The Neutral Atmosphere and Its Influence on Basic Orbital Dynamics at the Edge of Space

Delores KnippDepartment of PhysicsUS Air Force Academy

Colorado USAdelores.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

• Motivation

• Concepts

– Solar Cycle-Atmosphere Interaction

– Atmospheric Density and Temperature

– Mechanics/Dynamics of Drag

– Computational Concepts

• “What Ifs”

• Tomorrow

– Simulation

Objectives:

Understand sources of upper atmospheric heating

Appreciate the space weather regime- change from magnetized and non-collisional to gravitationally dominated and collisional interactions.

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 EffectsSpace 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

•Track and identify active payloads and debris (DOD)•Collision avoidance and re-entry prediction (NASA) •Study the atmosphere’s density and temperature profile (Science)

Skylab, 1978

April 9, 1979

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?

Dayside:

Solar EUV

and

Auroral particles

Nightside:

Joule Dissipation

and

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

120

160

200

240

280

320

360

400

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

Time (Days)

Alt

itu

de

(km

)

Thin curve Simulated STARSHINE orbits Thick curve actual STARSHINE data

Vertical Forces on a Static Parcel of Air

• 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)

z

z+dz

Fup=PA

Fdown=(P+dP)A

Weight

Fnet = Fup-Fdown-Weight=0

PA-(P+dP)A = Weight

-dP A = Weight

A=area

z

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

0

200

400

600

800

1000

1200

1.000E-17 1.000E-14 1.000E-11 1.000E-08 1.000E-05 1.000E-02 1.000E+01

Atmospheric Mass Density (kg/m3)

Alt

itu

de

(km

)

]

11

)(

)(exp[)()(

]11

exp[)(

11ln))(ln(

ln1

)(

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)(

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2

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2

2

222

0

0

EB

E

EB

Eo

Eo

rn

n

r

R

rn

n

r

R B

E

Bp

p

y

p

ppp

y

rrrTk

gRrmrndrrn

rrTk

mgRnrn

rrconstnrn

nr

const

n

dndr

rTk

mgR

Tdnkmndyr

GM

dPmndyr

GM

MaAdPPWPA

r

mnAdyGM

r

mnVGM

r

mNGM

r

GMWeight

MaF

E

E

m

]11

)(

)(exp[)()(

]11

exp[)(

11ln))(ln(

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EB

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Eo

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rn

n

r

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rn

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Bp

p

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ppp

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rrrTk

gRrmrndrrn

rrTk

mgRnrn

rrconstnrn

nr

const

n

dndr

rTk

mgR

Tdnkmndyr

GM

dPmndyr

GM

MaAdPPWPA

r

mnAdyGM

r

mnVGM

r

mNGM

r

GMWeight

MaF

E

E

mCorrecting for variations in “g”

Concept: What if “g” Varies?

MSIS Atmosphere

Altitude vs. Atmospheric Mass Density, Comparing Different Models

0

200

400

600

800

1000

1200

1E-17 1E-14 1E-11 0.00000001 0.00001 0.01 10

Atmospheric Mass Density (kg/m3)

Alt

itu

de

(km

)

Law of Atm, Corrected "g"

Law of Atm

Concept: What if the Temperature Varies?

Altitude vs. Temperature in the Atmosphere

0

200

400

600

800

1000

1200

0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0

Atmospheric Temperature (K)

Alt

itu

de

(km

)

MSIS Atmosphere

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) A, B, C b) C, B, A c) B, C, A d) A, C, B

Altitude vs. Atmospheric Mass Density, Comparing Different Models

0

200

400

600

800

1000

1200

1.0E-14 1.0E-11 1.0E-08 1.0E-05 1.0E-02 1.0E+01 1.0E+04

Atmospheric Mass Density (kg/m3)

Alt

itu

de

(km

)

Law of Atmospheres

MSIS Model Hot

Temperature K

Troposphere

Stratosphere

Thermosphere

MSIS Model Cool

a b

TIEGCM Density Profile

MSIS Hot

MSIS Cool

Mechanics Concepts Kinetic Energy

• Satellites in orbit experience a centripetal acceleration

• Solve for speed

• Associated kinetic energy

rr

GMmr

r

mvamF ˆˆ

2

2

r

GMv

r

mGMmv

22

1 2

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

r

GMmrdFU

B

A

AB

r

GMm

r

mGMmvE

22

1 2

hRE

GMmr E

2

Mechanics Concepts Drag Force and Work

• Drag Force

• Work Done by Drag

2

2

1|| vACF DD

lvACrdFW D

B

A

2

2

1

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

Work Done by

Drag Force

Boundary Conditions and Initial Physics

Reduced Mechanical

Energy

New Conditions And

Same Physics

More Work Done by Drag Force

Satellite De-Orbits

Iterate

Newton’s Second Law

Energy Conservation

Newton’s Second Law

Energy Conservation…Etc

Orbital Drag Laboratory Worksheet Flowchart of Orbit Decay Model:

