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Atmospheric Drag
Modeling the Space Environment
Manuel Ruiz Delgado
European Masters in Aeronautics and SpaceE.T.S.I. Aeronauticos
Universidad Politecnica de Madrid
April 2008
Atmospheric Drag – p. 1/29
Atmospheric Drag
Imag
eco
urte
syN
AS
A
Effects of Air Drag: MIR Station Reentry March 22, 2001Watch MIR deorbit video on Youtube (simulation by AGI)
Atmospheric Drag – p. 3/29
Aerodynamic Drag
Space AerodynamicsPerturbations of Keplerian motionFree molecular flowBallistic coefficientDrag computation
High atmosphereStructure of the atmosphereSun influence:F10.7
Geomagnetic activity influence:Kp
Atmospheric ModelsStatic: Exponential, Harris-Priester, US StandardDynamic: Jacchia, MSISE, COSMOS
Atmospheric Drag – p. 4/29
Perturbations of Keplerian Motion
1e−008
1e−006
0.0001
0.01
1
100
10000
1e+006
0 100 200 300 400 500 600 700 800 900
Acc
eler
atio
n (m
/s2 )
Height (km)
Accelerations of the Satellite (BC=50)
Shuttle
ISS
KeplerJ2
C22Sun
MoonDrag (low)
Drag (high)Prad
Atmospheric Drag – p. 5/29
Perturbations of Keplerian Motion
1e−008
1e−006
0.0001
0.01
1
100
10000
1e+006
0 5000 10000 15000 20000 25000 30000 35000 40000
Acc
eler
atio
n (m
/s2 )
Height (km)
Accelerations of the Satellite (BC=50)
GEOGPS
KeplerJ2
C22Sun
MoonDrag (low)
Drag (high)Prad
Atmospheric Drag – p. 6/29
Space Aerodynamics
Free molecular flow: Knudsen No. ≫ 1
Molecules interact one by one with the body: incident flow notdisturbedby the body.
Space Aerodynamics
Free molecular flow: Knudsen No. ≫ 1
Molecules interact one by one with the body: incident flow notdisturbedby the body.
Kn =L
d=
Ma
Re
L : Mean free path of the moleculesd : Characteristic longitude of satellite
Space Aerodynamics
Free molecular flow: Knudsen No. ≫ 1
Molecules interact one by one with the body: incident flow notdisturbedby the body.
Kn =L
d=
Ma
Re
L : Mean free path of the moleculesd : Characteristic longitude of satellite
Kn ≫ 1 Free molecular flow Space environmentKn ∼ 1 Transition (Complex: reentry)Kn ≪ 1 Continuum flow Classical aerodynamics
ECSS-E-10-04A definesKn > 3 as free molecular regime
Free molecular flow over 150 km (small satellites) or 250 km(shuttle, ISS)
Atmospheric Drag – p. 7/29
Impact Types
θ θp1 p2
n
Elastic impact: p2 = p1 + 2p1 cos θn
Drag coefficient: CD = 4
p1p2
n
Diffuse refflection: p2 = p1/2
Drag coefficient: CD = 2 − 4
Impact Types
θ θp1 p2
n
Elastic impact: p2 = p1 + 2p1 cos θn
Drag coefficient: CD = 4
p1p2
n
Diffuse refflection: p2 = p1/2
Drag coefficient: CD = 2 − 4
p1
Absorption (diffuse emission later): p2 = 0
Drag coefficient: CD = 2
p1
Abrasion: p2 =?Atmospheric Drag – p. 8/29
Atmospheric Drag
xy
z dA⊥
v
θ
v∆t
Force over the surfacedA⊥, incidence angleθ:
∆m = ρvdA⊥∆t ⇒ dF =∆p
∆t= ρv2[1 + f(θ)]dA⊥
Atmospheric Drag
xy
z dA⊥
v
θ
v∆t
Force over the surfacedA⊥, incidence angleθ:
∆m = ρvdA⊥∆t ⇒ dF =∆p
∆t= ρv2[1 + f(θ)]dA⊥
Integrating over the whole surface gives the dragacceleration:
aD =D
m= −
1
2
CDA
mρ |vrel|vrel
Atmospheric Drag
xy
z dA⊥
v
θ
v∆t
Force over the surfacedA⊥, incidence angleθ:
∆m = ρvdA⊥∆t ⇒ dF =∆p
∆t= ρv2[1 + f(θ)]dA⊥
Integrating over the whole surface gives the dragacceleration:
aD =D
m= −
1
2
CDA
mρ |vrel|vrel
Lateral drag: CD = CD⊥ + CD‖A‖
A⊥
vrel
vt Orbital speed:vrel ∼ 8 km/s
Thermal speed:vt ∼ 1 km/s (12mv2 = 3
2kT )
Important for light or svelte craft
Atmospheric Drag – p. 9/29
