ASEN 5050
SPACEFLIGHT DYNAMICS
Mars Odyssey
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 12: Mars Odyssey
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Announcements
• Homework #4 is due right now
• Homework #3 is re-active. Submit a new HW3 submission to
the Dropbox or in person by Friday 10/3!
– CAETE by Friday 10/10
– You can recover ½ of the points you lost, or get a 90%, whichever is
higher.
• Mid-term Exam will be handed out Friday, 10/17 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.
• Reading: Chapter 6
Lecture 12: Mars Odyssey
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Grading
• Homework grading
– Tough. We’re dropping points pretty easily.
• Units
• Work
• Not answering questions
– This is a graduate course, so it takes pretty good work to
get an A. At a minimum, you need to read the questions
and provide answers to what we’re asking.
– This class will ultimately be graded on a curve of some
sort. It’s soooo much easier to give everyone a better grade
than to knock everyone down at the end!
Lecture 12: Mars Odyssey
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HW3
• I’m posting the solutions online now.
• If you missed anything, go redo it until your answers
match the online solutions.
• If you do, we’ll give you half of your points back, or
a 90, whichever is higher.
Lecture 12: Mars Odyssey
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D2L
• Request:
– Please submit your answers in a Word Doc or a PDF
– It’s fine to include code in a .zip file, but it’s harder to
grade the HW if the HW is also included in the .zip file.
Lecture 12: Mars Odyssey
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Quiz #9
Lecture 12: Mars Odyssey
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Quiz #9
Lecture 12: Mars Odyssey
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Quiz #9
Lecture 12: Mars Odyssey
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ASEN 5050
SPACEFLIGHT DYNAMICS
Mars Odyssey
Prof. Jeffrey S. Parker
University of Colorado - Boulder
Lecture 12: Mars Odyssey
9
ASEN 5050
SPACEFLIGHT DYNAMICS
Launch
Prof. Jeffrey S. Parker
University of Colorado - Boulder
Lecture 12: Mars Odyssey
10
Launch
Launching a satellite:
For a direct launch, the launch site latitude must be less than or
equal to the desired inclination, otherwise we must change the
inclination of the orbit.
Lecture 12: Mars Odyssey
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Right Spherical Triangle
Lecture 12: Mars Odyssey
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Launch
We can show this using spherical trigonometry for a
right spherical triangle (eq. C-23):
i = inclination
cos i = cos f gc sin b
Thus, sinb =
cos i
cos f gc
f gc = launch site latitude
b = launch azimuth
Because |sin b | ≤ 1, the launch latitude fgc ≤ i
Cannot direct launch into orbit with inclination < fgc
Another useful relation: sin fgc = sin(i) sin(w+n)
Lecture 12: Mars Odyssey
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Launch
The launch site velocity is:
v L = wÅ ´ rsite or v L = wÅ ´ rsite = wÅ rsite cos fgc
Note all the velocity is Eastward in the SEZ system, so launching
from the equator on a 90 azimuth may be best.
The velocity at the equator is vL = 0.465 km/s. Westward
launches must make this up, so difference is 0.93 km/s.
Lecture 12: Mars Odyssey
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Launch Azimuths
Launch sites and allowable azimuths
Lecture 12: Mars Odyssey
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Launch Sites
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Noncoplanar Transfers
Lecture 12: Mars Odyssey
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Noncoplanar Transfers
Launch window – select UT to achieve orbit’s desired
initial nodal location (determine qgst)
First determine launch azimuth b (inverse sine gives
two possible answers: b and 180-b, for ascending (90 < u < 90) and descending (90 < u < 270)
passes.)
cos i
sinb =
cos f gc
cos b
Now, determine the auxiliary angle from: coslu =
sin i
The values lu and 360-lu represent prograde and
retrograde orbits respectively.
Lecture 12: Mars Odyssey
lu = q LST - W but, q LST = q GST + l
q GST = W + lu - l
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Noncoplanar Transfers
Tolerance on ascending node (±DW) creates “launch window”,
or range of values of qGST. Once qGST is chosen:
UT =
q GST - q GST 0
wÅ
Substitution of qGST0 for each day (GST at 0 hrs on that day)
gives the launch time on each day.
Dv is more complicated.
Lecture 12: Mars Odyssey
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