ASEN 5050 SPACEFLIGHT DYNAMICS Three-Body Orbits Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 24: General Perturbations 1

Announcements Homework #7 is out now! Due in one week (Monday morning). –Posted to D2L – I’ll post it to the 5050 website next. –Pretty easy homework – practice with numerical integration. Comparing it to Kepler. Reading: Chapters 8 and 9 Lecture 24: General Perturbations 2

Schedule from here out Lecture 24: General Perturbations 3 10/27: Three-Body Orbits 10/29: General Perturbations (Alan) 10/31: General Perturbations part 2 11/3: Mission Orbits / Designing with perturbations 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 19: Perturbations 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 24: General Perturbations 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 24: General Perturbations 6

Space News Lecture 24: General Perturbations 7 MESSENGER is surviving its exciting (and hot!) mission at Mercury June 17 th : OCM-9 raised its orbit. ~5.0 m/s –Periapse altitude km  km –Orbital period 8 hrs  8 hr 2 min Sept 12 th : OCM-10 raised its orbit. ~8.6 m/s –Periapse altitude 24.3 km  94.0 km –Orbital period 8 hrs 2 min  8 hrs 5 min Oct 24 th : OCM-11 raised its orbit. ~19.4 m/s –Periapse altitude 26.0 km  km –Orbital period 8 hrs 5 min  8 hrs 12 min Jan 21 st : OCM-12 will….raise its orbit again!

Space News Lecture 24: General Perturbations 8 China just launched a round-trip lunar demonstrator mission – a precursor to a sample return mission!

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 Atmospheric drag –Atmospheric entries Other perturbations General perturbation techniques Further discussions on mean motion vs. osculating motion. Lecture 24: General Perturbations 9 ✔ ✔ ✔ ✔ ✔ ✔

ASEN 5050 SPACEFLIGHT DYNAMICS Three-Body Orbits Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 24: General Perturbations 10