ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones

1. ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones Professor George H. Born Lecture 1: Course Introduction

2. Course Outline • Instructors • Professor Brandon A. Jones <brandon.jones@colorado.edu> • Office: ECNT 420 • Office Hours: Tues 11-12noon, Thurs 3-4pm • Professor George H. Born <georgeb@colorado.edu> • Office: ECNT 316 • Office Hour: By Appointment • Teaching/Course Assistants • Marc Balducci <marc.balducci@colorado.edu> • Office: ECAE 140 • Office Hours: MWF 3-4 PM • TBN

3. Introductions • Brandon A. Jones • Undergraduate: UT-Austin • Mathematics and Physics • Contractor at NASA/JSC • Titan Corporation (now L-3) • Odyssey Space Research • Graduate: CU-Boulder • M.S. and Ph.D. • Postdoc (2011-2013) • Assistant Research Professor (2013-present)

4. George Born: Wrote the book on Stat OD.

5. Course Textbook Tapley, B.D., B.E. Schutz, and G.H. Born, Statistical Orbit Determination, Elsevier Academic Press, New York, 2004.

6. Course Websites • Course website: ccar.colorado.edu/asen5070 • Homework, project, and reference materials • Desire2Learn: learn.colorado.edu • Forums, Dropbox, Links, Quizzes, News, etc. • Short quizzes after each lecture (starting Sept 4). • Details to come

7. Course Grade • Homework = 20% • 11 assignments + Concept Quizzes • Concept quizzes averaged to form a single homework • Quizzes/Exams = 50% • 2 mid-terms • 1 take-home final • Course Project = 30 %

8. Notes on Homework Delivery • Uploaded to D2L as a searchable PDF • Free converters available on the web • Some operating systems, e.g., Mac OS X, support direct conversion • Good opportunity to learn LaTeX • Software must be uploaded to D2L as appendix in assignment write-up • Plagiarism detection will be enabled!

9. Homework Late Policy • Each student is given one “freebie” • One assignment may be turned in up to a week late without penalty • Any late assignments after the freebie will be penalized 10% off maximum score per school day • Late is defined by the start of CAETE recording on the day due or time/day indicated on the assignment • Only exception: documented approval from instructor • Documented approval defined as written acknowledgement (e-mail or typed) by assignment and/or university prescribed deadlines • Meant to allow for concessions for religious holidays, medical emergencies, etc.

10. Important Homework Assignments • Several homework assignments establish tools for final project: • HW 1 • HW 2 • HW 7 • HW 9 • HW 10 • Make sure you get these right! • Final answers, but not full solutions, will be provided online

11. Honor Code • You are expected to follow the Honor Code • We will treat you as an engineer in the field as practice for your career. • This course teaches you to navigate spacecraft. Spacecraft are worth many $Millions. Don’t crash them. • You can work together, but give each other credit when credit is due. We use software to detect plagiarism. The Honor Code will be enforced. • If you’re concerned about your grade, please come talk to us rather than cheating.

12. University Policies • The university sets certain policies in regards to: • Accommodations due to disability • Medical conditions/injuries • Religious observances • Discrimination • etc. • See syllabus and university guidelines for more information

13. Syllabus • Full syllabus available online on D2L • File updated this morning (in case anyone downloaded it over the weekend) • Please let me know if you have any questions

14. CAETE Recording and Microphones • This class is being recorded via CAETE • You will have access to recordings through the CAETE website • If you miss class, use the recording as an opportunity to catch up! • You are also being recorded… • Desktop microphones are sensitive • Please be careful not to add a creative soundtrack for those viewing the recordings…

15. Notes on My Teaching Style • Text in blue is a question posed to you • A “cold call” is not beneficial to you or your fellow students • I will pause (a couple of seconds), let you think, and then call on a student • Where are you right now?

16. Introduction to Statistical Orbit Determination

17. What is Statistical Orbit Determination? • It is the process of estimating the state/orbit of a satellite using a collection of observations. • We never know where a satellite is. • Launch errors • Modeling errors • Spacecraft performance errors • maneuvers, electromagnetic interactions with the environment, etc • Track a satellite • Observation errors • Locations of tracking stations • Atmosphere • Hardware modeling • Geometry issues

18. These dots represent many measurements (with some error) of a single point. • How would you estimate the true point? (Remember, blue font is a question to think about!) Y X

19. What is Statistical Orbit Determination? • How would you alter the method for a moving object? • Use numerous observations of a satellite and estimate its state using a filter. Time • Required skills: • Astrodynamics, Linear Algebra • Signal Analysis, Creativity

