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 delores.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 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

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)

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)

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? Nightside: Joule Dissipation and Auroral Particles Dayside: Solar EUV 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 Orbit Prediction of debris is very hard and consequences are significant! Courtesy of US Air Force

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

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

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.

Correcting for variations in “g”

Concept: What if “g” Varies? MSIS Atmosphere

Concept: What if the Temperature Varies? MSIS Atmosphere

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

TIEGCM Density Profile

MSIS Hot

MSIS Cool

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

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

Mechanics Concepts Drag Force and Work Work Done by Drag

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 Newton’s Second Law Energy Conservation Energy Conservation…Etc

Iterative Technique

Iterative Technique

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

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

Atmospheric Drag EXPECTED POSITION ACTUAL POSITION Radar Receiver 24. -- 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.)

Time-Varying Activity

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

Joule Power –Two Hemispheres

10 Most Powerful Events of Last 30 Years (Knipp et al., 2005) 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 nominal Level 2 Disturbance All Hours

Altitude Speed Mechanical Energy Drag Force

Orbital Drag Lab: Boundary Values for Space Shuttle Orbit

Ideal and model atmospheres

Iterative Technique

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

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

Concept: Temporal Variations in Heating 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 Solar = Photon Effects Geomagnetic = Particle and Field Effects

Concept: What if the Temperature Varies?

Solar Spectrum