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ASEN 5050
SPACEFLIGHT DYNAMICS
Solar Radiation Pressure
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 22: SRP
1
Announcements
• Mid-Term due now!
– 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
2
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
3
Final Project
•
Instructions for delivery of the final project:
•
Build your webpage with every required file inside of a directory.
–
–
–
•
Name your main web page “index.html”
–
•
Name the directory “<LastName_FirstName>”
there are a lot of duplicate last names in this class!
You can link to external sites as needed.
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
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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
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Comet Siding Spring
Opportunity’s image from the Martian surface
Lecture 22: SRP
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Comet Siding Spring
MRO’s view of the nucleus – smaller than estimates indicated!
138 m/pixel – maybe 500 meters in size
Lecture 22: SRP
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ASEN 5050
SPACEFLIGHT DYNAMICS
Perturbations
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 22: SRP
8
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
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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
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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?
Force of Gravity:
Net Force of SRP:
•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)
•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)
• When/Why/How is SRP any different than gravity?
Lecture 22: SRP
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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
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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
3.823 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
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Solar Radiation Pressure
The acceleration due to solar radiation pressure is:
Unit vector from satellite to Sun
Lecture 22: SRP
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Solar Radiation Pressure
• Absorption
• Reflection: diffuse and specular
The light is either absorbed,
reflected diffusely, or
reflected specularly.
Depends on the material,
wavelength, and surface!
Lecture 22: SRP
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Solar Radiation Pressure
Fully absorbed
Fully diffusely reflected
Fully specularly reflected
Net force
All light is either absorbed, diffusely
reflected, or specularly reflected!
Lecture 22: SRP
Net force
Net force
16
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, 1.5 = combination of absorption,
diffuse reflection, and specular reflection, 2 = specular
To Sun
Lecture 22: SRP
Normal
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Different SRP Models
• Flat-Plate Model
– NOT pointed at the Sun
To Sun
θ
θ
θ
Normal
Lecture 22: SRP
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Different SRP Models
• Flat-Plate Model
– NOT pointed at the Sun
To Sun
θ
θ
θ
Net Force
Normal
1.0
Lecture 22: SRP
0.0
0.0
19
Different SRP Models
• Flat-Plate Model
– NOT pointed at the Sun
To Sun
θ
θ
Net Force
θ
Normal
0.0
Lecture 22: SRP
1.0
0.0
20
Different SRP Models
• Flat-Plate Model
– NOT pointed at the Sun
To Sun
Net Force
θ
θ
θ
Normal
0.0
Lecture 22: SRP
0.0
1.0
21
Different SRP Models
• Flat-Plate Model
– NOT pointed at the Sun
To Sun
θ
θ
Net Force
θ
Normal
0.33
Lecture 22: SRP
0.33
0.33
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Different SRP Models
• Cannonball Model
To Sun
Lecture 22: SRP
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Different SRP Models
• Cannonball Model
To Sun
Lecture 22: SRP
Fully Absorbed
Net Force
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Different SRP Models
• Cannonball Model
To Sun
Lecture 22: SRP
Fully Diffusely Reflected
Net Force
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Different SRP Models
• Cannonball Model
To Sun
Lecture 22: SRP
Fully Specularly Reflected
Net Force
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Different SRP Models
• Cannonball Model
To Sun
Lecture 22: SRP
1/3 absorbed, 1/3 diffused, 1/3 specular
Net Force
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Earth Albedo
• Earth reflects sunlight
• Earth emits IR radiation
• Moon does too.
Spacecraft
Sunlight
Earth
Lecture 22: SRP
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Earth Albedo
• Earth reflects sunlight
• Earth emits IR radiation
• Moon does too.
Spacecraft
Direct SRP
Emitted Radiation
Reflected Radiation
Sunlight
Earth
Lecture 22: SRP
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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
Sunlight
Earth
Lecture 22: SRP
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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
Sunlight
Earth
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Lecture 22: SRP
Credit: NASA/GSFC
Solar Radiation Pressure
Shadow analysis aSRP = 0 in shadow
Cylindrical Shadow Model (Sun infinite distance from Earth)
Lecture 22: SRP
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Solar Radiation Pressure
More complicated models take into account umbra/penumbra
Annular
Lecture 22: SRP
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Solar Radiation Pressure
The scale illustrates how narrow the penumbra is.
Lecture 22: SRP
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Shadow
Is satellite in sunlight?
Cylindrical model:
rSAT
rSUN
b
rSHADE
rSHADE = 6378 km
cos b =
rSAT × rSUN
rSAT rSUN
If b > 90° then
If rSATsinb > rSHADE ® In Sunlight
Lecture 22: SRP
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Yarkovsky Effect
Lecture 22: SRP
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YORP Effect
Lecture 22: SRP
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Poynting Robertson Effect
Lecture 22: SRP
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Announcements
• Mid-Term due now!
