principles of various aspects for human spaceflight such as
parabolic space flights, shuttle orbital payload capabilities, space station configurations,
unpowered glide landing configurations, change in orbital velocity (delta v), weight of a
crew capsule, and amount of propellant used, then relate t hese to a space mission d esign.
● Use mathematics to calculate parabolic space flights, shuttle orbital payload capabilities,
space station configurations, unpowered glide landing configurations, change in orbital
velocity (delta v), weight of a crew capsule, and amount of propellant used for a space
mission.
● Use financial a nalysis to d etermine i f i t is possible t o make a profit from a space venture.
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Application
● Use the Engineering Design Process to construct a realworld space mission app that is
constrained by c ertain a stronautics f actors.
Comprehension
● Define constraints t o t he realworld model.
● Explain how s olutions to the p roblem address the specific requirement.
Knowledge
● Explain the relationships of the principles of aerospace and astronautics to the concept of
parabolic spaceflight, orbital payload, space station configuration, landing configuration,
delta v , weight, and p ropellant.
● Demonstrate how their space mission design app addresses the requirements of the
parabolic spaceflight, orbital payload, space station configuration, landing configuration,
delta v , w eight, a nd p ropellant.
Science A s I nquiry
● Identify questions and concepts t hat guide s cientific i nvestigations.
● Design and c onduct scientific i nvestigations.
● Use t echnology and m athematics to i mprove i nvestigations and c ommunications.
● Formulate and revise s cientific e xplanations and models using l ogic and e vidence.
● Communicate a nd defend a scientific argument.
Physical Science
● Use mathematics a nd l ogic t o e xplain s cientific p rinciples.
● Look up and u se a stronomical a nd a stronautical c onstants.
Science and T echnology
● Identify a p roblem or design an o pportunity.
● Propose d esigns and c hoose b etween alternative s olutions.
● Implement a p roposed s olution.
● Evaluate a solution and i ts c onsequences.
● Communicate t he problem, p rocess, a nd s olution.
::
Time F rame
Two chapters are to be completed every quarter, or halfsemester. This means that there will be
four c hapters covered per semester, o r eight c hapters in o ne school y ear.
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The e ntire course, t herefore, s hould h ave the following pacing:
Chapter 1 : 4.5 weeks
Chapter 2 : 4.5 w eeks
Unit 1 : 9 .0 weeks
Chapter 3: 4 .5 weeks
Chapter 4: 4.5 weeks
Unit 2 : 9.0 w eeks
FALL SEMESTER: 18.0 w eeks
Chapter 5 : 4 .5 weeks
Chapter 6 : 4.5 weeks
Unit 3 : 9 .0 weeks
Chapter 7 : 4 .5 w eeks
Chapter 8: 4 .5 w eeks
Unit 4: 9.0 w eeks
SPRING SEMESTER: 18.0 weeks
This curriculum gives the students a little over four weeks to research, complete, and present
each mission design. During this time, students complete the calculations, update the
spreadsheet, finish the website, finish the slideshow presentation, and practice their
presentations.
S.T.E.M. S cenario
Each HSS is assigned different aerospace and astronautics missions that will be designed over
the course of the school year. To make learning an adventure, even creative for a change, the
student could create a callsign for themselves. Students pretend to be Space Mission Design
Cloud Engineers that focuses on the "software as a service" aspect of cloud computing (others
include "platform as a service", "infrastructure as a service", and "network as a service"). They
are employed t o build space apps by an aerospace/astronautics company.
Q: H ow many C loud E ngineers does i t take t o c hange a l ightbulb?
A: Z ero. It's a h ardware p roblem.
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For example, Virgin Galactic has announced a contract for an app that will calculate certain
spaceflight milestones. Various companies compete for the contract by having their engineers
(students) build a prototype Space Mission Design App (SMDA). The winning SMDA design
will be “ bought” b y V irgin Galactic.
The students will create and maintain a website to house the SMDA. A working prototype that
anyone can use will also be included in the website. They will write a report of the design
process for the Engineering PostDevelopment Analysis. They will present a progress slideshow
report of their software prototype to the rest of the company during four quarterly company
meetings.
::
The Presentation
As the due date of the presentations draws near, the entire class will have the opportunity to learn
the final lesson of these projects: dealing with a deadline, and its corollary time management.
Students will certainly get to experience the pressure of the presentation, in the same way an
actor g ets t he jitters before g oing on s tage.
