The Neutral Atmosphere and Its Influence on Basic
Orbital Dynamics at the Edge of Space
Delores Knipp
Department of Physics
US Air Force Academy
Colorado USA
delores.knipp@usafa.af.mil
Developed by members of the Department of Physics, USAFA
Special credit to Dr Evelyn Patterson USAFA and
Dr Esther Zirbel, Yale University
Lt Omar Nava, Naval Post Graduate School
Introduction: Neutral Atmosphere & Orbital Dynamics
Objectives:
•
Motivation
Understand sources of upper
atmospheric heating
•
Concepts
– Solar Cycle-Atmosphere Interaction
Appreciate the space weather regimechange from magnetized and noncollisional to gravitationally dominated
and collisional interactions.
–
Atmospheric Density and
Temperature
–
Mechanics/Dynamics of Drag
–
Computational Concepts
•
“What Ifs”
•
Tomorrow
– Simulation
Determine the effects of neutral
atmospheric drag on the motion of
satellites that are in low enough orbits to
be affected by the Earth’s atmosphere
Explore effects of time varying
atmospheric temperature and density
Space Weather Effects
The effects of solar and magnetic storms—what scientists call space weather—extend from
beyond Earth-orbit (BEO) to geostationary orbit (GEO) to the ground (Courtesy: L Lanzerotti)
MOTIVATION
Skylab, 1978
April 9, 1979
•Track and identify active payloads and debris (DOD)
•Collision avoidance and re-entry prediction
(NASA)
•Study the atmosphere’s density and temperature profile (Science)
Impacts of the Variable Sun
As the Sun’s activity increases during
the solar cycle the Earth’s upper
atmosphere heats up and heaves up
Are Sunspots Related to Satellite Drag?
Sunspots Up Close
Courtesy La Palma Telescope
How can a Sun with more Spots be Hotter/Brighter?
Courtesy of Robert Cahalan, NASA
Where Does Energy Enter the Upper Atmosphere?
Nightside:
Dayside:
Solar EUV
Joule
Dissipation
and
and
Auroral
particles
Auroral
Particles
After Killeen et al., 1988
The Solar Spectrum
(Courtesy S Solomon)
Courtesy of Judith Lean
Geomagnetic Activity Plays a Role in Upper Atmospheric Heating
Courtesy of US Air Force
Altitude-Time Profile for a Spherical Satellite
Observed and Simulated STARSHINE-1 Altitude Vs Time
400
360
Altitude (km)
320
280
240
200
160
120
0
20
40
60
80
100
120
140
160
180
200
220
240
Time (Days)
Thin curve Simulated STARSHINE orbits
Thick curve actual STARSHINE data
260
280
Vertical Forces on a Static Parcel of Air
Fdown=(P+dP)A
z+dz
z
z
A=area
Weight
•
•
•
•
Weight = mgn(Vol)
– m = average mass of air in amu
– g = local gravitational acceleration
– n = number density of gas molecules (#/Vol)
– Vol = volume = dz * A
dP
– Change in pressure (decreases upwards)
A
– Area of horizontal surface
P = nkT
– T = temperature in °K
– k = Boltzmann constant (=1.38x10-23 J/°K)
Fup=PA
Fnet = Fup-Fdown-Weight=0
PA-(P+dP)A = Weight
-dP A
=
Weight
More realistic Pressure-Height Variation
-dP A
=
Weight
-dP A = mgn dz A
dP =d(nkT)= -mgn dz
kT (dn) = - mgn dz
dn/n=-mgdz/kT
nz/n0=exp(-mgdz/kT)
mnz/mn0=exp(-mgdz/kT)
z/  0=exp(-mgdz/kT)
Atmospheric Concepts
•
Need to know about the atmosphere in which satellites are orbiting.
The simple law of atmospheres states that, close to the earth's surface, the
atmospheric density decreases exponentially with elevation.
(z) =  0exp(-mgz/kT)
This expression assumes that the acceleration due to gravity g, the temperature T,
and the mean gas molecule mass, m, remain constant.
Altitude vs. Atmospheric Mass Density, Simple Law of Atmospheres
1200
1000
800
Altitude (km)
•
•
600
400
200
0
1.000E-17
1.000E-14
1.000E-11
1.000E-08
Atmospheric Mass Density (kg/m3)
1.000E-05
1.000E-02
1.000E+01
F  Ma y  0
Weight 

GM p m
r2

GM p ( mN )
r2

GM p ( mnV )
r2
GM p ( mnAdy )
r2
PA  W  ( P  dP ) A  Ma y  0

GM p

GM p
r2
r2
( mndy )  dP
( mndy )  k BTdn
 gRE2 m 1
R ( k BT ) r 2 dr 
E
r
n(r )

n0
dn
n
r
n(r )
 1
(const )     ln n n
0
 r  RE
 1 1
ln( n( r ))  ln no  const   
 r rE
mgR E2
n ( r )  no exp[
k BT
 1 1
  
 r rE
m ( r ) gRE2
n ( r  dr )  n( r ) exp[
k BT ( r )




