ASEN 5050 SPACEFLIGHT DYNAMICS GRAIL

1
ASEN 5050SPACEFLIGHT DYNAMICSGRAIL

• Prof. Jeffrey S. Parker
• University of Colorado Boulder

2
Announcements

• Alans office hours are today at 100 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.

3
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.

4
Final Project

• Instructions for delivery of the final project
• Build your webpage with every required file
  inside of a directory.
• Name the directory ltLastName_FirstNamegt
• there are a lot of duplicate last names in this
  class!
• You can link to external sites as needed.
• Name your main web page index.html
• 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.
• We will move this directory around, and the links
  have to work!
• Test your webpage! Change the location of the
  page on your computer and make sure it still
  works!
• Zip everything up into a single file and upload
  that to the D2L dropbox.

5
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)

6
500 meters in diameter
7
Concept Quiz 12

• Im still waiting for a few CAETE students to
  complete quiz 12. Then Ill fix everyones
  grades on that quiz. Dont worry ?

8
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 dont round too much!
• Document which equations / process you use, and
  then verify that your math is correct using a
  computer.
• Try to learn something ? Im not JUST doing this
  exam to torture you.

9
Review Requests (first 43)

• CW/H x14
• Groundtracks x2
• Coordinate systems x5
• Transformations x7
• f and g series x4
• Canonical units x2
• Odd orbital elements
• Geocentric/geodetic
• Keplers Equation derivation
• Lamberts Problem x3
• Synodic period
• Plane changes / maneuvers not covered in HW x5
• EVERYTHING x4
• NOTHING x5

10
Orbit Maneuvering

• 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
• Lamberts Problem

11
Changing Orbital Elements

• ?a ? Hohmann Transfer
• ?e ? Hohmann Transfer
• ?i ? Plane Change
• ?O ? Plane Change
• ?? ? Coplanar Transfer
• ?? ? Phasing/Rendezvous

12
Changing Inclination

• ?i ? Plane Change
• Inclination-Only Change vs. Free Inclination
  Change

13
Changing Inclination

• Lets start with circular orbits

Vf
V0
14
Changing Inclination

• Lets start with circular orbits

Vf
V0
15
Changing Inclination

• Lets start with circular orbits

Are these vectors the same length? Whats the
?V? Is this more expensive in a low orbit or a
high orbit?
Vf
V0
?i
16
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
17
Changing Inclination

• More general inclination-only maneuvers

18
Changing The Node
19
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. Lamberts Problem gives easier solutions.
20
Changing Argument of Perigee
21
Changing Argument of Perigee
22
Changing Argument of Perigee
Which ?V is cheaper?
23
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
• 34 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
• Ones initial and final orbit do not always
  intersect if they dont you have to build a
  transfer orbit.

24
Questions

• These are the sorts of questions I hope you can
  answer
• 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.

25
ASEN 5050SPACEFLIGHT DYNAMICSGRAIL

• Prof. Jeffrey S. Parker
• University of Colorado Boulder

26
ASEN 5050SPACEFLIGHT DYNAMICSPerturbations

• Prof. Jeffrey S. Parker
• University of Colorado Boulder

27
Perturbation Discussion Strategy
?

• Introduce the 3-body and n-body problems
• Well 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.

?
?