The presentation takes on the form of a “Science Fair,” where each student stands at a separate
table next to a computer that is displaying their website. As each guest walks up to student, they
make their presentation. The HSS should be encouraged to dress professionally and to practice
their presentations beforehand. The presentation should take between two and three minutes,
unless there are a lot of questions from the guests. Students will navigate through the website,
discussing the project development, displaying the SMDA, and demonstrating his or her working
model.
It is suggested that other classes be allowed to walk through the class, so that the young’uns can
see what they get to do some day. Posters about this event can be made by the students and hung
at various locations around the school. Make sure the students invite their parents too! Of course,
the event is incomplete without the Principal being there as well. A call to the local press about a
feelgood high school education story couldn't hurt either. All of this creates an atmosphere of a
special event, which, by the way, it really is. Namely, students get to experience another way of
correlating learning with doing something fun, the parents get to beam at their child's brilliance,
and t he class gets to l ook good on t he 6 o'clock news. It's a w inning situation for e veryone.
Now t hat's t he w ay t o learn science and technology a nd engineering and mathematics!
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FALL SEMESTER
AEROSPACE
Unit 1: Vehicles
Chapter 1: Suborbital S paceflight 13
Chapter 2 : O rbital Spaceflight 2 5
Unit 2: D estinations
Chapter 3: S pace Station 3 9
Chapter 4: Spaceport 51
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Chapter 1: Suborbital S paceflight
1.01 Narrative 13
1.02 V ocabulary 1 6
1.03 A nalysis 1 6
1.04 Guided Practice 9 9
1.05 Cross Curricula Activities 99
1.06 S uborbital M ission Design W ebsite D evelopment 99
1.07 S uborbital Mission D esign Spreadsheet App D evelopment 9 9
1.08 Suborbital M ission Design M obile A pp Development 30
1.09 Suborbital M ission Design Presentation Development 9 9
1.10 Chapter Test 3 2
::
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1. S paceliner Suborbital S paceflight
1.01 N arrative
In this, the first of four aerospacebased
S.T.E.M. lessons, students will calculate
various Virgin Galactic S paceShipTwo
(SS2) spaceflight parameters and
milestones, create an app, and write a
report a bout it.
Time Frame
4.5 w eeks
Aerospace Problems
Maximum A ltitude
Time Weightless
Time i n S pace
Spaceflight Duration
Mathematics U sed
Quadratic Equations
Science T opics
Physics, A erospace
Activating Previous L earning
Basic Algebra
Scientific C alculator
Image 0 2: V irgin G alactic S paceliner Cover
Essential Questions
● Who a re the pioneers o f s uborbital s paceflight?
● What i s the altitude a t rocket burnout of a suborbital spacecraft?
● What i s the maximum h eight o f a suborbital s pacecraft?
● Where d oes s pace a ctually b egin?
● When was t he first COMMERCIAL parabolic s paceflight?
● How c an I b e weightless i f I a m s till increasing my altitude?
● Wait. I have to do science, t echnology, e ngineering, a nd math? All at the same time?
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This l esson i s powered by E8 :
1. Engage
○ Lesson O bjectives
○ Lesson G oals
○ Lesson O rganization
2. Explore
○ The Quadratic Equation
○ The Q uadratic Formula
○ The Parabola and its Components a nd Definitions
○ Additional Terms a nd D efinitions
3. Explain
○ The Vertex
○ The Vertex a s a M aximum
○ Mission Duration Equation
4. Elaborate
○ Other S uborbital Spacecraft E xamples
5. Exercise
○ Suborbital S pace M ission Parameters
○ Suborbital Space M ission Design Scenario
6. Engineer
○ The Engineering D esign P rocess
○ SMDA S paceflight P lan
○ Designing a P rototype
○ SMDA S oftware
7. Express
○ Displaying the S MDC
○ Progress R eport
8. Evaluate
○ Post Engineering Assessment
Lesson O verview
Students first learn the basics of suborbital spaceflight 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.
They will also create a document of their experiences engineering the SMDA and presenting
their f indings t o the rest o f t he class.
