ASEN 5050 SPACEFLIGHT DYNAMICS Mars Odyssey Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 12: Mars Odyssey 1

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 2

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 3

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 4

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 5

Quiz #9 Lecture 12: Mars Odyssey 6

Quiz #9 Lecture 12: Mars Odyssey 7

Quiz #9 Lecture 12: Mars Odyssey 8

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

Lecture 12: Mars Odyssey 11 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 12 Right Spherical Triangle

Lecture 12: Mars Odyssey 13 We can show this using spherical trigonometry for a right spherical triangle (eq. C-23): Thus, Because |sin  | ≤ 1, the launch latitude  gc ≤ i Another useful relation: sin  gc = sin(i) sin(  + ) Launch Cannot direct launch into orbit with inclination <  gc

Lecture 12: Mars Odyssey 14 Launch The launch site velocity is: 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 v L = km/s. Westward launches must make this up, so difference is 0.93 km/s.

Lecture 12: Mars Odyssey 15 Launch Azimuths Launch sites and allowable azimuths

Lecture 12: Mars Odyssey 16 Launch Sites

Lecture 12: Mars Odyssey 17 Noncoplanar Transfers

Lecture 12: Mars Odyssey 18 Noncoplanar Transfers Launch window – select UT to achieve orbit’s desired initial nodal location (determine  gst ) First determine launch azimuth  (inverse sine gives two possible answers:  and 180  - , for ascending (- 90  < u < 90  ) and descending (90  < u < 270  ) passes.) Now, determine the auxiliary angle from: The values u and 360  - u represent prograde and retrograde orbits respectively.

Lecture 12: Mars Odyssey 19 Noncoplanar Transfers Tolerance on ascending node (±  ) creates “launch window”, or range of values of  GST. Once  GST is chosen: Substitution of  GST0 for each day (GST at 0 hrs on that day) gives the launch time on each day.  v is more complicated.