Initial values

Energy at this

altitude

Altitude

Speed

Atmospheric density at this

altitude

Drag Force Work done

by drag force in this orbit

Next values

Energy at the next

orbit

Altitude

Speed

Atmospheric density at this

altitude Drag Force Work done

by drag force in this orbit

(from Atmosphere spreadsheet) = 4.25x10-11

kg/m3

Iterative Technique

Orbital Drag Lab: Modeling Satellite Orbital Decay in a Realistic Atmosphere

m, Mass of Shuttle (kg) = 91974 G, Gravitational Constant (Nm2/kg2) = 6.67E-11

CD, Drag Coefficient = 2 M, Mass of Earth (kg) = 5.97E+24

A, Cross Sectional Area of Shuttle(m2)= 362 Re, Radius of Earth (m) = 6.37E+06

hi, Initial Altitude (km) = 350 350000 = hi in meters

End of

Orbit

Total Time

Mass DensityShuttle's Total

Energy (J)Altitude

(km)Altitude (m) Velocity (m/s) Drag (N)

Work Due To Drag (J)

# (hours) (kg/m3)0.00 4.25E-11 -2.72500E+12 350.0 350000.0 7697.8 0.91 -3.85E+07 Initial

1 1.52 4.32E-11 -2.72504E+12 349.9 349905.2 7697.8 0.93 -3.92E+07 Typical2 3.05 4.32E-11 -2.72507E+12 349.8 349808.6 7697.9 0.93 -3.92E+07

529 797.86 1.18E-07 -2.82766E+12 106.0 106026.2 7841.4 2,618.47 -1.07E+11530 799.30 #N/A -2.93420E+12 -129.1 -129129.3 7987.8 #N/A #N/A

Iterative Technique

Shuttle's Altitude vs. Time

0

50

100

150

200

250

300

350

400

0 100 200 300 400 500 600 700 800 900

Time (hours)

Shuttle's Drag vs. Time

0

1

10

100

1,000

10,000

0 100 200 300 400 500 600 700 800 900

Time (hours)

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

7650

7700

7750

7800

7850

7900

7950

8000

8050

0 100 200 300 400 500 600 700 800 900

Time (hours)

Ve

loc

ity

(m

/s)

Shuttle's Total Mechanical Energy vs. Time

-2.95000E+12

-2.90000E+12

-2.85000E+12

-2.80000E+12

-2.75000E+12

-2.70000E+120 100 200 300 400 500 600 700 800 900

Time (hours)

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

Radar

Receiver

Atmospheric Drag

EXPECTED POSITION

ACTUAL POSITION

Time-Varying Activity

Heating Activity Level vs. Time

0

1

2

3

4

0 100 200 300 400 500 600 700 800 900 1000 1100

Time (hours)

He

ati

ng

Ac

tiv

ity

Le

ve

l (0

, 1

, 2

, o

r 3

)

Shuttle's Altitude vs. Time

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

0.00 50.00 100.00 150.00 200.00 250.00

Time (hours)

Alt

itu

de

(km

)

Shuttle's Drag vs. Time

0.10

1.00

10.00

100.00

1,000.00

10,000.00

0.00 50.00 100.00 150.00 200.00 250.00

Time (hours)

Dra

g (

N)

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

0

500

1000

1500

2000

2500

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Year

Po

wer

(G

W)

Solar Power

Cycle 21 Cycle 22 Cycle 23

Particle Power

Joule Power –Two Hemispheres

Daily Average Joule Power Values for Solar Cycles 21-23

0

500

1000

1500

2000

2500

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Year

Po

wer

(G

W)

10 Most Powerful Events of Last 30 Years(Knipp et al., 2005)

Daily Average Power Values for Solar Cycles 21-23

0

500

1000

1500

2000

2500

3000

3500

1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Year

Po

wer

(G

W)

Total Power

Joule Power

Solar Power

SKYLAB Reenters

NORAD Space TrackingDisrupted

JapaneseSatelliteMalfunctionAttributedto Satellite Drag

Particle Power

15 Apr 7 Jul 3 Mar 10 Oct 6 Jun 5 May 15&16 Jul 6 Nov 30 Oct

79 82 89 89 91 92 00 01 03

Altitude Profile

nominal

Level 3 disturbance at hr 100 for 10 hr

Return to nominalLevel 2Disturbance

All Hours

Altitude Speed

Mechanical Energy Drag Force

Orbital Drag Lab: Boundary Values for Space Shuttle Orbit

m, Mass of Shuttle (kg) = 91974CD, Drag Coefficient = 2

A, Cross Sectional Area of Shuttle(m2)= 362hi, Initial Altitude (km) = 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