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Constants
● Standard G ravity ( m/s2 )
Input
● Rocket B urnout Time (min M ET)
● Rocket Burnout Altitude (ft MSL)
● Rocket Burnout Velocity (mph)
Output
● Maximum A ltitude ( m MSL)
● Time S pent Weightless ( min)
● Time Spent I n Space (min)
● Spaceflight Duration (min)
Weightless P hase
1. Begin Weightlessness
2. Begin S paceflight
3. Maximum A ltitude
4. End S paceflight
5. End Weightlessness
Spaceflight D uration
1. Carrier P hase
2. Boost Phase
3. Weightless Phase
4. Reentry P hase
5. Glide P hase
1.02 V ocabulary
Begin Spaceflight Begin W eightlessness
Drop
Boost P hase Glide P hase
Mission E lapsed T ime ( MET)
Carrier Phase Duration Rocket B urnout
Suborbital S paceflight
End Spaceflight End Weightlessness
Maximum Altitude Mean S ea L evel (MSL)
Reentry Interface Reentry Phase
Space I nterface SpaceShipTwo (SS2)
White Knight 2 Weightless Phase
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Image 0 3: S paceShipTwo (middle) mated to the mothership.
1.03 A nalysis
A suborbital spacecraft, such as SS2, after a Drop from the White Knight 2 carrier aircraft,
follows a flight profile that takes the shape of a parabola.. A parabola can be described with a
quadratic e quation, s o t hat is what we will use.
The SS2 follows a similar trajectory that a baseball thrown to another baseball player follows. As
all baseball players are aware, a baseball is never thrown in a straight line; rather it is thrown
slightly u pward. A s a r esult, t he p ath the b aseball follows i s curved (parabolic).
If the same baseball is thrown straight into the air, it will continue moving upward after it leaves
the ball player's hand. The baseball at that point has an initial thrust to it, and the moment the ball
is released it immediately begins to s low down. The ball will eventually reach a maximum
height, where the speed becomes zero, and then drop back down to Earth (in this case, into the
player's glove). The ball increased speed on the way down and arrived at the glove with the same
energy that it l eft with.
Note: the moment the player releases the ball, the ball is weightless. Weight returns when the ball
is c atched.
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That baseball (spacecraft) follows a nice parabolic curve and can be described by a quadratic
equation.
Virgin Galactic’s SpaceShipTwo is poised to go into space in the near future. Many people have
already paid for their ticket, and will be flying into space as soon as the spaceship is ready. You
are asked to b uild the p rototype space mission a pp for your c ompany.
Given t he initial conditions a s input, the a pp should display t he following:
● Rocket B urnout T ime ( TimeR BO )
● Initial Velocity ( InitVel )
● Initial Height (I nitHt)
1. How high into space you will go [Maximum A ltitude ( m)]
2. How long you will be w eightless [Time S pent Weightless ( min)]
3. How l ong y ou w ill be i n s pace [Time Spent In Space ( min)]
4. How l ong y our space flight w ill be [ Spaceflight D uration ( hr:min)]
5. A graph o f t he weightless p eriod [ Time (min) vs. A ltitude (m)]
Image 04 : SpaceShipTwo S paceflight Profile Graph
The graph represents a typical weightless period spaceflight profile for S paceShipTwo . The
horizontal axis of the graph represents time (in seconds), and the vertical axis represents height
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(in m eters). Space i s d efined as b eginning at 1 00,000 m.
As you can see from the graph, the spaceflight takes the shape of an inverted parabola. This
means t hat w e can use a Quadratic Equation.
To find the maximum height and the time spent weightless, first determine the time component
of t he vertex, a.k.a, the a xis o f symmetry .
To find t he t ime spent in space, f ind t he t ime t hat t he s pacecraft e ntered space.
But f irst, t he Quadratic E quation i s:
h(t) = − 1 g0 t2 + v0 t + h0
2
where,
● g 0 = S tandard Gravity (9.80665 m /s 2)
● t = t ime (s)
● v0 = i nitial v elocity of the spacecraft (m/s)
● h 0 = initial h eight of the spacecraft ( m M SL)
● h(t) = h eight of t he spacecraft a t t ime t ( m M SL)
Therefore t he t ime c omponent o f the vertex i s:
vertext = −v01 = −v0 = v0
2(− 2 g 0) −g 0 g0
The time spent weightless i s t wice v ertext , t aking advantage o f the s ymmetry o f a parabola.
T imeweightless = 2(vertext)
To f ind t he maximum h eight ( vertexh ), j ust plug vertext into t he Quadratic Equation.
vertexh = h(vertext) = − 1 g0 (vertext)2 + v0 (vertext ) + h0
2
To find the time the spacecraft enters space, let h = 100,000, make the Quadratic Equation equal
to z ero, then u se t he Quadratic F ormula:
100, 000 = − 1 g0 t2 + v0 t + h0
2
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0 = − 1 g0 t2 + v0 t + h0 − 100, 000
2
0 = − 1 g0 t2 + v0 t + h1
2
where,
● h 1 = h eight a t s pace = h 0 100,000
Now we use t he Quadratic Formula t o s olve for t he t ime you enter s pace:
√spacet = −v0 + vo2 − 4(− 1 g 0 )(h1)
2
2(− 1 g 0)
2
√ = vo2 + 2 g 0 h 1
−v0 + −g 0
√ = v0 − vo2 + 2 g 0 h 1
g0
Once you have the time you enter space, subtract it from the vertext , double it (again, because of
symmetry), and we have the T ime S pent i n S pace.
