ASEN 5050 SPACEFLIGHT DYNAMICS Mid-Term Review, A-Train Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 27: Mid-Term Review, A-Train 1

Announcements Homework #7 is due! HW 8 will be released Wednesday. Mid-Term handed back Wednesday (the grading is almost done…) Reading: Chapter 12 Lecture 27: Mid-Term Review, A-Train 2

Schedule from here out Lecture 27: Mid-Term Review, A-Train 3 10/27: Three-Body Orbits 10/29: General Perturbations (Alan) 10/31: General Perturbations part 2 11/3: Mid-Term Review, A-Train 11/5: Interplanetary 1 11/7: Interplanetary 2 11/10: Entry, Descent, and Landing 11/12: Low-Energy Mission Design 11/14: STK Lab 3 11/17: Low-Thrust Mission Design (Jon Herman) 11/19: Finite Burn Design 11/21: STK Lab 4 Fall Break 12/1: Constellation Design, GPS 12/3: Spacecraft Navigation 12/5: TBD 12/8: TBD 12/10: TBD 12/12: Final Review

Schedule from here out Our last lecture will be Friday 12/12. –Final review and final Q&A. –Showcase your final projects – at least any that are finished! Final Exam –Handed out on 12/12 –Due Dec 18 at 1:00 pm – either into D2L’s DropBox or under my door. I heartily encourage you to complete your final project website by Dec 12th so you can focus on your finals. However, if you need more time you can have until Dec 18th. As such the official due date is Dec 18th. The final due date for everything in the class is Dec 18th - no exceptions unless you have a very real reason (medical or otherwise - see CU's policies here: Of course we will accommodate real reasons. If you are a CAETE student, please let me know if you expect an issue with this timeframe. We normally give CAETE students an additional week to complete everything, but the grades are due shortly after the 18th for everyone. So please see if you can meet these due dates. Lecture 27: Mid-Term Review, A-Train 4

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. Lecture 27: Mid-Term Review, A-Train 5

Final Project Instructions for delivery of the final project: Build your webpage with every required file inside of a directory. –Name the directory “ ” –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. Lecture 27: Mid-Term Review, A-Train 6

Space News Lecture 27: Mid-Term Review, A-Train 7 It’s looking like Space Ship 2’s feathering system was deployed while accelerating through Mach 1, causing the disintegration. Rosetta’s Philae lander prepping for its big descent in 9 days!

ASEN 5050 SPACEFLIGHT DYNAMICS Mid-Term Exam Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 27: Mid-Term Review, A-Train 8

Mid-Term Exam Lecture 27: Mid-Term Review, A-Train 9 Problem 1 Common errors: –Since this isn’t a circular orbit, the DT is not half of the orbital period. Though the Delta-nu is indeed 180 deg.

Mid-Term Exam Hard way: generate the two-body orbit and map the latitude: Lecture 27: Mid-Term Review, A-Train 10 ?

Mid-Term Exam Problem 1 solution Easy way (and precise): –Argument of latitude: u = ω + ν –At ascending node: u = 0 deg –At descending node: u = 180 deg –ω = 310 deg –At ascending node: ν = -310 deg = 50 deg –At descending node: ν =-130 deg = 230 deg –Compute time past periapse for both –Delta-t = hours Lecture 27: Mid-Term Review, A-Train 11 Quadrant Checks! Ascending  Descending Quadrant Checks! Ascending  Descending

Mid-Term Exam Problem 2 Lecture 27: Mid-Term Review, A-Train 12

Mid-Term Exam Problem 2 Lecture 27: Mid-Term Review, A-Train 13 Periapsis Range: km

Mid-Term Exam Problem 2 Lecture 27: Mid-Term Review, A-Train 14

Mid-Term Exam Problem 2 Lecture 27: Mid-Term Review, A-Train 15 Use eccentricity and semi-major axis, and find the eccentric anomaly needed to make radius = km. Convert to TimePastPeriapse. And also compute TimePastPeriapse of initial state. We find: Time past periapse of initial state: sec Time past periapse of impact: sec Duration of time to impact: sec = hours Quadrant Checks!