]

 1 1
  
 r rE

]

Correcting for
variations in “g”
Concept: What if “g” Varies?
MSIS Atmosphere
Altitude vs. Atmospheric Mass Density, Comparing Different Models
1200
1000
Law of Atm, Corrected "g"
Law of Atm
Altitude (km)
800
600
400
200
0
1E-17
1E-14
1E-11
0.00000001
0.00001
3
Atmospheric Mass Density (kg/m )
0.01
10
Concept: What if the Temperature Varies?
MSIS Atmosphere
Altitude vs. Temperature in the Atmosphere
1200
1000
Altitude (km)
800
600
400
200
0
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
Atmospheric Temperature (K)
800.0
900.0
1000.0
1100.0
1200.0
Concept Check
The figure on the right shows
the altitude versus atmospheric
mass density curves for three
different temperatures. Which of
the following is the correct
ranking, from lowest
temperature to highest
temperature, for the three
curves shown?
a)
b)
c)
d)
A, B, C
C, B, A
B, C, A
A, C, B
Altitude vs. Atmospheric Mass Density, Comparing Different Models
1200
a
b
1000
800
Altitude (km)
MSIS Model
Hot
600
MSIS Model
Cool
400
Thermosphere
200
Law of Atmospheres
Tropo
sphere
0
1.0E-14
1.0E-11
1.0E-08
1.0E-05
Atmospheric Mass Density (kg/m3)
1.0E-02
Strato
sphere
1.0E+01
Temperature K
1.0E+04
TIEGCM Density Profile
MSIS Hot
MSIS Cool
Mechanics Concepts
Kinetic Energy
•
Satellites in orbit experience a
centripetal acceleration
•
Solve for speed
•
Associated kinetic energy


mv2
GMm
F  ma  
rˆ   2 rˆ
r
r
GM
v
r
1 2 mGM
mv 
2
2r
Mechanics Concepts
Potential and Total Energy
•
Potential Energy
Significance of “-” sign?
•
Total Mechanical Energy
•
Solve for Altitude
•
Total Mechanical Energy is constant
unless non-conservative forces act
 
GMm
   F  dr  
r
A
B
U AB
1 2
mGM
GMm
E  mv  

2
r
2r
GMm
r
 RE  h
2E
Mechanics Concepts
Drag Force and Work
•
•
Drag Force
Work Done by Drag