T imespace = 2(vertext − spacet)
To find the Mission Elapsed Time for the five milestones of the Weightless Phase use the
following e quations:
W eightlessBegin = T imeRBO
SpaceBegin = T imeRBO + spacet
Altitudemax = T imeRBO + vertext
SpaceEnd = T imeRBO + 2(spacet)
W eightlessEnd = T imeRBO + 2(vertext)
We c an now tackle the s paceflight duration c alculations.
::
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Given:
● Boost Phase = 70 s = 1.17 m in
● Reentry P hase = 3 .50 m in
● Glide P hase = 2 5.00 min
Then
Carrier P hase = T imeRBO − Boost P hase
and
DurationSpaceflight = Carrier + Boost + T imeWeightless + Reentry + Glide
We c an n ow d etermine t he entire flight p rofile o f S paceShipTwo.
Example
Suppose we h ave a n input of
● TimeR BO = 110 m in
● InitHt = 135,000 f t MSL
● InitVel = 2 ,600 m ph
What i s the Time S pent W eightless, t he M aximum Height a chieved, t he Time S pent I n Space,
and t he Time S pent on S paceflight aboard S paceShipTwo?
First, l et’s c onvert the input into S.I. Units:
v0 = 2,600 mi 1,609 m hr = 1, 162 mps
hr mi 3,600 s
h0 = 135,000 f t m = 41, 148 m M SL
1 3.28 f
t
So, v0
g0
vertext = = 1162 = 118.49 s
9.80665
The Time Spent Weightless is:
T imeweightless = 2(vertext)
= 2(118.49)
= 236.98 s
= 3.95 min
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and the m aximum a ltitude is:
vertexh = f (vertext) = − 1 g0 (vertext)2 + v0 (vertext ) + h0
2
= − 1 (9.80665)(118.49)2 + 1162(118.49) + 41148
2
= 110, 027 m M SL
Finding h 1 ,
h1 = h0 − 100000 = − 58, 852 m
we can use it to find t he t ime y ou e nter s pace:
√ spacet = v0 − vo2 + 2 g 0 h1
g0
√ = 1162 − (1162)2 + 2(9.80665)(−58852)
9.80665
= 73 s
Once we know when w e enter s pace w e can calculate the Time Spent in Space:
T imespace = 2(vertext − spacet)
= 2(118.49 − 73) s
= 90.98 s
= 1.52 min
We now c alculate the o ther mission m ilestones a nd t he t otal mission duration:
Carrier P hase = T imeRBO − Boost P hase
= 110 min − 1.17 min
= 108.83 min
and
DurationSpaceflight = Carrier + Boost + T imeWeightless + Reentry + Glide
= (108.83 + 1.17 + 3.95 + 3.50 + 25.00) min
= 142.45 min
= 2 hrs 22.45 min
::
So, given an initial velocity at Rocket Burnout Time of 110 min going 2,600 mph , with an initial
height o f 1 35,000 ft M SL , we c an m ake t he f ollowing c onclusions:
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1. Time Spent Weightless i s 3 .95 min
2. Maximum Height achieved is 110,027 m M SL
3. Time S pent In S pace is 1 .51 m in
4. Time S pent o n S paceflight aboard SpaceShipTwo i s 2 hr 2 2.45 min
Therefore, out of an almost two and a half hour flight, the passengers spend less than four
minutes weightless, and less than two minutes in space. If each ticket costs $250,000, that comes
out to about $2,747 for each second spent in space! The time spent in space is irrelevant anyway;
that the passengers w ent into s pace is t he r eal s tory.
::
1.04 Guided Practice
You are an spaceliner pilot responsible for the passengers flying into space. Use the
SpaceShipTwo Equation to calculate e ach suborbital altitude.