Atmospheric Drag
aD =D
m= −
1
2
CDA
mρ |vrel| vrel
vrel Speed relative to the atmosphere Rotation, winds
Atmospheric Drag
aD =D
m= −
1
2
CD A
mρ |vrel|vrel
vrel Speed relative to the atmosphere Rotation, winds
CD Drag Coefficient: difficult to measure
CD ∼ 2 − 2.4 (1-4)
Atmospheric Drag
aD =D
m= −
1
2
CD A
mρ |vrel|vrel
vrel Speed relative to the atmosphere Rotation, winds
CD Drag Coefficient: difficult to measure
CD ∼ 2 − 2.4 (1-4)
A Frontal area depends on attitude
Atmospheric Drag
aD =D
m= −
1
2
CDA
mρ |vrel|vrel
vrel Speed relative to the atmosphere Rotation, winds
CD Drag Coefficient: difficult to measure
CD ∼ 2 − 2.4 (1-4)
A Frontal area depends on attitude
ρ Atmospheric density: ∼ 15% error
Atmospheric Drag
aD =D
m= −
1
2
CDA
mρ |vrel|vrel
vrel Speed relative to the atmosphere Rotation, winds
CD Drag Coefficient: difficult to measure
CD ∼ 2 − 2.4 (1-4)
A Frontal area depends on attitude
ρ Atmospheric density: ∼ 15% error
β =m
CDABallistic coefficient: (β ↑, aD ↓)
Some authors use the opposite form: BC=CDA
m
Atmospheric Drag – p. 10/29
Computing Drag
4 problems:
Calibrating CD or β : Differential Correction MapleOD
Propagating orbits with drag:atmospheric model
Computing satellite lifetime: averaged equations King-Hele
Atmospheric research
Computing Drag
4 problems:
Calibrating CD or β : Differential Correction MapleOD
Propagating orbits with drag:atmospheric model
Computing satellite lifetime: averaged equations King-Hele
Atmospheric research
Effects on the orbit
Seculars:a ↓, e ↓→ Reentry Spiral Maplanim
Circularization phase Mir ISS
Spiral phase: reenty Mars
Periodic:Ω, ω, i (through atmospheric rotation)
Atmospheric Drag – p. 11/29
Structure of the Atmosphere
km
100
101
102
103
Sea Level
Tropopause
Stratopause
Mesopause
Thermopause
Troposphere
Stratosphere
Iono
sphe
re
Mesosphere
Thermosphere
Exosphere
Mt Everest
Clouds↑
ISS, Shuttle
Dominant constituent
N2
O
He
Atmospheric Drag – p. 12/29
Constituents - Solar low
1e−010
1e−005
1
100000
1e+010
1e+015
1e+020
1e+025
1e+030
0 100 200 300 400 500 600 700 800 900
Den
sity
(m
olec
/m3 )
Height (km)
Constituents: Low Solar Activity
N2O
O2HeArHN
Atmospheric Drag – p. 13/29
Exospheric TemperatureT∞ vs Solar Activity
0
200
400
600
800
1000
1200
1400
1600
1800
0 100 200 300 400 500 600 700 800 900
T (
ºK)
Height (km)
HighMeanLow
Atmospheric Drag – p. 14/29
Density vs Solar Activity
1e−016
1e−014
1e−012
1e−010
1e−008
1e−006
0.0001
0.01
1
100
0 100 200 300 400 500 600 700 800 900
Den
sity
(kg
/m3 )
Height (km)
HighMeanLow
Atmospheric Drag – p. 15/29
Location-Related Changes
In Static Models,properties change only withlocation:
*** Height: Hydrostatic equilibrium⇒ ρ = ρ0eh0−h
H hell
Location-Related Changes
In Static Models,properties change only withlocation:
*** Height: Hydrostatic equilibrium⇒ ρ = ρ0eh0−h
H hell
** Latitude:change ofheight through flattening φg
Height over the Ellipsoidchanges with longitude:∆hell = 0 − 21 km ⇔ ∆ρ
S
S
h
h'' S
h'
φg
E
ell
ell
ell
hcir
Location-Related Changes
In Static Models,properties change only withlocation:
*** Height: Hydrostatic equilibrium⇒ ρ = ρ0eh0−h
H hell
** Latitude:change ofheight through flattening φg
Height over the Ellipsoidchanges with longitude:∆hell = 0 − 21 km ⇔ ∆ρ
S
S
h
h'' S
h'
φg
E
ell
ell
ell
hcir
* Longitude: λg
Temporal change (day/night) Subsolar hump
Small space variation (seas, mountains→ atmosphere), mainlyat low heights.