1
| FD | ACD v 2
2
 
1
W   F  dr   ACD v 2l
2
A
B
Assumptions
•
•
•
•
•
Circular orbit
No change in orbital parameters during the satellite period
Satellite does not tumble (A and Cd constant)
Atmosphere
– Law of Atmospheres
– MSIS Atmosphere—temperature and density
No seasonal, day/night or spatial variations in the atmospheric density
Iterative Techniques and Formulation and Graphics
Concepts
Newton’s Second Law
Energy Conservation
Newton’s Second Law
Energy Conservation…Etc
Boundary
Conditions
and Initial
Physics
New Conditions
And
Same Physics
Work Done by
Drag Force
Iterate
More Work Done
by Drag Force
Reduced
Mechanical
Energy
Satellite
De-Orbits
Iterative Technique
Orbital Drag Laboratory Worksheet
Flowchart of Orbit Decay Model:
Altitude
Initial
values
Energy
at this
altitude
Speed
Atmospheric
density
at this
altitude
(from Atmosphere
spreadsheet)
= 4.25x10-11
kg/m3
Drag Force
Work done
by drag force
in this orbit
Altitude
Next
values
Atmospheric
density
at this
altitude
Energy
at the next
orbit
Speed
Drag Force
Work done
by drag force
in this orbit
Iterative Technique
Orbital Drag Lab: Modeling Satellite Orbital Decay in a Realistic Atmosphere
1
2
529
530
M, Mass of Earth (kg) =
5.97E+24
Re, Radius of Earth (m) =
6.37E+06
Shuttle's Total
Energy (J)
Altitude
(km)
Altitude (m)
Velocity (m/s)
Drag (N)
Work Due To Drag
(J)
-2.72500E+12
-2.72504E+12
-2.72507E+12
350.0
349.9
349.8
350000.0
349905.2
349808.6
7697.8
7697.8
7697.9
0.91
0.93
0.93
-3.85E+07
-3.92E+07
-3.92E+07
-2.82766E+12
-2.93420E+12
106.0
-129.1
106026.2
-129129.3
7841.4
7987.8
2,618.47
#N/A
Total
Time
Mass Density
(hours)
0.00
1.52
3.05
(kg/m )
4.25E-11
4.32E-11
4.32E-11
797.86
799.30
6.67E-11
hi, Initial Altitude (km) =
CD, Drag Coefficient =
2
A, Cross Sectional Area of Shuttle(m )=
End
of
Orbit
#
G, Gravitational Constant (Nm2/kg2) =
91974
2
362
350
m, Mass of Shuttle (kg) =
350000
= hi in meters
3
1.18E-07
#N/A
-1.07E+11
#N/A
Initial
Typical
Concept Check
In a subsequent orbit, after work has been done by the drag
force, the satellite would have
a) less kinetic energy and less potential energy
b) more kinetic energy and less potential energy
c) less kinetic energy and more potential energy
Shuttle's Speed vs. Time
8050
8000
7950
Velocity (m/s)
7900
7850
7800
7750
7700
7650
0
100
200
300
400
500
Time (hours)
600
700
800
90
Concept Check
A satellite orbiting in a dense atmosphere will (at next orbit) be
a) at lower altitude and ahead of schedule
b) at higher altitude and ahead of schedule
c) at lower altitude and behind schedule
d) at higher altitude and behind schedule
Atmospheric Drag
EXPECTED POSITION
ACTUAL POSITION
Radar
Receiver
Time-Varying Activity
Heating Activity Level vs. Time
4
Heating Activity Level (0, 1, 2, or 3)
3
2
1
0
0
100
200
300
400
500
600
Time (hours)
700
800
900
1000
Shuttle's Altitude vs. Time
400.0
350.0
300.0
Altitude (km)
250.0
200.0
150.0
100.0
50.0
0.0
0.00
50.00
100.00
150.00
Time (hours)
200.00
250
Shuttle's Drag vs. Time
10,000.00
1,000.00
Drag (N)
100.00
10.00
1.00
0.10
0.00
50.00
100.00
150.00
Time (hours)
200.00
25
The Atmosphere can have Significant Temporal and
Spatial Variability in Temperature and Density
Location of heating associated
with low energy particles
bombarding the nightside auroral
zone
Solar EUV and Particle Power
Daily Average Solar and Particle Power Values for Solar Cycles 21-23
2500
Power (GW)
2000
1500
Cycle 21
Cycle 22
Cycle 23
Solar Power
1000
500
Particle
Power
0
1975
1977 1979
1981
1983
1985 1987
1989
1991
Year
1993 1995
1997
1999
2001 2003
2005
Joule Power –Two Hemispheres
Daily Average Joule Power Values for Solar Cycles 21-23
2500
Power (GW)
2000
1500
1000
500
0
1975
1977 1979
1981
1983
1985 1987
1989
1991
Year
1993 1995
1997
1999
2001 2003
2005
10 Most Powerful Events of Last 30 Years
(Knipp et al., 2005)
Daily Average Power Values for Solar Cycles 21-23
3500
15 Apr
7 Jul
79
3000
82
2500
Power (GW)
SKYLAB
Reenters
2000
3 Mar
10 Oct
89
89
NORAD
Space
Tracking
Disrupted
6 Jun
91
5 May
15&16 Jul 6 Nov
92
00
01
30 Oct
03
Japanese
Satellite
Malfunction
Attributed
to Satellite
Drag
Solar Power
1500
1000
500
Total
Power
Joule
Power
Particle
Power
0
1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Altitude Profile
nominal
Level 3
disturbance at
hr 100 for 10 hr
Return to nominal
Level 2
Disturbance
All Hours
Altitude
Mechanical Energy
Speed
Drag Force
Orbital Drag Lab: Boundary Values for Space Shuttle Orbit
m, Mass of Shuttle (kg) =
CD, Drag Coefficient =
A, Cross Sectional Area of Shuttle(m2)=
hi, Initial Altitude (km) =
91974
2
362
350
G, Gravitational Constant (Nm2/kg2) =
6.67E-11
M, Mass of Earth (kg) =
5.97E+24
Re, Radius of Earth (m) =
6.37E+06
Ideal and model atmospheres
Altitude vs. Atmospheric Mass Density, Comparing Different Models
1200
MSIS Model (T + 20%)
MSIS Model (T + 10%)
MSIS Model (T + 5%)
MSIS Model (Std. Temp)
Law of Atm, Corrected "g" & T
Law of Atm, Corrected "g"
Law of Atm
1000
Altitude (km)
800
600
400
200
0
1.000E-17
1.000E-14
1.000E-11
1.000E-08
Atmospheric Mass Density (kg/m3)
1.000E-05
1.000E-02
1.000E+01
Iterative Technique
NAME _______
SECTION_____
Altitude
Initial
values
Energy
at this
altitude
GMm
E 
2r
 2.725 x10 12 J
h  350 ,000 m
(from Atmosphere
spreadsheet)
= 4.25x10-11 kg/m3
Speed
v
GM

r
Atmospheric
density
at this
altitude
Drag Force
1
 AC D v 2
2
 0 .91 N
GM
RE  h
FD 
 7697 .8m/s
WD