Spaceflight 1
● Rocket B urnout: 1 10s MET
● Burnout A ltitude: 1 35,000 ft MSL
● Burnout Speed: 2 ,600 mph
Maximum Altitude = _ _________ m M SL Astronaut? Y N
Spaceflight 2
● Rocket B urnout: 1 25s M ET
● Burnout Altitude: 1 30,000 ft M SL
● Burnout Speed: 2 ,400 mph
Maximum Altitude = __________ m MSL Astronaut? Y N
Spaceflight 3
● Rocket Burnout: 100s M ET
● Burnout A ltitude: 1 40,000 f t M SL
● Burnout S peed: 2,700 m ph
Maximum Altitude = __________ m M SL Astronaut? Y N
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1.05 C ross Curricula Activities
The arts must be included with any c urriculum.
ARTWORK
● Find images o f t he V irgin Galactic S paceShipTwo s paceplane o n t he Internet.
● Use t he images that you h ave r esearched to draw a p icture o f the s paceplane r ocketing
into s pace.
R.A.F.T. W RITING
● Ro le: T eacher
● Au dience: M iddle S chool s tudents
● Fo rmat: Five paragraph essay
● T opic: The X–15. Who were some of the astronauts that flew the missions? Did any of
the pilots fly into space? What was unique about their missions? What was in common
with all the missions? How does an X–15 suborbital space mission differ from the space
mission presented in this textbook? How are they the same? Why even bother to fly a
suborbital s paceflight a nyway?
DISCUSSION T OPICS
● Was the mathematics i n this c hapter d ifficult to understand?
● The authors c onclude t hat f lying i nto s pace is worth i t, e ven if it’s o nly for a s hort w hile.
Do you a gree with t he authors? Why o r W hy n ot?
● What w ould it be l ike to fly a board a s paceship that takes off like an o rdinary airliner?
Would y ou like t o fly o n t he S paceShipTwo s paceplane? W hy o r why n ot?
1.06 S uborbital Space Mission D esign W ebsite
We now p roceed to create the suborbital w ebsite t hat includes the e ngineering logs a nd the app
embedded in a w ebpage.
Insert Text H ere
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Insert T ext H ere
1.07 Suborbital Space Mission Design S preadsheet A pp
Given the above information, we can use a spreadsheet to enter equations and data to create a
Space M ission Design A pp (SMDA).
The S.T.E.M. for t he Classroom/Google A pp i s broken down into f our (4) parts:
1. Input/Output Interface
2. Graph
3. Constants
4. Calculations
The App c an now be developed.
Sample G oogle S heets A pp D esign O pen S ource Code
Once t he c ells h ave been named referencing c ells is e asy.
● CALCULATIONS
○ VertexTime=v0/g0
○ TimeWeightless=2*VertexTime
○ MaxAlt=0.5*g0*VertexTime^2+v0*VertexTime+h0
○ h1=h0Space
○ SpaceTime=(v0SQRT(v0^2+2*g0*h1))/g0
○ TimeInSpace=2*(VertexTime SpaceTime)
● GRAPHING
○ BeginWt=RBO
○ BeginSpace=RBO+TimeSpace
○ MaxAlt=RBO+VertexTime
○ EndSpace=RBO+2*TimeSpace
○ EndWt=RBO+2*VertexTime
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I NSERT CODE HERE
I NSERT C ODE HERE
I NSERT CODE H ERE
INSERT CODE H ERE
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Sample Google S heets A pp D esign
Image 05: S uborbital S pace Mission Design Spreadsheet A pp
::
1.08 Suborbital S pace Mission Design Mobile A pp
Sample A ppSheet Mobile App D esign O pen S ource C ode
Once the Google S preadsheet has b een c ompleted, i t c an b e u sed t o help c reate t he m obile a pp.
I NSERT C ODE HERE
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I NSERT CODE HERE
Sample A ppSheet Mobile A pp D esign
Image 0 6: S uborbital S pace M ission D esign Mobile A pp
INSERT I MAGES H ERE
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1.09 Suborbital M ission Design Presentation D evelopment
INSERT T EXT H ERE
INSERT TEXT H ERE
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INSERT TEXT H ERE
INSERT T EXT H ERE
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1.10 Chapter Test
I. VOCABULARY
Match the aerospace term with its d efinition.
1. End S paceflight A. The moment a rocket engine shuts itself off, where the
spacecraft continues upward o n i ts o wn m omentum.
2 . M ission E lapsed Time B. T he spacecraft that is dropped from W hite Knight 2. After
rocket burnout, t he s pacecraft c oasts up t o s pace a nd back.
3 . R ocket B urnout C. The third of six phases in a parabolic spaceflight, where the
spacecraft a nd its o ccupants experience w eightlessness.
4 . S paceShipTwo D. The moment a spacecraft exits from space. The spacecraft
returns to the atmospheric environment.