Atmospheric Drag – p. 16/29
Causes of Time-Related Changes
In Time-varying Models,properties change withlocationandtime:
Solaractivity
Internalgeomagnetic
field
Sunspots
UV/EUVradiation
Solarwind
Geomagneticactivity Index
Kp / Ap
IndexF10.7
Densityρ(t)
Atmospheric Drag – p. 17/29
Time Changes Due to the Sun
Sunspot 11 year cycle: ∼ 85%Sunspot Number∼ EUV (10-120 nm)⇒ T∞ ⇒ ρ
EUV not measurable: PROXYF10,7 ,(
F10.7
)
81
Imag
eco
urte
syN
AS
A
Atmospheric Drag – p. 18/29
Time Changes: Sun and Geomagnetic Field
Diurnal variations: ∼ 15%
Solar UV radiation heats up the atmosphere:ρ ↑
Max: subsolar hump, delayed 2-2:30 pm. Antipod MinDensity ρ depends on:
Apparent local solar time LHA⊙ of satellite jach/hed
Solar declination δ⊙
Geodetic latitude φg of satellite
Time Changes: Sun and Geomagnetic Field
Diurnal variations: ∼ 15%
Solar UV radiation heats up the atmosphere:ρ ↑
Max: subsolar hump, delayed 2-2:30 pm. Antipod MinDensity ρ depends on:
Apparent local solar time LHA⊙ of satellite jach/hed
Solar declination δ⊙
Geodetic latitude φg of satellite
Magnetic storms:
Earth field’s fluctuations: small effectSolar storms: short but large effect: Up to30%
Influence ρ through the geomagnetic indicesKp or Ap
Atmospheric Drag – p. 19/29
Other Changes
Solar rotation period of 27 days: Variable 0 − 10%Visible sunspots change
EUV radiation changes
Affects ρ through F10.7 and(
F10.7
)
81(81 day average)
Other Changes
Solar rotation period of 27 days: Variable 0 − 10%Visible sunspots change
EUV radiation changes
Affects ρ through F10.7 and(
F10.7
)
81(81 day average)
Semi-annual variation:Sun distance changes. Small
Cyclical variations:11-year cycles are not regular.ESA’s standardcycle. Small
Atmospheric rotation:difficult to know. Decreases with height.Co-rotation is a good estimate. < 5%
Winds: Not well known. Models not mature. Low orbits. Small
Tides:The atmosphere also suffers tides. Models. Small
Atmospheric Drag – p. 20/29
Data Sources
Before Space Age: nothing known about the properties of theatmosphere above 150 km
Early satellites: orbit tracking. AssumeCD, computeρ
Careful with NORAD TLE’sn: may include other accelerations
On-board accelerometers: non-gravitational accelerations
On-board mass spectrometers: chemical composition, temperature
Incoherent scatter ground-based radar: electron and ion distribution,which is related to neutral density and composition
Atmospheric Drag – p. 21/29
Static Models
Properties
Simple, low computation time, reasonable results
Good for theoretical or long-range studies (averaged)
Errors up to 40% (Mean Sun) or 60% (High Sun)
Time-varying models also have errors (∼15%)
Static Models
Properties
Simple, low computation time, reasonable results
Good for theoretical or long-range studies (averaged)
Errors up to 40% (Mean Sun) or 60% (High Sun)
Time-varying models also have errors (∼15%)
Exponential structure:
Spherical symmetry, co-rotating with Earth
Hydrostatic equilibrium + perfect gas:ρ = ρ0eh0−h
H
Reference density and height,ρ0, h0
Scale heightH (changes withh!)