Altitude
E 
Next
values
Energy
at the next
orbit
GMm
2r
 r  RE  h  
 GMm
2E
GMm
 RE
2E
 349905 m
 h
Ethis  Elast  Wlast
Speed
 2.725x1012 J
v
GM

r
 7697 .8m/s
GM
RE  h
Atmospheric
density
at this
altitude
(from Atmosphere
spreadsheet)
= 4.32x10-11 kg/m3
Drag Force
1
AC D v 2
2
 0.93 N
FD 
Plot characteristics of satellites (in near circular orbit)
under the influence of drag
Velocity
Shuttle's Altitude vs. Time
400.0
8050.0
350.0
8000.0
300.0
7950.0
250.0
7900.0
Velocity (m/s)
Altitude (km)
Altitude
200.0
7850.0
150.0
7800.0
100.0
7750.0
50.0
7700.0
0.0
Shuttle's Velocity vs. Time
7650.0
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
900.00
0.00
100.00
200.00
300.00
400.00
Time (hours)
Mechanical Energy
600.00
700.00
800.00
900.00
600.00
700.00
800.00
900.00
Drag Force
Shuttle's Total Mechanical Energy vs. Time
Shuttle's Drag vs. Time
10,000.00
-2.72400E+12
0.00
500.00
Time (hours)
50.00
100.00
150.00
200.00
250.00
300.00
350.00
400.00
450.00
500.00
-2.72600E+12
1,000.00
-2.73000E+12
100.00
Drag (N)
Total Mechanical Energy (J)
-2.72800E+12
-2.73200E+12
-2.73400E+12
10.00
-2.73600E+12
-2.73800E+12
1.00
-2.74000E+12
0.10
-2.74200E+12
0.00
Time (hours)
100.00
200.00
300.00
400.00
Time (hours)
500.00
Are Lab Results Realistic?
Observed and Simulated STARSHINE-1 Altitude Vs Time
400
360
Altitude (km)
320
280
240
200
160
120
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
Time (Days)
Thin curve Simulated STARSHINE orbits with MSIS temperature-6%
Thick curve actual STARSHINE data
Concept: Temporal Variations in Heating
Shuttle's Altitude vs. Time
400.0
350.0
300.0
250.0
Altitude (km)
Shuttle's Altitude vs. Time
400.0
Level 0 Activity Orbital Decay
Level 1 Activity Orbital Decay
350.0
Level 2 Activity Orbital Decay
200.0
150.0
Level 3 Activity Orbital Decay
300.0
100.0
50.0
200.0
0.0
0.00
50.00
100.00
150.00
100.0
250.00
Solar Activity Level vs. Time
4
50.0
0.0
0.00
200.00
Time (hours)
150.0
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
900.00
Time (hours)
Altitude vs Time Profiles for
0,5,10 and 20%
Temperature Increases
3
Solar Activity Level (0, 1, 2, or 3)
Altitude (km)
250.0
2
1
0
0
100
200
300
400
500
600
Time (hours)
Impulsive heating event
700
800
900
1000
1100
Sources of Temporal Variations
•
•
•
Solar Cycle variations (Proxy
F10.7 cm index)
Day to Day solar variations (Solar
Flare) (Proxy F10.7 cm index)
– Minimal effects except in most
extreme cases
– Short-lived
Daily Geomagnetic Heating
Variations (Magnetic Storm) (Ap
Index)
– Maybe long lived if under
certain solar wind conditions
• Shock followed by Mass
Ejection followed by High
Speed Stream
Daily Average Power Values for Solar Cycles 21-23
3500
Jul 14
1982
Mar 13
1989
Oct 21
1989
Jun 6 Jul 13 May 10
1991 1991 1992
Jul 14
2000
Mar 31
2001
Nov 6 & 24
2001
3000
Power (GW)
2500
2000
Solar
Power
1500
Total
Power
1000
Joule
Power
500
Particle
Power
0
1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Year
Concept: What if the Temperature Varies?
Shuttle's Altitude vs. Time
400
8050
350
8000
300
7950
Altitude (km)
250
Altitude Profile
Using Hot Model
Atmosphere
7900
7850
200
150
Velocity Profile
Using Hot Model
Atmosphere +5%
100
7800
Velocity Profile
Using Hot Model
Atmosphere
7750
50
7700
0
0
100
200
300
400
500
Time (hours)
600
700
800
7650
900
Speed (m/s)
Altitude Profile
Using Hot Model
Atmosphere +5%
Solar Spectrum