5. W eightless Phase E. Time since the b eginning o f t he spaceflight.
II. M ULTIPLE C HOICE
Circle t he correct a nswer.
6. The Q uadratic Equation describing the parabolic flight p rofile of a Virgin G alactic suborbital
spaceflight h as a l eading c oefficient t hat is l ess than zero.
A. True B. False
7. After r eaching m aximum altitude, weight returns a nd the V irgin Galactic passengers are no
longer weightless.
A. T rue B. F alse
8 . If V ertext = 1.75 m in, then the T ime Spent Weightless is
A. 1.75 m in B. 3 .50 min C. 5.25 min D. N one
9 . Y ou reach the m aximum a ltitude 30 s econds after crossing i nto space. How l ong w ill y ou be
in s pace?
A. 30 sec B. 6 0 s ec C. 9 0 s ec D. N one.
10. A V irgin Galactic s uborbital spacecraft is going 1 ,100 mps at t he moment o f R ocket B urnout.
How long will it take t o c oast up to t he m aximum altitude?
A. 56.12 sec B. 1 12.24 sec C. 224.48 s ec D. 336.72 sec
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III. C ALCULATIONS
A V irgin Galactic s uborbital spacecraft h as a n initial v elocity a t R ocket Burnout Time of 1 08
minutes, going 2 ,550 mph, w ith a n i nitial h eight o f 1 40,000 f eet M SL.
11. How l ong does it t ake to r each maximum a ltitude after rocket burnout?
12. W hat is the m aximum a ltitude o f this spaceflight?
13. H ow long d oes i t t ake t o r each space after r ocket b urnout?
14. How l ong w ere t he V irgin G alactic p assengers w eightless?
15. How l ong w ere the Virgin Galactic passengers i n space?
16. H ow l ong w as t he C arrier P hase o f t he s uborbital s paceflight?
17. How long w as t he spaceflight?
18. W hat p ercent o f t he suborbital spaceflight w as spent d uring the Weightless Phase?
19. What percent o f the s uborbital s paceflight was spent i n s pace?
20. What percent of t he s uborbital s paceflight was not spent i n space o r during t he W eightless
Phase?
IV. WRITING
Write a one paragraph essay o n the t opics below.
21. Explain why the leading coefficient of t he q uadratic e quation describing t he parabolic
spaceflight profile of a V irgin Galactic suborbital s pacecraft is n egative.
22. E xplain why the total t ime weightless can be c alculated by doubling t he time i t takes to r each
the v ertex o f t he parabola o f a V irgin Galactic s uborbital s paceflight.
23. Explain why p assengers f eel weightless even t hough t he s pacecraft is coasting to a maximum
altitude i n t he U P direction.
24. Describe t he s tepbystep procedure t o calculating t he m aximum a ltitude reached b y a Virgin
Galactic suborbital spacecraft given the time that the m aximum altitude occurred.
25. W rite a s hort story about w hat it would feel l ike t o f loat weightlessly inside of S paceShipTwo
while g azing a t t he c urvature o f t he E arth as i t flies a parabolic spaceflight profile.
END O F C HAPTER 1 E XAM
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Chapter 2: Orbital Spaceflight
2.01 Narrative 99
2.02 Vocabulary 99
2.03 A nalysis 99
2.04 G uided P ractice 9 9
2.05 C ross C urricula Activities 99
2.06 L aunch P ayload Design Website Development 99
2.07 L aunch P ayload D esign S preadsheet App Development 99
2.08 Launch P ayload D esign Mobile A pp D evelopment 9 9
2.09 L aunch P ayload Design Presentation Development 9 9
2.10 Chapter T est 99
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2. O rbital Spaceflight
2.01 Narrative
In this, the second of four aerospace–based
S.T.E.M. projects, students will calculate the
payload capacity of the R.E.L. Skylon
spaceliner. Students will use the launch site
latitude to determine the mass of an orbiting
payload.
Time Frame
4.5 w eeks
Aerospace P roblems
Orbital Inclination
Orbital A ltitude
Payload M ass
Mathematics U sed
Polynomial E quations
Science T opics
Physics, Aerospace
Activating Previous Learning
Basic Algebra
Image 07: R .E.L. S kylon Spaceliner C over
Essential Questions
● Who a re the pioneers o f spaceliner technology?
● What is the O rbital Inclination of a s pacecraft?
● Where i s t he payload b ay o f t he R.E.L. Skylon located?
● When will be t he first f light o f the Skylon spaceplane?
● Why do people want t o f ly p ayload i nto o rbit o n a spaceliner?