Mid-Term Exam Problem 2 Lecture 27: Mid-Term Review, A-Train 16 The missile will strike the surface traveling m/s in velocity

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 17

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 18

Mid-Term Exam Lecture 27: Mid-Term Review, A-Train 19 C/W Equations: Algorithm 48

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 20

Mid-Term Exam Problem 3 omega: rad/s Satellite A will be located at a position of [0.0, 0.0, ] in meters, after 7 minutes, relative to Shuttle Satellite B will be located at a position of [ , , 0.0] in meters, after 7 minutes, relative to Shuttle Satellite A will have a velocity relative to the shuttle of [0.0, 0.0, ] in m/s, after 7 minutes Satellite B will have a velocity relative to the shuttle of [ , , 0.0] in m/s, after 7 minutes Lecture 27: Mid-Term Review, A-Train 21

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 22

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 23

Mid-Term Exam Problem 3 Satellite A's state relative to Satellite B at t=7 minutes, in meters and m/s, before executing any maneuver (A-B): –x0: m –y0: m –z0: m –vx0: m/s –vy0: m/s –vz0: m/s Lecture 27: Mid-Term Review, A-Train 24

Mid-Term Exam Problem 3 What velocity is NEEDED? Equation 6-66 Lecture 27: Mid-Term Review, A-Train 25 t = 13 min = 780 sec

Mid-Term Exam Problem 3 What velocity is NEEDED? Equation 6-66 The velocity that Satellite A needs to obtain (m/s): vx: m/s vy: m/s vz: m/s Lecture 27: Mid-Term Review, A-Train 26

Mid-Term Exam Problem 3 What CHANGE in velocity is needed? The Delta-V impulse that A has to perform, in m/s relative to B: Delta-Vx: m/s Delta-Vy: m/s Delta-Vz: m/s Delta-V magnitude: m/s Lecture 27: Mid-Term Review, A-Train 27

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 28

Mid-Term Exam Problem 3 Use Algorithm 48 again to propagate state of A relative to B. You should see the position go to zero!!! The rendezvous Delta-V impulse that A has to perform, in m/s relative to B: Delta-Vx: m/s Delta-Vy: m/s Delta-Vz: m/s Delta-V magnitude: m/s Lecture 27: Mid-Term Review, A-Train 29

Mid-Term Exam Problem 3 Lecture 27: Mid-Term Review, A-Train 30

Mid-Term Exam Problem 3 Answer: yes! If satellite A does not do anything, it will collide with the shuttle in about 45 minutes. Half an orbit later. If satellite A DOES perform one maneuver, and then no more, it will collide with Satellite B. Lecture 27: Mid-Term Review, A-Train 31

Mid-Term Exam Problem 4 Inclination = = 104 deg Altitude = km Lecture 27: Mid-Term Review, A-Train 32 Big error: sidereal time!

Mid-Term Exam Problem 5 Lecture 27: Mid-Term Review, A-Train 33

Mid-Term Exam Problem 5 Lecture 27: Mid-Term Review, A-Train 34

Mid-Term Exam Problem 5 Lecture 27: Mid-Term Review, A-Train 35

Mid-Term Exam Problem 5 mu = mu Earth + mu Moon = km 3 /s 2 r p = km r a = km a = 384,000 km e = Period of lunar orbit: sec = min = hours = days Lecture 27: Mid-Term Review, A-Train 36

Mid-Term Exam Problem 5 Lecture 27: Mid-Term Review, A-Train 37

Mid-Term Exam Problem 5 use equation (for example): r = 380,000 km + rEarth = 386, km E = rad = deg Time past periapse: sec = min = hours = days Total Duration within km: sec = min = hours = days Lecture 27: Mid-Term Review, A-Train 38

Mid-Term Exam Problem 5 Lecture 27: Mid-Term Review, A-Train 39 Percentage of time the Earth and Moon are within km: %

ASEN 5050 SPACEFLIGHT DYNAMICS A-Train Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 27: Mid-Term Review, A-Train 40