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Topics in Space WeatherTopics in Space Weather

Lecture 14

Topics in Space WeatherTopics in Space Weather

Lecture 14

Space Weather EffectsOn Technological Systems

Robert R. Meier

School of Computational SciencesGeorge Mason University

rmeier@gmu.edu

CSI 76929 November & 6 December 2005

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Topics• Meier

– Introductory comments– Drag effects on orbiting space objects– Thermospheric density decreases due to

greenhouse gas cooing

• Goodman– Introduction to Space Weather & Technological

Systems– Telecommunication Systems and Space Weather

Vulnerabilities– Large Storms and Impacts upon Systems– Modeling and Compensation Methods used in

Practice– Prediction Systems & Services

www.nas.edu.ssb/cover.html

Solar Radiation and Solar Radiation and Plasma Can Affect EarthPlasma Can Affect Earth

spacecraft drag, collisions, loss communications & navigation aurora currents induced in power grids spacecraft detector upsets hazards to humans in space ozone depletion in major events speculated climate impacts

LASCO Detector: 1997-11-06

March 1989:Auroral Oval

Solar radiation, magnetospheric and galactic particles ionize and heat Earth’s atmosphere and ionosphere

Power System Events

Lecture 14

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Effect of Drag on Satellite Orbits

• Assume elliptical orbit a = semi-major axism= satellite massM = Earth mass >> mG = gravitational constant

• Calculate change in a resulting from drag

• Expressions derived from Kepler’s Laws

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Drag, cont.

The dynamical equation to be solved is

– 1st term on the rhs is the centripetal acceleration, Fg

– 2nd term is the drag force– The orbital speed is:

ˆ

g D D2

GMmF = ma = F +F = - r +F

r

Fg

FD

v

GM 2 1v = -

r r a2a

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Drag, cont.

• The drag force is

• CD = drag coefficient– Accounts for

• Momentum transfer on all sides

• Fluid flow around satellite

• Turbulent effects

– Is a function of speed, shape,

air composition, and aerodynamic environment

– CD = 2.2 for a spherical satellite around 200 km

2D D

1F C Aρ v

2

D

2

2D

dLF

dtdL ρA dx v

dx vdt

dL ρAv dt

F ρAv

F = rate of changeof momentum, L

= air density in AdxA = satellite front surface areav = satellite velocity

dx

A

v mass

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Drag, cont.

• The total energy is:

• The orbital period is:

21 GMm GMmE = K +U = mv - = -

2 r 2a

3

2

1

2

2πaT =

GM

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Drag, cont.

• The work done by drag is:

• The rate of change of energy due to drag is:

• The rate of change of orbital period is:

D2

dE GMm da= = F v

dt 2a dt

1 dT 3 1 da=

T dt 2 a dt

•DdW = F dr = dE

23DC Ada a

= ρ vdt GM m

Solving for da/dt &substituting for FD:

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Drag, cont.

• Eliminating da/dt from the last two equations on slide 10, and substituting in for the drag force leads to:

• The relative change in orbital period over 1 rev is:

• The rate of change of period depends on B = CDA/m (the ballistic coefficient)

• If orbital parameters and the ballistic coefficient are known, the average atmospheric density can be determined

3DC AdT 3a= ρv dt

T 2MG m

3T 3a

= B ρv dtT 2MG

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Decay of Elliptical Orbit

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A Simple Example: Decay Rate of the Solar Max Mission (SMM) Satellite

Courtesy, J. Lean

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Another Example: Same Satellite 30 Years Apart

Emmert et al. [2004]

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Secular Trend from 27 Objects from 1966 - 2001

Emmert et al. [2004]

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Secular Trend

• Density decreases consistent with theoretical predictions of greenhouse gas increases with thermospheric GCMs– Heating of troposphere– Cooling of stratosphere, mesosphere and

thermosphere

• Observation: – Emmert et al. [J. Geophys Res., 109, A02301,

2004]

• Theory: – Roble, R. G., and R. E. Dickinson [Geophys. Res.

Lett., 16, 1441– 1444, 1989]