Transcript ASEN 5050 SPACEFLIGHT DYNAMICS

ASEN 5050
SPACEFLIGHT DYNAMICS
GRAIL
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 20: GRAIL
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Announcements
• Alan’s office hours are today at 1:00 pm.
• STK LAB 2, due right now
• Homework #6 will be due Friday 10/24 (2014 not 2013)
– CAETE by Friday 10/31
• Mid-term Exam will be uploaded right after class and will be
due Wed 10/22. (CAETE 10/29)
– Take-home. Open book, open notes.
– Once you start the exam you have to be finished within 24 hours.
– It should take 2-3 hours.
• Today: GRAIL and more perturbation fun.
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Final Project
• Get started on it!
• Worth 20% of your grade, equivalent to 6-7 homework assignments.
• Find an interesting problem and investigate it – anything related to
spaceflight mechanics (maybe even loosely, but check with me).
• Requirements: Introduction, Background, Description of
investigation, Methods, Results and Conclusions, References.
• You will be graded on quality of work, scope of the investigation,
and quality of the presentation. The project will be built as a
webpage, so take advantage of web design as much as you can
and/or are interested and/or will help the presentation.
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Final Project
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Instructions for delivery of the final project:
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Build your webpage with every required file inside of a directory.
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Name your main web page “index.html”
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Name the directory “<LastName_FirstName>”
there are a lot of duplicate last names in this class!
You can link to external sites as needed.
i.e., the one that you want everyone to look at first
Make every link in the website a relative link, relative to the directory structure
within your named directory.
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We will move this directory around, and the links have to work!
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Test your webpage! Change the location of the page on your computer and make
sure it still works!
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Zip everything up into a single file and upload that to the D2L dropbox.
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Space News
• Comet Siding Spring flies by Mars on SUNDAY
• Nov 12 (about 4 weeks from now), Rosetta will
release Philae to land here…(next slide)
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~500 meters
in diameter
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Concept Quiz 12
• I’m still waiting for a few CAETE students to
complete quiz 12. Then I’ll fix everyone’s grades on
that quiz. Don’t worry 
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Mid-Term Logistics
• Please write your name on the exam
• Carry “infinite” precision in your math at all steps.
At the very end you are welcome to round your
answers, but don’t round too much!
• Document which equations / process you use, and
then verify that your math is correct using a
computer.
• Try to learn something  I’m not JUST doing this
exam to torture you.
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Review Requests (first 43)
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CW/H x14
Groundtracks x2
Coordinate systems x5
Transformations x7
f and g series x4
Canonical units x2
Odd orbital elements
Geocentric/geodetic
Kepler’s Equation derivation
Lambert’s Problem x3
Synodic period
Plane changes / maneuvers not covered in HW x5
EVERYTHING x4
NOTHING x5
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Orbit Maneuvering
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Hohmann Transfers
Bi-elliptic Transfers
Circular Rendezvous
Coplanar Rendezvous
Changing orbital elements
– a, e, rp, ra, P, M, AOP are all coplanar
– i, RAAN are plane changes
• Lambert’s Problem
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Changing Orbital Elements
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Δa  Hohmann Transfer
Δe  Hohmann Transfer
Δi  Plane Change
ΔΩ  Plane Change
Δω  Coplanar Transfer
Δν  Phasing/Rendezvous
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Changing Inclination
• Δi  Plane Change
• Inclination-Only Change vs. Free Inclination Change
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Changing Inclination
• Let’s start with circular orbits
Vf
V0
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Changing Inclination
• Let’s start with circular orbits
Vf
V0
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Changing Inclination
• Let’s start with circular orbits
Are these vectors the
same length?
Vf
Δi
V0
What’s the ΔV?
Is this more expensive
in a low orbit or a high
orbit?
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Changing Inclination
• More general inclination-only maneuvers
Where do you perform
the maneuver?
How do V0 and Vf
compare?
What about the FPA?
Line of Nodes
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Changing Inclination
• More general inclination-only maneuvers
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Changing The Node
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Changing The Node
Where is the
maneuver located?
Neither the max latitude
nor at any normal
feature of the orbit!
There are somewhat
long expressions for
how to find uinitial and
ufinal in the book for
circular orbits.
Lambert’s Problem
gives easier solutions.
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Changing Argument of Perigee
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Changing Argument of Perigee
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Changing Argument of Perigee
Which ΔV is
cheaper?
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Maneuver Combinations
• General rules to consider:
– Energy changes are more efficient when traveling FAST
• Periapse
– Plane changes are more efficient when traveling SLOW
• Apoapse
– Combinations take advantage of vector addition
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3+4 = 5 not 7 
Some inclination change at periapse is optimal
Some energy change at apoapse is optimal (or necessary)
Delta-V vector = V final vector – V initial vector
– One’s initial and final orbit do not always intersect; if they
don’t you have to build a transfer orbit.
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Questions
• These are the sorts of questions I hope you can
answer:
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Given orbit X, when does the satellite reach radius R?
Where in orbit Y is the satellite at its maximum latitude?
Compute element XYZ given element ABC
And all of those concept quiz type questions.
There will be math and concepts.
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ASEN 5050
SPACEFLIGHT DYNAMICS
GRAIL
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 20: GRAIL
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ASEN 5050
SPACEFLIGHT DYNAMICS
Perturbations
Prof. Jeffrey S. Parker
University of Colorado – Boulder
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Perturbation Discussion Strategy
✔• Introduce the 3-body and n-body problems
– We’ll cover halo orbits and low-energy transfers later
✔• Numerical Integration
✔• Introduce aspherical gravity fields
– J2 effect, sun-synchronous orbits
• Solar Radiation Pressure
• Introduce atmospheric drag
– Atmospheric entries
• Other perturbations
• General perturbation techniques
• Further discussions on mean motion vs. osculating
motion.
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