● How does t he l atitude o f the L aunch S ite e ffect an orbital payload?
● How does t he d esired o rbital altitude e ffect a n o rbital p ayload?
● Wait. I h ave to d o science, technology, e ngineering, a nd m ath, a ll a t the same time?
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This l esson is powered b y E8 :
1. Engage
○ Lesson Objectives
○ Lesson Goals
○ Lesson Organization
2. Explore
○ The Quadratic E quation
○ The L inear Equation
○ The A ltitudePayload L ine a nd its C omponents and D efinitions
○ Additional Terms and D efinitions
3. Explain
○ Orbital Inclination
○ Orbital Altitude v s. Payload Mass
○ Payload Mass v s. O rbital Altitude
4. Elaborate
○ Other Orbital S pacecraft Examples
5. Exercise
○ Orbital S pace M ission P arameters
○ Orbital Space Mission D esign Scenario
6. Engineer
○ The Engineering D esign Process
○ SMDA Spaceflight P lan
○ Designing a P rototype
○ SMDA S oftware
7. Express
○ Displaying the S MDC
○ Progress R eport
8. Evaluate
○ Post E ngineering Assessment
::
Lesson O verview
Students first learn the basics of spaceflight launch payload using pencil, paper, and scientific
calculator. They 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.
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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 their findings t o the r est of the class.
Constants
● (none)
Input
● Launch S ite Latitude ( deg)
● Payload M ass (lbs)
● Orbital A ltitude ( mi)
Output
● Payload Mass (kg)
○ At Latitude (km)
○ To I.S.S. ( km)
○ To Polar O rbit (km)
● Orbital A ltitude (km)
○ At Latitude (kg)
○ To I .S.S. (kg)
○ To Polar O rbit (kg)
::
2.02 Vocabulary
International S pace S tation Latitude Launch Site
Launch Site Latitude Orbital Altitude Orbital I nclination
Payload Payload M ass Polar O rbit
SABRE Skylon Spaceliner
Spaceplane
::
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Image 08: Cross s ection d iagram of the Synergetic A ir Breathing R ocket E ngine (SABRE)
2.03 A nalysis
To determine the mass and orbital altitude of a spacecraft climbing into earth orbit, we need
information on the space plane's capabilities at various launch latitudes. Fortunately, R.E.L.
provides u s w ith exactly what we need.
Image 09: P ayload–Altitude graph f or a n equatorial l aunch site
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Image 1 0: Payload–Altitude graph f or a 15o l aunch site latitude
Image 11: P ayload–Altitude Graph for a 30 o l aunch site latitude
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Image 1 2: Payload–Altitude Graph f or a 45 o L aunch Site latitude
Image 1 3: Payload–Altitude Graph for a 6 0o Launch Site latitude
::
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Using these graphs, we can determine the general formula for each of these lines. So, let's make a
couple of tables, s hall w e?
We will concentrate on the Launch Site Latitude equal to the Orbital Inclination. For the Launch
Site Latitude of 0 o , we will look for the graph at 250 km for the Orbital Inclination of 0 o . For the
15o graph, we will look at the 250 km point on the 15 o Orbital Inclination line. This process
continues for e ach graph:
250 KM 800 KM
0o 15,500 kg 0 o 11,000 k g
15o 15,250 k g 15o 10,750 k g
30o 14,500 kg 30 o 10,000 kg
45 o 13,250 kg 45o 8,750 kg
60 o 11,750 kg 60o 7 ,000 k g
Now we can analyse the tables to see what kind of equation that we have. We can use the old
trick of subtracting the dependent variables (absolute value) to determine the degree of the
polynomial equation. If all the subtractions keep coming up with the same number it is a linear
(degree 1) polynomial. If after 2 subtractions we get a constant, then it is a quadratic (degree 2)
polynomial. If 3 , then a cubic (degree 3 ), etc. L et's s ee w hat w e get for the f irst table:
15,500
15,250 => |15,500 1 5,250| = 2 50
14,500 = > |15,250 1 4,500| = 750 => | 250 750| = 500
13,250 = > |14,500 13,250| = 1 ,250 = > | 750 1 ,250| = 500
11,750 = > | 13,250 11,750| = 1,750 => |1,250 1,750| = 5 00
So we get a constant after two iterations. Therefore, we are dealing with a second degree
polynomial, o r a q uadratic equation.