Atmospheric Drag – p. 22/29
Static Models
US Standard Atmosphere 62, 76 (0-1000 km)
Tabulated
Ideal, stationary atmosphere, at 45oN, moderate solar activity
CIRA 65-90 (0-2500 km)
COSPAR-International Reference Atmosphere.
CIRA-72 and -86 incorporate dynamic models forh > 100km
Harris-Priester (0-1000 km)
Static. Fast. Tabulated forT∞ ⇒ Interpolate
Includessubsolar hump(only LHA⊙ , equinoctial)
Atmospheric Drag – p. 23/29
Time-Varying Models
Comprehensive: include all the main effects
Inherent errors: unpredictable Sun, proxies, data fit ∼ 15%
Better with past measured data. Reasonable predictions
Numerically intensive
Time-Varying Models
Comprehensive: include all the main effects
Inherent errors: unpredictable Sun, proxies, data fit ∼ 15%
Better with past measured data. Reasonable predictions
Numerically intensive
Jacchia-Roberts (65,71,77, 81) (70-700 km)
The first.Uses satellite data. Late, also ISR
Profile for T∞(F10,7, F 10,7,Kp, φg, λ, δ⊙, LHA⊙, MJD, UT)
Numerical int.diffusion PDE of each constituent:ρ(h) .
Roberts:Integrate several profiles, tabulated polynomial fit
Computationally intensive FORTRAN: MET/71, 77
ValladoandMontenbruckdescribe different modifications of the Jacchia model
Atmospheric Drag – p. 24/29
Time-Varying Models
MSIS 83, 86, MSISE 90, 2000 (0-2000 km)
Mass Spectrometer & Incoherent Scatter +satellite tracking
Profile T∞(JD, hel, λg, φg, LST, F10.7, F10.7, Api, Api)
Diffusion PDE for each constituent:1ni
dni
dh + 1
Hi+ 1+αi
TdTdh = 0 ,
series integration (faster)
Add partial densities:ρ(h) =∑
ρi
More recent, faster, exact;J-R still better in some cases
ESA recommended standard/ Mean cycle for predictions
FORTRAN code available/ Indices data sources:• ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/
• http://celestrak.com/SpaceData/ (AverageF107 computed)
Atmospheric Drag – p. 25/29
Time-Varying Models
COSMOS (160-600 km)
Tracking data fit of the COSMOS satellites
ρ = ρn k1 k2 k3 k4
ρn - Night density profile: exponential
k1 - Solar activity correction,F10.7, 4 values
k2 - Day/Night correction
k3 - Semi-annual correction (small)
k4 - Geomagnetic correction,ap
Very simple, modular, fast, available(cf. Vallado)
Good for orbits similar to the COSMOS satellites
“Density Model for Satellite Orbit Predictions.” GOST 25645-84
Atmospheric Drag – p. 26/29
Comparison of Time-Varying Models
Model CPU ∆ρ ∆ρmax
Jacchia 71 1,00 - -Jacchia-Roberts 0,22 0,01 0,03Jacchia-Lineberry 0,43 0,13 0,35Jacchia-Gill 0.11 0,02 0,08Jacchia 77 10,69 0,13 0,35Jacchia-Lafontaine 0,86 0,13 0,36MSIS 77 0,06 0,18 0,53MSIS 86 0,32 0,21 1,45TD88 0,01 0.91 7,49DTM 0,03 0,40 1,22
Data from Montenbruck, p. 100
Atmospheric Drag – p. 27/29
Conclusions
Atmospheric Drag is significant between 200-700 km
Uncertainties inCD, ρ, A
Static models have large erros
Time-varying models’ typical error is about15%Because of the model: indirect proxyBecause of the Sun’s uncertaintyBecause of the fast solar storms
Density is the heaviest computation load of orbit propagation
Use the simplest model within the required precision
New models coming, error down to5% : Solar-2000, HASDM
Space sensors allow direct measuring of EUV, without proxies
Atmospheric Drag – p. 28/29