2. Overview of lecture 14
• In this lecture we will look at the effects of Solar Extreme Ultra-Violet
(EUV) radiation on the atmospheric region known as the thermosphere
– Although the total solar irradiance varies only very little over the solar
cycle, solar EUV irradiance can vary by two or three orders of magnitude
over the solar cycle and by similar amounts over just a few days
– This radiation causes heating of the thermosphere which affects
atmospheric drag on spacecraft in Earth orbits
• We investigate how uncertainty in solar EUV forecasts leads to substantial
uncertainty in estimates of satellite positions
• This lecture will link very closely to the topics covered in next week’s
lectures, geospace climate change (long-term changes in the
thermosphere)
Space Environment – Space Weather
3. Solar irradiance Space Environment – Space Weather
Total Solar Irradiance (TS):
• TSI varies by 0.1% over the solar cycle:
4. Solar irradiance Space Environment – Space Weather
Extreme Ultraviolet (EUV):
• Solar EUV photons are absorbed in the Earth’s thermosphere (~90 km to ~500 km)
causing its temperature to increase with altitude
• Solar EUV irradiance varies over the 11-year solar cycle by factors of two to ten
https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2010JA015901
5. Solar irradiance Space Environment – Space Weather
Extreme Ultraviolet (EUV):
• Solar EUV irradiance can vary by the large amounts over just a few days:
https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2010JA015901
7. Why temperature matters Space Environment – Space Weather
Kinetic energy is proportional to temperature:
k = Boltzmann constant, T = temperature, m = molecular mass, v = speed
Increasing temperature (e.g. due to increased solar EUV irradiance at solar maximum)
leads to higher speeds
In free molecular flow regime this causes atmosphere to expand, as particles with higher energies
reach higher altitudes
Decreasing temperature leads to lower speeds
Particles with lower energies can’t climb to high altitudes so atmosphere contracts
3
2
𝑘𝑘𝑘𝑘 =
1
2
𝑚𝑚𝑣𝑣2
8. Why temperature matters Space Environment – Space Weather
Solar max to Solar min density variability:
CIRA-72
9. Thermospheric composition & mass
density
Space Environment – Space Weather
Number Density
(NRLMSISE-00)
O2
N2
O
N
He
H
Solar Maximum
Solar
Minimum
Total Mass Density
(NRLMSISE-00)
10. Magnetic field deflection Space Environment – Space Weather
Variations in the solar wind (gusts & changes caused by space weather) result in
deflections of the Earth’s magnetic field and changes to thermospheric density
The thermospheric density can change substantially & over very short time periods
Deflection
(nT)
“Halloween storms of 2003”:
deflection* measured by
magnetometers in Kiruna, Sweden
*deflection from quiet level of
10,650 nT
http://www.spaceweatherlive.com/en/help/the-kiruna-magnetometer
11. Effect of aerodynamic drag on orbits Space Environment – Space Weather
Principal effects upon the orbit are to reduce its size and to circularise it (both
semi-major axis, a, and eccentricity, e, decrease)
Original orbit
Successive orbits
Earth’s
atmosphere
12. Decrease in orbit height due to air drag Space Environment – Space Weather
Orbit energy/vis-viva equation:
Sum of the kinetic and potential energy is constant at all
points on the orbit:
The change in energy per orbit corresponding
to a change in orbit radius δa is:
𝑉𝑉2
2
−
𝜇𝜇
𝑟𝑟
= −
𝜇𝜇
2𝑎𝑎
= 𝜀𝜀 (for unit mass)
𝛿𝛿𝛿𝛿 =
𝜇𝜇𝜇𝜇
2𝑎𝑎2
𝛿𝛿𝛿𝛿 (1)
13. Decrease in orbit height due to air drag Space Environment – Space Weather
If the altitude decrease is due to air drag, then the
energy change is equal to the work done by the drag
force per orbit:
The combination of (1) and (2) gives:
If we know key satellite parameters and we can
measure the decrease in orbit height, we can estimate
the atmospheric mass density (and infer
temperatures?)
𝐹𝐹𝑑𝑑𝑑𝑑 = −
1
2
𝜌𝜌𝑉𝑉2
𝑆𝑆𝐶𝐶𝐷𝐷 2𝜋𝜋𝜋𝜋
WD by drag =
𝛿𝛿𝛿𝛿 = −2𝜋𝜋𝜋𝜋
𝑆𝑆𝐶𝐶𝐷𝐷
𝑀𝑀
𝑎𝑎2
(2)
14. Decrease in orbit height due to air drag Space Environment – Space Weather
Example of height vs. δa per orbit:
Based on ERS1 (S = 20 m2, M = 2400 kg, CD = 2.2)
2 m/day
20 m/day
15. Forecast error Space Environment – Space Weather
400 km
Actual Daily Solar EUV Forecasts
Simulated Hourly Solar EUV Forecasts
https://amostech.com/TechnicalPapers/2014/Space_Weather/EMMERT.pdf
16. Forecast error Space Environment – Space Weather
Distribution of in-track uncertainty:
TLE Catalog, 7-day forecast, 7%
EUV uncertainty
https://amostech.com/TechnicalPapers/2014/Space_Weather/EMMERT.pdf
17. Forecast error Space Environment – Space Weather
Distribution of in-track uncertainty:
TLE Catalog, 7-day forecast, 7%
EUV uncertainty
• Solar EUV irradiance forecast errors grow
approximately as the square root of time
(like a random walk) during 7-day forecasts.
• These errors induce density forecast errors
that grow at the same rate.
• Via atmospheric drag, the density forecast
errors accumulate in the prediction of
satellite orbits. The resulting in-track error
grows as the 5/2 power of time.
• The magnitude of the in-track error varies
widely depending on altitude, ballistic
coefficient, solar cycle phase, and
eccentricity.
https://amostech.com/TechnicalPapers/2014/Space_Weather/EMMERT.pdf
18. Recap of lecture 14
• In this lecture we looked at the effects of Solar Extreme Ultra-Violet (EUV)
radiation on the atmospheric region known as the thermosphere
– We saw that solar EUV irradiance can vary by two or three orders of magnitude
over the solar cycle and by similar amounts over just a few days, and
– That this radiation causes heating of the thermosphere, affecting atmospheric
drag on spacecraft in Earth orbits. We explained the process by which this
occurs
• We then saw how uncertainty in solar EUV forecasts leads to substantial
uncertainty in estimates of satellite positions, which has impacts on space
safety (e.g. collision risk)
• This lecture links to the topics covered in next week’s lectures, geospace
climate change (long-term changes in the thermosphere)
Space Environment – Space Weather
19. Activity
• The papers by Judith Lean and by John
Emmert et al. referred to in this lecture are
available on the Blackboard site:
• Read these papers to support your learning of this
topic (and those to come next week)
Space Environment – Space Weather