y = ax2 + bx + c
Writing t he quadratic i n aerospace form, the g eneral equation b ecomes:
AtLatitudeP ayloadALT = aDEG 2 + bDEG + P ayload0
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where
● AtLatitudePayload ALT = Mass of t he orbital c argo h eaded to a c ertain altitude i n space
● a = C onstant
● DEG = Orbital Inclination of Payload
● b = C onstant
● Payload 0 = Initial P ayload
Since the i nitial m ass of t he p ayload i s i rrelevant, w e can zero o ut b :
AtLatitudeP ayloadALT = aDEG 2 + P ayload0
Using the table of data for a 250 km orbital altitude, we can calculate Payload 0 by plugging in
DEG = 0 o and Payload2 50 = 1 5,500:
AtLatitudeP ayload250 = aDEG 2 + 15, 500
We can then easily calculate a by using the table (again) and plugging DEG = 15 o and
AtLatitudePayload 250 = 15,250:
15, 250 = a(15)2 + 15, 500
− 1.11 = a
And so:
AtLatitudeP ayload250 = − 1.11DEG 2 + 15, 500
We now have the equation that we need to determine the payload capability
(AtLatitudePayload ALT) depending on the latitude of the launch site which is equal to the orbital
inclination ( DEG) for a 2 50 k m O rbital Altitude.
The other p olynomial e quation c an be d etermined using the s ame technique on the 800 k m table:
AtLatitudeP ayload800 = − 1.11DEG 2 + 11, 000
We now have the equation that we need to determine the payload capability
(AtLatitudePayload ALT) depending on the latitude of the launch site which equals the orbital
inclination (DEG), t his t ime for an 8 00 km O rbital A ltitude.
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We c an now determine t he t wo p oints n eeded t o d raw the graph of the l inear e quation for t he
payload.
Example
An R.E.L. Skylon is conducting spaceflight operations from Spaceport America. A customer has
a satellite that needs to be placed in an orbital altitude of 490 miles. The Orbital Inclination is
irrelevant. W hat i s the m aximum m ass o f the s atellite?
Spaceport America has a location in New Mexico of 32.998o North Latitude, which means that
the orbital inclination will a lso b e 32.998o , s o we w ill set our independent variable DEG to 3 3.
AtLatitudeP ayload250 = − 1.11(33) 2 + 15, 500 = 14, 290 kg
and
AtLatitudeP ayload800 = − 1.11(33) 2 + 11, 000 = 9, 790 kg
So, the endpoints to to our linear equation are (250, 14,290) and (800, 9,790). We can finally
write the linear equation in slopeintercept (y=mx+b) form by finding the slope (m) and the
yintercept (b). The slope is the change in y divided by the change in x . Plugging one of the
points back into t he e quation yields the yintercept.
Slope = m = 9,790 − 14,290 = − 8.18
800 − 250
and
y − int = b = y1 − mx1 = 14, 250 − (− 8.18)(250) = 16, 335 km
Therefore, the linear equation for the Skylon operating out of Spaceport America given a desired
orbital altitude o f b etween 250 km a nd 8 00 k m is:
Spaceport − to − AtLatitude ALT = − 8.18ALT + 16, 335
Converting 490 m iles t o 789 k ilometers, and p lugging t hat i nto o ur formula, w e get:
Spaceport − to − AtLatitude 789 = − 8.18(789) + 16, 335
= 9, 883 kg
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Therefore, the satellite can h ave a m aximum w eight of a lmost t en t housand kilograms.
The same technique described above can be used to determine the equations to reach the NASA’s
International Space Station (I.S.S.) and for a polar orbit from Spaceport America. These will be
exercises left up to the s tudent.
Spaceport − to − ISS ALT = − 7.73ALT + 13, 982
Spaceport − to − P olar ALT = − 7.27ALT + 8, 118
2.04 Guided P ractice
You are a n s paceliner Captain responsible f or the payload s ent into L EO. Use t he S kylon Payload
Equation found in the article t o c alculate each orbital a ltitude.
Payload 1: Launch L ocation: S paceport America Orbital A ltitude: 5 70 mi
Maximum Payload M ass = _ _________ kg t o L EO.
Payload 2: L aunch L ocation: Guiana S pace Center Orbital A ltitude: 6 35 mi
Maximum Payload Mass = __________ kg to LEO.
Payload 3 : Launch Location: S paceport America Orbital Altitude: 850 m i
Maximum P ayload M ass = __________ k g t o LEO.
::
2.05 C ross Curricular E xercises
ARTWORK
Find i mages o f the R .E.L. Skylon s paceplane o n t he I nternet. U se t he i mages t hat you have
researched to draw a picture of the s paceplane r ocketing i nto orbit.
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