1. ASEN 5050 SPACEFLIGHT DYNAMICS Solar Radiation Pressure
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 22: SRP

2. Announcements Mid-Term due now! Homework #6 is due Friday 10/24
CAETE due date next week
After which I’ll talk through all of the answers!
I’ll be grading the mid-terms this Friday – about the earliest I can. I’ll hand them back after the CAETE due date.
Homework #6 is due Friday 10/24
CAETE by Friday 10/31
Concept Quiz 13 after lecture! If you pay attention to the lecture today, it’ll be easy.
Reading: Chapters 8 and 9
I have to leave my office hours early today – if you need something, please come by 2 – 2:30.
Lecture 22: SRP

3. 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 22: SRP

4. Final Project Instructions for delivery of the final project:
Build your webpage with every required file inside of a directory.
Name the directory “<LastName_FirstName>”
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 22: SRP

5. Space News Comet Siding Spring images
Partial solar eclipse tomorrow, at sunset
Cassini is flying by Titan on Friday for the 107th 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)
Lecture 22: SRP

6. Comet Siding Spring Opportunity’s image from the Martian surface
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7. Comet Siding Spring
MRO’s view of the nucleus – smaller than estimates indicated!
138 m/pixel – maybe 500 meters in size
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8. ASEN 5050 SPACEFLIGHT DYNAMICS Perturbations
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 22: SRP

9. 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 22: SRP

10. Solar Radiation Pressure
SRP is the effect of solar photons striking the spacecraft and imparting a force on it.
Many things can and do happen
Photons are absorbed by the spacecraft and transmit energy to the spacecraft.
Photons are reflected off of the spacecraft, imparting more energy to the spacecraft.
Photons heat up the spacecraft, which can change the thermal radiative characteristics of the spacecraft.
Photons act on average through the center of pressure; if that isn’t aligned or coincident with the center of mass then a torque is applied to the spacecraft.
Lecture 22: SRP

11. Solar Radiation Pressure
If we treat the spacecraft as a uniform sphere, SRP may be perceived as merely an offset of the Sun’s gravity. Why?
When/Why/How is SRP any different than gravity?
Force of Gravity:
Originates from the Sun’s center of mass;
Falls off as the square of the distance;
Is transmitted at the speed of light (if the Sun moved, we’d perceive a change in the gravitational acceleration some 8 minutes later)
Net Force of SRP:
Originates from the Sun’s optical center;
Falls off as the square of the distance;
Is transmitted at the speed of light (if the Sun moved, we’d perceive a change in SRP some 8 minutes later)
Lecture 22: SRP

12. Solar Radiation Pressure
SRP differs from gravity in several key ways:
Gravity attracts mass, SRP acts on a surface
Absorption, diffuse reflection, specular reflection, refraction, torques applied to a real spacecraft
Variations in the solar flux over time
Shadow / eclipse passages
Lecture 22: SRP

13. Solar Radiation Pressure
8 x 1017 photons / cm2 with λavg = 556 nm at 1 AU
Intensity, irradiance, solar flux (different names for the same thing): ~1367 W/m2
Computed by estimating the total output of the Sun and dividing it by the surface area at our radius from the Sun x 1026 Watts / 4πr2
You can use a varying flux based on radius to be more accurate!
We can relate this solar flux to a pressure (i.e., a change in momentum) by measuring the momentum of the energy being transferred using Einstein’s famous relationship:
The force of solar pressure per unit area (change in momentum) is:
Lecture 22: SRP

14. Solar Radiation Pressure
The acceleration due to solar radiation pressure is:
Unit vector from satellite to Sun
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15. Solar Radiation Pressure
Absorption
Reflection: diffuse and specular
incident light
The light is either absorbed, reflected diffusely, or reflected specularly.
Depends on the material, wavelength, and surface!
Lecture 22: SRP

16. Solar Radiation Pressure
Fully absorbed
Fully diffusely reflected
Fully specularly reflected
incident light
Net force
All light is either absorbed, diffusely reflected, or specularly reflected!
Net force
Net force
Lecture 22: SRP

17. Different SRP Models Flat-Plate Model
Assume you have a flat plate that is pointed at the Sun
CR defines how much reflection the plate generates
0 = no force, 1 = absorbed, = combination of absorption, diffuse reflection, and specular reflection, 2 = specular
To Sun
Normal
Lecture 22: SRP

18. Different SRP Models Flat-Plate Model NOT pointed at the Sun θ θ
To Sun θ
Normal
Lecture 22: SRP

19. Different SRP Models Flat-Plate Model NOT pointed at the Sun θ θ
To Sun θ
Net Force
Normal
1.0
0.0
0.0
Lecture 22: SRP

20. Different SRP Models Flat-Plate Model NOT pointed at the Sun θ
Net Force θ
To Sun θ
Normal
0.0
1.0
0.0
Lecture 22: SRP

