Atmospheric Drag. Modeling the Space Environment. Manuel Ruiz Delgado. European Masters in Aeronautics and Space

Transcription

1 Atmospheric Drag p. 1/29 Atmospheric Drag Modeling the Space Environment Manuel Ruiz Delgado European Masters in Aeronautics and Space E.T.S.I. Aeronáuticos Universidad Politécnica de Madrid April 2008

2 Atmospheric Drag Atmospheric Drag p. 2/29 Image courtesy NASA

3 Atmospheric Drag Atmospheric Drag p. 3/29 Effects of Air Drag: MIR Station Reentry March 22, 2001 Watch MIR deorbit video on Youtube (simulation by AGI) Image courtesy NASA

4 Aerodynamic Drag Atmospheric Drag p. 4/29 Space Aerodynamics Perturbations of Keplerian motion Free molecular flow Ballistic coefficient Drag computation High atmosphere Structure of the atmosphere Sun influence: F 10.7 Geomagnetic activity influence: K p Atmospheric Models Static: Exponential, Harris-Priester, US Standard Dynamic: Jacchia, MSISE, COSMOS

5 Perturbations of Keplerian Motion Acceleration (m/s 2 ) 1e Accelerations of the Satellite (BC=50) Shuttle ISS Kepler J 2 C 22 Sun Moon Drag (low) Drag (high) P rad 1e 006 1e Height (km) Atmospheric Drag p. 5/29

6 Perturbations of Keplerian Motion Acceleration (m/s 2 ) 1e Accelerations of the Satellite (BC=50) GPS Kepler J 2 C 22 Sun Moon Drag (low) Drag (high) P rad GEO 1e 006 1e Height (km) Atmospheric Drag p. 6/29

7 Space Aerodynamics Free molecular flow: Knudsen No. 1 Molecules interact one by one with the body: incident flow not disturbed by the body.

8 Space Aerodynamics Free molecular flow: Knudsen No. 1 Molecules interact one by one with the body: incident flow not disturbed by the body. K n = L d = Ma Re { L : Mean free path of the molecules d : Characteristic longitude of satellite

9 Space Aerodynamics Atmospheric Drag p. 7/29 Free molecular flow: Knudsen No. 1 Molecules interact one by one with the body: incident flow not disturbed by the body. K n = L d = Ma Re { L : Mean free path of the molecules d : Characteristic longitude of satellite K n 1 Free molecular flow Space environment K n 1 Transition (Complex: reentry) K n 1 Continuum flow Classical aerodynamics ECSS-E-10-04A defines Kn > 3 as free molecular regime Free molecular flow over 150 km (small satellites) or 250 km (shuttle, ISS)

10 Impact Types n θ θ p 1 p 2 Elastic impact: Drag coefficient: C D = 4 p 2 = p 1 + 2p 1 cosθn p 1 n p 2 Diffuse refflection: p 2 = p 1 /2 Drag coefficient: C D = 2 4

11 Impact Types n θ θ p 1 p 2 Elastic impact: Drag coefficient: C D = 4 p 2 = p 1 + 2p 1 cosθn p 1 n p 2 Diffuse refflection: p 2 = p 1 /2 Drag coefficient: C D = 2 4 p 1 Absorption (diffuse emission later): p 2 = 0 Drag coefficient: C D = 2 p 1 Atmospheric Drag p. 8/29

12 Atmospheric Drag Force over the surface da, incidence angle θ: x m = ρvda t df = p t = ρv2 [1 + f(θ)]da θ z v t da y v

13 Atmospheric Drag Force over the surface da, incidence angle θ: x m = ρvda t df = p t = ρv2 [1 + f(θ)]da Integrating over the whole surface gives the drag acceleration: θ z v t da y v a D = D m = 1 2 C D A m ρ v rel v rel

14 Atmospheric Drag Atmospheric Drag p. 9/29 Force over the surface da, incidence angle θ: x m = ρvda t df = p t = ρv2 [1 + f(θ)]da Integrating over the whole surface gives the drag acceleration: θ z v t da y v a D = D m = 1 2 C D A m ρ v rel v rel Lateral drag: C D = C D + C D A A v rel v t Orbital speed: v rel 8 km/s Thermal speed: v t 1 km/s ( 1 2 mv2 = 3 2 kt ) Important for light or svelte craft

15 Atmospheric Drag a D = D m = 1 2 C D A m ρ v rel v rel v rel Speed relative to the atmosphere Rotation, winds

16 Atmospheric Drag a D = D m = 1 C D A 2 m ρ v rel v rel v rel Speed relative to the atmosphere Rotation, winds C D Drag Coefficient: difficult to measure C D (1-4)

