1. The Neutral Atmosphere and Its Influence on Basic Orbital Dynamics at the Edge of Space
Delores Knipp
Department of Physics
US Air Force Academy
Colorado USA
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

2. Introduction: Neutral Atmosphere & Orbital Dynamics
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
Motivation
Concepts
Solar Cycle-Atmosphere Interaction
Atmospheric Density and Temperature
Mechanics/Dynamics of Drag
Computational Concepts
“What Ifs”
Tomorrow
Simulation

3. Space Weather Effects Space Weather Effects
Space weather effects in the upper atmosphere come from many sources, however we know that variability of the Sun is a leading cause of upper atmospheric variability. You may have heard of an 11- year solar cycle during which the number of sunspots rises and falls. Associated with the number of sunspots is an increase the output of solar radiation at short wave lengths (X-rays and Ultra-Violet rays). These rays are really high energy photons that can interact with and hear the earth’s upper atmosphere. Indeed the earth’s upper atmosphere is much hotter, by several hundred degrees, during and just after the maximum in the number of sunspots. As you already know, a hot atmosphere is an expanded atmosphere. An expanded atmosphere has more mass at higher levels and this can interfere with satellite orbits. The heating of the upper atmosphere due to absorption of high energy photons is usually a gradual process that occurs over many months. Even if there is a noticeable “flare” of radiative energy from the Sun the atmosphere will only absorb a small amount of the energy on the sunlit side of the earth.
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)

4. MOTIVATION Skylab, 1978 April 9, 1979
Satellite drag led to the premature reentry of the USA’s first manned space station, Skylab (all s/c <1000 km alt.)
Skylab, 1978
April 9, 1979
Track and identify active payloads and debris (DOD)
Collision avoidance and re-entry prediction (NASA)
Study the atmosphere’s density and temperature profile (Science)

5. 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

6. Are Sunspots Related to Satellite Drag?

7. Sunspots Up Close
Courtesy La Palma Telescope

8. How can a Sun with more Spots be Hotter/Brighter?
Courtesy of Robert Cahalan, NASA

9. Where Does Energy Enter the Upper Atmosphere?
Nightside:
Joule Dissipation
and
Auroral Particles
Dayside:
Solar EUV
and
Auroral particles
After Killeen et al., 1988

11. The Solar Spectrum
(Courtesy S Solomon)

12. Courtesy of Judith Lean

13. Geomagnetic Activity Plays a Role in Upper Atmospheric Heating
Orbit Prediction of debris is very hard and consequences are significant!
Courtesy of US Air Force

14. Altitude-Time Profile for a Spherical Satellite
Thin curve Simulated STARSHINE orbits
Thick curve actual STARSHINE data

15. Vertical Forces on a Static Parcel of Air
Fdown=(P+dP)A
z+dz z z
A=area
Weight
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)
Fup=PA
Fnet = Fup-Fdown-Weight=0
PA-(P+dP)A = Weight
-dP A = Weight

16. 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)

17. 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.

18. Correcting for variations in “g”

19. Concept: What if “g” Varies?
MSIS Atmosphere

20. Concept: What if the Temperature Varies?
MSIS Atmosphere

21. Concept Check a) A, B, C b) C, B, A c) B, C, A d) A, C, B
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

23. TIEGCM Density Profile

24. MSIS Hot

25. MSIS Cool

26. Mechanics Concepts Kinetic Energy
Satellites in orbit experience a centripetal acceleration
Solve for speed
Associated kinetic energy

27. 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

28. Mechanics Concepts Drag Force and Work
Work Done by Drag

29. 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

30. Iterative Techniques and Formulation and Graphics Concepts
Newton’s Second Law
Energy Conservation
Energy Conservation…Etc

31. Iterative Technique

32. Iterative Technique

35. Concept Check a) less kinetic energy and less potential energy
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

38. Concept Check a) at lower altitude and ahead of schedule
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

39. Atmospheric Drag EXPECTED POSITION ACTUAL POSITION Radar Receiver
A source for space object positioning errors is either more or less atmospheric drag than expected on low orbiting objects (generally those at less than about 1000 km altitude). Energy deposited in the Earth’s upper atmosphere by EUV, X-ray, and charged particle bombardment heats the atmosphere, causing it to expand outward. Low earth-orbiting satellites and other space objects then experience denser air and more drag than expected. This drag decreases the object’s altitude and increases its orbital speed. The result is the satellite will be some distance below and ahead of its expected position when a ground radar or optical telescope attempts to locate it. (Conversely, less atmospheric heating and drag than expected will cause a low orbiting object to be some distance above and behind its expected position.)
-- The consequences of drag-induced orbital changes include:
(1) Delayed acquisition of SATCOM links for commanding or data transmission. (NOTE: The impact of drag is greatest on low orbiting satellites--the very satellites that spend the least amount of time above the horizon and for which we can least afford delays in acquisition.)
(2) Costly orbit maintenance maneuvers become necessary.
(3) De-orbit predictions become unreliable. (NOTE: A classic case was Sky Lab. Geomagnetic activity was so severe, for such an extended period, that Sky Lab burned-in before a planned Space Shuttle rescue mission was ready to launch.)

40. Time-Varying Activity

43. 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

44. Solar EUV and Particle Power

45. Joule Power –Two Hemispheres

46. 10 Most Powerful Events of Last 30 Years (Knipp et al., 2005)
15 Apr Jul Mar Oct 6 Jun May &16 Jul 6 Nov Oct

47. Altitude Profile nominal Level 3 disturbance at hr 100 for 10 hr
Return to nominal
Level 2
Disturbance
All Hours

48. Altitude
Speed
Mechanical Energy
Drag Force

49. Orbital Drag Lab: Boundary Values for Space Shuttle Orbit

50. Ideal and model atmospheres

51. Iterative Technique

52. Plot characteristics of satellites (in near circular orbit) under the influence of drag
Altitude
Velocity
Mechanical Energy
Drag Force

53. Are Lab Results Realistic?
Thin curve Simulated STARSHINE orbits with MSIS temperature-6%
Thick curve actual STARSHINE data

54. Concept: Temporal Variations in Heating
Altitude vs Time Profiles for 0,5,10 and 20%
Temperature Increases
Impulsive heating event

55. 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
Solar = Photon Effects
Geomagnetic = Particle and Field Effects

57. Concept: What if the Temperature Varies?

58. Solar Spectrum