1. ASEN 5050 SPACEFLIGHT DYNAMICS Atmospheric Drag Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 23: Drag 1

2. Announcements Homework #6 is due right now –CAETE by Friday 10/31 Homework #7 will be released either today or soon. Due date depends on when I get it out –Pretty easy homework – practice with numerical integration. Comparing it to Kepler. Reading: Chapters 8 and 9 Lecture 23: Drag 2

3. Concept Quiz 13 Lecture 23: Drag 3

4. Concept Quiz 13 Lecture 23: Drag 4

5. Concept Quiz 13 Lecture 23: Drag 5

6. 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 23: Drag 6

7. 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 23: Drag 7

8. Space News Lecture 23: Drag 8 More Siding Spring pics Partial solar eclipse yesterday Cassini is flying by Titan on Friday for the 107 th time. –This time its doing a bistatic radar observation of Titan’s lakes. –Altitude of closest approach: 629 miles (1013 km) –Speed: 13,000 mph (5.6 km/s)

9. Siding Spring’s hydrogen coma Lecture 23: Drag 9

10. ASEN 5050 SPACEFLIGHT DYNAMICS Perturbations Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 23: Drag 10

11. 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 23: Drag 11 ✔ ✔ ✔ ✔

12. Atmospheric Drag Atmospheric drag is familiar, since we experience it all the time. Force experienced by any body that travels through a gaseous medium, acting against the relative velocity. The force passes through the center of pressure. –If the center of mass is not aligned with the center of pressure, then a torque is introduced. Lecture 23: Drag 12

13. Lecture 23: Drag Atmospheric Drag Drag tends to change a and e the most. The drag acceleration can be written as: 13

14. Atmospheric Drag How does this relationship impact a satellite in orbit? Lecture 23: Drag 14

15. Lecture 23: Drag Atmospheric Drag Density varies due to: –Changes in the magnetic field (charged particles) – geomagnetic index –Changes in the solar flux (F10.7 – flux at 10.7cm wavelength) Many models (Jacchia, MSIS, DTM, etc.). Simplest is Exponential: where  0 = ref density, h 0 = ref. altitude, h ellp = altitude, H = scale height 15

16. Lecture 23: Drag Atmospheric Drag 16

17. Atmospheric Drag Variability Latitudinal Variations –Earth’s oblateness; the actual height of the satellite varies even in a circular orbit! Longitudinal Variations –Those darn mountains cause weather variations. Time-Varying –Diurnal –27-day solar cycle –11-year cycle of sunspots –Seasonal variations –Winds –Magnetic storms –Tides Lecture 23: Drag 17

18. Lecture 23: Drag Atmospheric Drag 18

19. Lecture 23: Drag Atmospheric Drag 19

20. Lecture 23: Drag Atmospheric Models 20

21. Measuring Atmospheric Density Using Satellite Data Lecture 23: Drag 21

22. Lecture 23: Drag Along-track The end-of-mission altitude, after 5 years, will be 250 km. This objective will be attained by natural decay and orbit corrections (function of solar activity). Initial mass: 522 kg Attitude control: (2 ± 0.1)° STAR sampling rate: 1 Hz STAR resolution: 3·10 -9 m/s 2 /Hz 0.5 Tracking: GPS and SLR 87° orbit inclination LST precession 5.44 min/day 24-hr local time sampling in 133 days Altitude range: 460-250 km The CHAMP Mission 22