20. What can you do with Stat OD? • Navigate satellites and spacecraft! • A huge portion of the population of people in the world who navigate satellites learned their skills from Born, Tapley and Schutz. • Commercial: • GEO communication sats • Human spaceflight • Defense: • Spy satellites • Interplanetary: • JPL, Goddard, APL • Human Exploration: • ISS, Orion • Missions to LEO, Moon, NEOs, Mars

21. Three Levels of OD: • Low accuracy (~1 km) • Low resolution imaging, space surveillance • Medium accuracy (~100 m) • Medium resolution imaging, orbit prediction, laser tracking • High accuracy (<10 cm) • Relative motion/formation flying • Scientific studies of the Earth

22. Tentative Course Outline

23. Tentative Course Outline

24. Tentative Course Outline • Exam Three – Take Home, Due: TBD • Project, Due : TBD (details in early-Oct.)

25. Remainder of the Week • I am in Albuquerque the week for a research seminar • Wednesday’s lecture will be a quick overview of MATLAB • Friday’s lecture is pre-recorded, and will be available online through the CAETE website • Directions for access may be found here • My office hours are cancelled for this week

26. Any Questions?

27. Quick Survey • What programming experience do you have? • MATLAB? • Python? • C/C++/Fortran/Ada/… • None? • Most students use MATLAB in this class, but you are free to choose! • MATLAB overview on Wednesday, with follow-up offered by AGSO

28. Homework 0.5 • Due with Homework 1, but you could finish it today. • Introduction to ode45() (MATLAB) • Who has experience with ode45()? • Use ode45() to model the motion of a simple harmonic oscillator • Assignment is more of a tutorial

29. Homework # 1 • Problem 1: • Problem 2:

30. Homework # 1 • Problem 3: • Problem 4:

31. Homework # 1 • Problem 5: • Problem 6:

32. Homework # 1 • Problem 7: Solution method discussed next week!

33. Brief Review of Astrodynamics

34. Review of Astrodynamics • What’s μ (other than a greek letter)?

35. Review of Astrodynamics • What’s μ (other than a greek letter)? • μ is the gravitational parameter of a massive body • μ = GM

36. Review of Astrodynamics • What’s μ? • μ is the gravitational parameter of a massive body • μ = GM • What’s G? • What’s M?

37. Review of Astrodynamics • What’s μ? • μ is the gravitational parameter of a massive body • μ = GM • What’s G? Universal Gravitational Constant • What’s M? The mass of the body

38. Review of Astrodynamics • What’s μ? • μ = GM • G = 6.67384 ± 0.00080 × 10-20 km3/kg/s2 • MEarth ~ 5.97219 × 1024 kg • or 5.9736 × 1024kg • or 5.9726 × 1024 kg • Use a value and cite where you found it! • μEarth = 398,600.4415 ± 0.0008 km3/s2 (Tapley, Schutz, and Born, 2004) • How do we measure the value of μEarth?

39. Review of Astrodynamics Problem of Two Bodies µ = G(M1 + M2) XYZ is nonrotating, with zero acceleration; an inertial reference frame

40. Review of Astrodynamics • How many degrees of freedom are present to fit the orbits of 2 bodies in mutual gravitation (known masses, no SRP, no drag, no perturbations) • 2 • 4 • 6 • 12 6 for each body: 3 position and 3 velocity X 2

41. Integrals of Motion • Center of mass of two bodies moves in straight line with constant velocity • Angular momentum per unit mass (h) is constant, h = r x V = constant, where V is velocity of M2 with respect to M1, V= dr/dt • Consequence: motion is planar • Energy per unit mass (scalar) is constant

42. Orbit Plane in Space

43. Equations of Motion in the Orbit Plane The uθcomponent yields: which is simply h = constant

44. Solution of ur Equations of Motion • The solution of the ur equation is (as function of θ instead of t): where e and ω are constants of integration.

45. The Conic Equation • Constants of integration: e and ω • e = ( 1 + 2 ξ h2/µ2 )1/2 • ω corresponds to θ where r is minima • Let f = θ – ω, then r = p/(1 + e cos f) which is “conic equation” from analytical geometry (e is conic “eccentricity”, p is “semi-latus rectum” or “semi-parameter”, and f is the “true anomaly”) • Conclude that motion of M2 with respect to M1 is a “conic section” • Circle (e=0), ellipse (0<e<1), parabola (e=1), hyperbola (e>1)

46. Types of Orbital Motion Statistical Orbit Determination University of Colorado at Boulder

47. End of Lecture 1 • This is a good place to stop for today • Any questions?