21. Different SRP Models Flat-Plate Model NOT pointed at the Sun Net Forceθ θ
To Sun θ
Normal
0.0
0.0
1.0
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22. Different SRP Models Flat-Plate Model NOT pointed at the Sun θ
Net Force θ
To Sun θ
Normal
0.33
0.33
0.33
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23. Different SRP Models
Cannonball Model
To Sun
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24. Different SRP Models Cannonball Model Fully Absorbed To Sun Net Force
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25. Different SRP Models Cannonball Model Fully Diffusely Reflected To Sun
Net Force
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26. Different SRP Models Cannonball Model Fully Specularly Reflected
To Sun
Net Force
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27. Different SRP Models Cannonball Model
1/3 absorbed, 1/3 diffused, 1/3 specular
To Sun
Net Force
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28. Earth Albedo Earth reflects sunlight Earth emits IR radiation
Moon does too.
Spacecraft
Earth
Sunlight
Lecture 22: SRP

29. Earth Albedo Earth reflects sunlight Earth emits IR radiation
Moon does too.
Spacecraft
Direct SRP
Emitted Radiation
Reflected Radiation
Earth
Sunlight
Lecture 22: SRP

30. Earth Albedo Earth reflects sunlight Earth emits IR radiation
Moon does too.
1367 Watts/m2 energy arrives at the Earth
Earth’s albedo is ~0.3
239 W/m2 is reflected away, as a diffuse/specular cannonball
The rest eventually gets emitted.
Spacecraft
Direct SRP
Emitted Radiation
Reflected Radiation
Earth
Sunlight
Lecture 22: SRP

31. Earth Albedo Earth reflects sunlight Earth emits IR radiation
Moon does too.
1367 Watts/m2 energy arrives at the Earth
Earth’s albedo is ~0.3
239 W/m2 is reflected away, as a diffuse/specular cannonball
The rest eventually gets emitted.
Spacecraft
Direct SRP
Emitted Radiation
Reflected Radiation
Earth
Sunlight
Lecture 22: SRP
Credit: NASA/GSFC

32. Solar Radiation Pressure
Shadow analysis in shadow
Cylindrical Shadow Model (Sun infinite distance from Earth)
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33. Solar Radiation Pressure
More complicated models take into account umbra/penumbra
Annular
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34. Solar Radiation Pressure
The scale illustrates how narrow the penumbra is.
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35. Shadow
Is satellite in sunlight?
Cylindrical model: b
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36. Yarkovsky Effect
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37. YORP Effect
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38. Poynting Robertson Effect
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39. Announcements Mid-Term due now! Homework #6 is due Friday 10/24
CAETE due date next week
After which I’ll talk through all of the answers!
I’ll be grading the mid-terms this Friday – about the earliest I can. I’ll hand them back after the CAETE due date.
Homework #6 is due Friday 10/24
CAETE by Friday 10/31
Concept Quiz 13 after lecture! If you pay attention to the lecture today, it’ll be easy.
Reading: Chapters 8 and 9
I have to leave my office hours early today – if you need something, please come by 2 – 2:30.
Lecture 22: SRP

40. ASEN 5050 SPACEFLIGHT DYNAMICS Atmospheric Drag
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 22: SRP

41. Atmospheric Drag
Atmospheric drag is a touch more 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 22: SRP

42. Atmospheric Drag
Drag tends to change a and e the most. The drag acceleration can be written as:
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43. Atmospheric Drag
How does this relationship impact a satellite in orbit?
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44. 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 r0 = ref density, h0 = ref. altitude, hellp = altitude, H = scale height
Lecture 22: SRP

45. Atmospheric Drag
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46. 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
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47. Atmospheric Drag
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48. Atmospheric Drag
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49. Atmospheric Models
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50. Measuring Atmospheric Density Using Satellite Data
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51. The CHAMP Mission Initial mass: 522 kg Attitude control: (2 ± 0.1)°
Along-track
Initial mass: 522 kg
Attitude control: (2 ± 0.1)°
STAR sampling rate: 1 Hz
STAR resolution: 3·10-9 m/s2/Hz0.5
Tracking: GPS and SLR
87° orbit inclination
LST precession 5.44 min/day
24-hr local time sampling in 133 days
Altitude range: km
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).
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52. Accelerometers - ONERA
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53. The STAR Reference Frame
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54. Champ Along-Track Accelerations
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55. STAR Accelerations vs Models
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56. April 15-24, 2002
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57. CHAMP Total Density at 410 km
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58. CHAMP Density at 410 km
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59. Density versus Latitude/Time
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60. Day/Night Animation
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61. North Pole Animation
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62. South Pole Animation
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63. CHAMP Coverage, Sept 1-15, 2002
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64. Total Density: September 1-14, 2002
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65. Total Density: September 1-14, 2002
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66. Total Density: September 1-14, 2002
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67. Wave Structures Observed
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68. CHAMP Density at 400 km, Ascending
303
305
304
302
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69. CHAMP Density at 400 km, Ascending
323
324
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70. Zonal Winds Observed
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71. Density Ratios: May 14 - Aug 15, 2001
DTM2000
Jacchia 70
DTM94
MSIS86
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72. Density Ratio: May 14, 2001 - May 1, 2002
DTM2000
Jacchia 70
DTM94
MSIS86
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73. Announcements Mid-term due Tuesday for CAETE students
No HW7 yet, maybe Thursday.
Next week: STK Lab 2 Tuesday and Thursday (2 sessions)
I’ll be out of town so Josh will run the lab.
Reading: Chapters 8 and 9
Lecture 22: SRP