0

200

400

600

800

1000

1200

1.000E-17 1.000E-14 1.000E-11 1.000E-08 1.000E-05 1.000E-02 1.000E+01

Atmospheric Mass Density (kg/m3)

Alt

itu

de

(km

)

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

Initial values

Energy at this

altitude

Altitude

Speed

Atmospheric density at this

altitude

Drag Force

Next values

Energy at the next

orbit

Altitude

Speed

Atmospheric density at this

altitude Drag Force

NAME ________KEY_______ SECTION___________________

J

r

GMmE

1210x725.2

2

mh 000,350

(from Atmosphere spreadsheet)

= 4.25x10-11 kg/m3

m/s8.7697

hR

GM

r

GMv

E

(from Atmosphere spreadsheet)

= 4.32x10-11 kg/m3

m/s8.7697

hR

GM

r

GMv

E

J

WEE lastlastthis

1210x725.2

N

vACF DD

91.021 2

J

hRF

rFW

ED

DD

710x85.3

])[2(*

)2(*

J

hRF

rFW

ED

DD

710x92.3

])[2(*

)2(*

m

ERE

GMmh

E

GMmhERr

r

GMmE

3499052

2

2

N

vACF DD

93.02

1 2

Iterative Technique

Plot characteristics of satellites (in near circular orbit) under the influence of drag

Shuttle's Altitude vs. Time

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00

Time (hours)

Alt

itu

de

(km

)

Shuttle's Velocity vs. Time

7650.0

7700.0

7750.0

7800.0

7850.0

7900.0

7950.0

8000.0

8050.0

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00

Time (hours)

Vel

oci

ty (

m/s

)

Shuttle's Total Mechanical Energy vs. Time

-2.74200E+12

-2.74000E+12

-2.73800E+12

-2.73600E+12

-2.73400E+12

-2.73200E+12

-2.73000E+12

-2.72800E+12

-2.72600E+12

-2.72400E+12

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00

Time (hours)

To

tal

Mec

han

ical

En

erg

y (J

)

Shuttle's Drag vs. Time

0.10

1.00

10.00

100.00

1,000.00

10,000.00

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00

Time (hours)

Dra

g (

N)

Altitude

Mechanical Energy

Velocity

Drag Force

Are Lab Results Realistic?

Observed and Simulated STARSHINE-1 Altitude Vs Time

120

160

200

240

280

320

360

400

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

Time (Days)

Alt

itu

de

(km

)

Thin curve Simulated STARSHINE orbits with MSIS temperature-6%Thick curve actual STARSHINE data

Concept: Temporal Variations in Heating

Shuttle's Altitude vs. Time

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00

Time (hours)

Alt

itu

de

(km

)

Level 0 Activity Orbital Decay

Level 1 Activity Orbital Decay

Level 2 Activity Orbital Decay

Level 3 Activity Orbital Decay

Shuttle's Altitude vs. Time

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

0.00 50.00 100.00 150.00 200.00 250.00

Time (hours)

Alt

itu

de

(km

)

Solar Activity Level vs. Time

0

1

2

3

4

0 100 200 300 400 500 600 700 800 900 1000 1100

Time (hours)

So

lar

Act

ivit

y L

evel

(0,

1,

2, o

r 3)

Altitude vs Time Profiles for 0,5,10 and 20%

Temperature Increases

Impulsive heating event

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

0

500

1000

1500

2000

2500

3000

3500

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Year

Po

wer

(G

W)

Jul 14 Mar 13 Oct 21 Jun 6 Jul 13 May 10 Jul 14 Mar 31 Nov 6 & 24 1982 1989 1989 1991 1991 1992 2000 2001 2001

Solar Power

Total Power

Joule Power

Particle Power

Concept: What if the Temperature Varies?

Shuttle's Altitude vs. Time

0

50

100

150

200

250

300

350

400

0 100 200 300 400 500 600 700 800 900

Time (hours)

Alt

itu

de

(km

)

7650

7700

7750

7800

7850

7900

7950

8000

8050

Altitude Profile Using Hot ModelAtmosphere

Altitude Profile Using Hot ModelAtmosphere +5%

Velocity Profile Using Hot ModelAtmosphere

Velocity Profile Using Hot ModelAtmosphere +5%

Solar Spectrum