17 Atmospheric Drag a D = D m = 1 2 C D A m ρ v rel v rel v rel Speed relative to the atmosphere Rotation, winds C D Drag Coefficient: difficult to measure C D (1-4) A Frontal area depends on attitude

18 Atmospheric Drag a D = D m = 1 2 C D A m ρ v rel v rel v rel Speed relative to the atmosphere Rotation, winds C D Drag Coefficient: difficult to measure C D (1-4) A Frontal area depends on attitude ρ Atmospheric density: 15% error

19 Atmospheric Drag Atmospheric Drag p. 10/29 a D = D m = 1 2 C D A m ρ v rel v rel v rel Speed relative to the atmosphere Rotation, winds C D Drag Coefficient: difficult to measure C D (1-4) A Frontal area depends on attitude ρ Atmospheric density: 15% error β = m C D A Ballistic coefficient: (β, a D ) Some authors use the opposite form: BC= C DA m

20 Computing Drag 4 problems: Calibrating C D or β : Differential Correction Propagating orbits with drag: atmospheric model Computing satellite lifetime: averaged equations Atmospheric research MapleOD King-Hele

21 Computing Drag Atmospheric Drag p. 11/29 4 problems: Calibrating C D or β : Differential Correction Propagating orbits with drag: atmospheric model Computing satellite lifetime: averaged equations Atmospheric research MapleOD King-Hele Effects on the orbit Seculars: a, e Reentry Spiral Maplanim Circularization phase Mir ISS Spiral phase: reenty Periodic: Ω, ω, i (through atmospheric rotation) Mars

22 Structure of the Atmosphere Atmospheric Drag p. 12/ km Ionosphere Exosphere Thermopause Thermosphere Mesopause Mesosphere Stratopause Stratosphere Tropopause Dominant constituent He O N 2 ISS, Shuttle Clouds Troposphere Mt Everest 10 0 Sea Level

23 Constituents - Solar low Atmospheric Drag p. 13/29 Density (molec/m 3 ) 1e+030 1e+025 1e+020 1e+015 1e e 005 1e 010 Constituents: Low Solar Activity Height (km) N 2O O 2 He Ar H N

24 Exospheric Temperature T vs Solar Activity Atmospheric Drag p. 14/ T (ºK) High Mean Low

25 Density vs Solar Activity Atmospheric Drag p. 15/ High Mean Low Density (kg/m 3 ) e 006 1e 008 1e 010 1e 012 1e 014 1e

26 Location-Related Changes In Static Models, properties change only with location:

27 Location-Related Changes In Static Models, properties change only with location: *** Height: Hydrostatic equilibrium ρ = ρ 0 e h 0 h H h ell

28 Location-Related Changes In Static Models, properties change only with location: *** Height: Hydrostatic equilibrium ρ = ρ 0 e h 0 h H h ell ** Latitude: change of height through flattening φ g Height over the Ellipsoid changes with longitude: h ell = 0 21 km ρ h cir S h'' ell h' S ell φ g h ell S E

29 Location-Related Changes Atmospheric Drag p. 16/29 In Static Models, properties change only with location: *** Height: Hydrostatic equilibrium ρ = ρ 0 e h 0 h H h ell ** Latitude: change of height through flattening φ g Height over the Ellipsoid changes with longitude: h ell = 0 21 km ρ h cir S h'' ell h' S ell φ g h ell S E * Longitude: λ g Temporal change (day/night) Subsolar hump Small space variation (seas, mountains atmosphere), mainly at low heights.

30 Causes of Time-Related Changes Atmospheric Drag p. 17/29 In Time-varying Models, properties change with location and time: Solar activity Sun spots Solar wind UV/EUV radiation Index F 10.7 Density ρ(t) Internal geomagnetic field Geomagnetic activity Index K p / A p

31 Time Changes Due to the Sun Atmospheric Drag p. 18/29 Sunspot 11 year cycle: 85% Sunspot Number EUV ( nm) T ρ EUV not measurable: PROXY F 10,7, ( F 10.7 )81 Image courtesy NASA

32 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 Min Density ρ depends on: Apparent local solar time LHA of satellite jach/hed Solar declination δ Geodetic latitude φ g of satellite