23. Lecture 23: Drag Accelerometers - ONERA http://www.onera.fr 23

24. Lecture 23: Drag The STAR Reference Frame 24

25. Lecture 23: Drag Champ Along-Track Accelerations 25

26. Lecture 23: Drag STAR Accelerations vs Models 26

27. Lecture 23: Drag April 15-24, 2002 27

28. Lecture 23: Drag CHAMP Total Density at 410 km 28

29. Lecture 23: Drag CHAMP Density at 410 km 29

30. Lecture 23: Drag Density versus Latitude/Time 30

31. Lecture 23: Drag Day/Night Animation 31

32. Lecture 23: Drag North Pole Animation 32

33. Lecture 23: Drag South Pole Animation 33

34. Lecture 23: Drag CHAMP Coverage, Sept 1-15, 2002 34

35. Lecture 23: Drag Total Density: September 1-14, 2002 35

36. Lecture 23: Drag Total Density: September 1-14, 2002 36

37. Lecture 23: Drag Total Density: September 1-14, 2002 37

38. Lecture 23: Drag Wave Structures Observed 38

39. Lecture 23: Drag CHAMP Density at 400 km, Ascending 302 303 304 305 39

40. Lecture 23: Drag CHAMP Density at 400 km, Ascending 323 324 40

41. Lecture 23: Drag Zonal Winds Observed 41

42. Lecture 23: Drag Density Ratios: May 14 - Aug 15, 2001 DTM2000 DTM94 MSIS86 Jacchia 70 42

43. Lecture 23: Drag Density Ratio: May 14, 2001 - May 1, 2002 DTM2000 DTM94MSIS86 Jacchia 70 43

44. GOCE Lecture 18: Perturbations 44

45. GOCE Uses electric propulsion to remain at an altitude of ~167 km Not long ago, it ran out of fuel. Not long ago, it re-entered Earth’s atmosphere Lecture 18: Perturbations 45

46. ISS Altitude Lecture 18: Perturbations 46

47. ISS Altitude Lecture 18: Perturbations 47

48. lecture16.ppt ©R.S. Nerem 2011 48 Oblateness Perturbations

49. lecture16.ppt ©R.S. Nerem 2011 49 General Perturbation Techniques Which is a “secularly precessing ellipse”. The equatorial bulge introduces a force component toward the equator causing a regression of the node (for prograde orbits) and a rotation of periapse. Note:

50. lecture16.ppt ©R.S. Nerem 2011 50 General Perturbation Techniques

51. lecture16.ppt ©R.S. Nerem 2011 51 General Perturbation Techniques

52. lecture16.ppt ©R.S. Nerem 2011 52 General Perturbation Techniques Periapse also precesses. = 0 at the critical inclination, i  = 63.4  (116.6  )

53. lecture16.ppt ©R.S. Nerem 2011 53 General Perturbation Techniques

54. lecture16.ppt ©R.S. Nerem 2011 54 General Perturbation Techniques Gravity perturbations also affect geosynchronous orbits.

55. lecture16.ppt ©R.S. Nerem 2011 55 General Perturbation Techniques Application: Sun Synchronous orbits

56. lecture16.ppt ©R.S. Nerem 2011 56 General Perturbation Techniques Sun Synchronous orbits: –Orbit plane remains at a constant angle (  ’ ) with respect to the Earth-Sun line. –Orbit plane precession about the Earth is equal to period of Earth’s orbit about the Sun.

57. Lecture 18: Perturbations 57 Perturbations Special Perturbation Techniques – Numerical integration. Straightforward – however obtaining a good understanding of the effects on the orbit is difficult General Perturbations – Use approximations to obtain analytical descriptions of the effects of the perturbations on the orbit. Assumes perturbative forces are small Early work used general perturbations because of a lack of computational power. Modern work uses special perturbations (numerical integration) because of the wide availability of computers. GP still useful for increasing your understanding. Still used by AF for maintaining space object catalog (> 7000 objects).

58. Trend Analyses While it’s useful to be able to numerically integrate high- fidelity equations of motion, it’s also useful to have an expectation for what may appear! Drag –Clear reduction in a and e SRP –Depends, but in some circumstances it can increase e Earth’s oblateness –Dramatic change in Ω, ω, and M Third-body effects –Precession of the nodes, same effect as oblateness. Lecture 18: Perturbations 58

59. Trend Analyses Secular Trends Long periodic effects Short periodic effects Mean elements Osculating elements Lecture 18: Perturbations 59

60. lecture15.ppt ©R.S. Nerem 2011 60 General Perturbation Techniques Perturbations can be categorized as secular, short period, long period.

61. lecture15.ppt ©R.S. Nerem 2011 61 Perturbations secular long-periodic mixed-periodic short-periodic This equation is known as a “Poisson Series”

62. Perturbation Magnitudes Lecture 18: Perturbations 62 ISS Orbit

63. Perturbation Magnitudes Lecture 18: Perturbations 63 GPS Orbit

64. Perturbation Magnitudes Lecture 18: Perturbations 64 Earth – Mars