– 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
39
ASEN 5050
SPACEFLIGHT DYNAMICS
Atmospheric Drag
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 22: SRP
40
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
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Atmospheric Drag
Drag tends to change a and e the most. The drag acceleration can
be written as:
1 CD A
2 Vrel
adrag = -
2 m
r Vrel
Vrel
C D = coefficient of drag, dimensionless, susceptibility to drag forces, ~ 2
CD A
m
= ballistic coefficient (
)
m
CD A
r = atmospheric density
A = cross - sectional area normal to the sat' s velocity vector é dx
ù
+
w
x
Å ú
ê dt
Þ need attitude
ê dy
ú
dr
Vrel = velocity relative to a rotating atmosphere = - wÅ ´ r = ê - wÅ y ú
dt
ê dt
ú
dz
ê
ú
êë dt úû
Lecture 22: SRP
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Atmospheric Drag
• How does this relationship impact a satellite in orbit?
1 CD A
2 Vrel
adrag = r Vrel
2 m
Vrel
Lecture 22: SRP
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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:
h -h
r = r0 e
-
ellp
0
H
where r0 = ref density, h0 = ref. altitude, hellp = altitude,
H = scale height
Lecture 22: SRP
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Atmospheric Drag
r = r0
Lecture 22: SRP
hellp -h0
e H
45
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 22: SRP
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Atmospheric Drag
Lecture 22: SRP
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Atmospheric Drag
Lecture 22: SRP
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Atmospheric Models
Lecture 22: SRP
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Measuring Atmospheric Density
Using Satellite Data
Lecture 22: SRP
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The CHAMP Mission
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).
Lecture 22: SRP
• 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: 460-250 km
51
Accelerometers - ONERA
http://www.onera.fr
Lecture 22: SRP
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The STAR Reference Frame
Lecture 22: SRP
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Champ Along-Track Accelerations
Lecture 22: SRP
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STAR Accelerations vs Models
Lecture 22: SRP
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April 15-24, 2002
Lecture 22: SRP
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CHAMP Total Density at 410 km
Lecture 22: SRP
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CHAMP Density at 410 km
Lecture 22: SRP
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Density versus Latitude/Time
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Day/Night Animation
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North Pole Animation
Lecture 22: SRP
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South Pole Animation
Lecture 22: SRP
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CHAMP Coverage, Sept 1-15, 2002
Lecture 22: SRP
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Total Density: September 1-14, 2002
Lecture 22: SRP
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Total Density: September 1-14, 2002
Lecture 22: SRP
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Total Density: September 1-14, 2002
Lecture 22: SRP
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Wave Structures Observed
Lecture 22: SRP
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CHAMP Density at 400 km, Ascending
304
305
303
302
Lecture 22: SRP
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CHAMP Density at 400 km, Ascending
323
324
Lecture 22: SRP
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Zonal Winds Observed
Lecture 22: SRP
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Density Ratios: May 14 - Aug 15, 2001
Density Ratio: Observed / DTM2000, May 14 - Aug 15, 2001
90
60
60
30
30
Latitude
90 DTM2000
0
Jacchia 70
0
-30
-30
-60
Density Ratio: Observed
/ MSIS86
-60
-90
90
Density Ratio: Observed/DTM94,
May 14 - Aug 15, 2001
Observed
/ MSIS86,
May1614 - Aug20
15, 2001 24
0Density Ratio:
4
8
12
0
4
8
12
16
20
24
Local Time
90
60Time
90
Local
DTM94
-90
MSIS86
0.5
0.7
0
30
60
0
0.8 1.0 1.2
Density
-30 Ratio
-30
-60
-60
-90
1.3
0
4
8
0.7
0
-60
12
Local Time
1
3
16
20
0.5
Lecture 22:0.5
SRP
0.5 0.6 0.8 0.9 1.1 1.2 1.4 1.5
time1_doc_14
30
-30
0
-90
1.5
Latitude
30
Latitude
60
0.8 1.0 1.2
Density Ratio
1.3
1.5
0.7
-90
24 Kp
4
6
0
0.8 1.0 1.2
Density Ratio
4
1.3
7
8
12
Local Time
16
20
24
1.5
0.5
0.7
0.8 1.0 1.2
Density Ratio
1.3
1.5
71
Density Ratio: Observed
/ DTM2000
Density
Ratio:
May 14, 2001 - May 1, 2002
90
90
DTM2000
60
30
30
Latitude
60
0
Jacchia 70
0
-30
-30
Density Ratio:-60
Observed / MSIS86
-60
90
Density Ratio: Observed / DTM94
0
1
3
4
6
60
90
Kp
DTM94
30
60
-90
-90
0
0
0.70 0.90 1.10 1.30
-30
Density Ratio
-30
-60
-60
-90
Latitude
0.50
1
3
3
3
30
4
6
0.70
7
0
-60
4
6
1
6
7
0.90 1.10 1.30
Density Ratio
7
3
4
Kp
0.5
0.50
6
0.5 0.6 0.8 0.9 1.1 1.2 1.4
all_dat1_14_md
Kp
Lecture 22: SRP
4
Kp
MSIS86
-90Kp
0
7
-90
1
1
-30
0
0
90
60
Latitude
30
7
Density Ratio: Observed / MSIS86
0
0.7
0.8 1.0 1.2
Density Ratio
1.3
1.5
0.5
0.7
0.8 1.0 1.2
Density Ratio
1.3
1.5
72
Announcements
•
•
Mid-term due Tuesday for CAETE students
No HW7 yet, maybe Thursday.
•
Next week: STK Lab 2 Tuesday and Thursday (2 sessions)
–
•
Lecture 22: SRP
I’ll be out of town so Josh will run the lab.
Reading: Chapters 8 and 9
73