33 Time Changes: Sun and Geomagnetic Field Atmospheric Drag p. 19/29 Diurnal variations: 15% Solar UV radiation heats up the atmosphere: ρ Max: subsolar hump, delayed 2-2:30 pm. Antipod Min Density ρ depends on: Apparent local solar time LHA of satellite jach/hed Solar declination δ Geodetic latitude φ g of satellite Magnetic storms: Earth field s fluctuations: small effect Solar storms: short but large effect: Up to 30% Influence ρ through the geomagnetic indices K p or A p

34 Other Changes Solar rotation period of 27 days: Variable 0 10% Visible sunspots change EUV radiation changes Affects ρ through F 10.7 and ( F 10.7 )81 (81 day average)

35 Other Changes Atmospheric Drag p. 20/29 Solar rotation period of 27 days: Variable 0 10% Visible sunspots change EUV radiation changes Affects ρ through F 10.7 and ( F 10.7 )81 (81 day average) Semi-annual variation: Sun distance changes. Small Cyclical variations: 11-year cycles are not regular. ESA s standard cycle. 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. Tides: The atmosphere also suffers tides. Models. Small Small

36 Data Sources Atmospheric Drag p. 21/29 Before Space Age: nothing known about the properties of the atmosphere above 150 km Early satellites: orbit tracking. Assume C D, compute ρ Careful with NORAD TLE s ṅ: 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

37 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%)

38 Static Models Atmospheric Drag p. 22/29 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 = ρ 0 e h 0 h H Reference density and height, ρ 0, h 0 Scale height H (changes with h!)

39 Static Models Atmospheric Drag p. 23/29 US Standard Atmosphere 62, 76 ( km) Tabulated Ideal, stationary atmosphere, at 45 o N, moderate solar activity CIRA ( km) COSPAR-International Reference Atmosphere. CIRA-72 and -86 incorporate dynamic models for h > 100km Harris-Priester ( km) Static. Fast. Tabulated for T Interpolate Includes subsolar hump (only LHA, equinoctial)

40 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

41 Time-Varying Models Atmospheric Drag p. 24/29 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) ( km) The first. Uses satellite data. Late, also ISR Profile for T (F 10,7,F 10,7,K p,φ g,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 Vallado and Montenbruck describe different modifications of the Jacchia model

42 Time-Varying Models Atmospheric Drag p. 25/29 MSIS 83, 86, MSISE 90, 2000 ( km) Mass Spectrometer & Incoherent Scatter + satellite tracking Profile T (JD,h el,λ g,φ g,lst,f 10.7, F 10.7,Ap i, Ap i ) Diffusion PDE for each constituent: series integration (faster) 1 dn i ni dh + H 1 i + 1+α i T dt dh = 0, Add partial densities: ρ(h) = ρ i 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/ (Average F 107 computed)

43 Time-Varying Models Atmospheric Drag p. 26/29 COSMOS ( km) Tracking data fit of the COSMOS satellites ρ = ρ n k 1 k 2 k 3 k 4 ρ n - Night density profile: exponential k 1 - Solar activity correction, F 10.7, 4 values k 2 - Day/Night correction k 3 - Semi-annual correction (small) k 4 - Geomagnetic correction, a p Very simple, modular, fast, available (cf. Vallado) Good for orbits similar to the COSMOS satellites Density Model for Satellite Orbit Predictions. GOST

44 Comparison of Time-Varying Models Atmospheric Drag p. 27/29 Model CPU ρ ρ max Jacchia 71 1, Jacchia-Roberts 0,22 0,01 0,03 Jacchia-Lineberry 0,43 0,13 0,35 Jacchia-Gill ,02 0,08 Jacchia 77 10,69 0,13 0,35 Jacchia-Lafontaine 0,86 0,13 0,36 MSIS 77 0,06 0,18 0,53 MSIS 86 0,32 0,21 1,45 TD88 0, ,49 DTM 0,03 0,40 1,22 Data from Montenbruck, p. 100

45 Conclusions Atmospheric Drag p. 28/29 Atmospheric Drag is significant between km Uncertainties in C D, ρ, A Static models have large erros Time-varying models typical error is about 15% Because of the model: indirect proxy Because of the Sun s uncertainty Because 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 to 5% : Solar-2000, HASDM Space sensors allow direct measuring of EUV, without proxies

46 COWELL with drag acceleration Atmospheric Drag p. 29/29 Begin ẏ = f(y, t) Input data KB/File Initializations Load Indices Common block ITRF / H, Lat-Long Density r GCRF H ell, φ g, λ ODE Integrator Call Int step Call Derivs Drag Accel Save Data FILE Other Accel End