## Modeling the Effect of Thermospheric Changes on Satellite Orbit Lifetime

# Modeling the Effect of Thermospheric Changes on Satellite Orbit Lifetime

*Aerospace conducted a series of simulations to quantify the effect of declining mesospheric density on low Earth orbital lifetimes.*

##### Chia-Chun Chao, Richard Walterscheid, and Bernard Yoo

First published Summer 2011, Crosslink® magazine.

During the past 35 years, atmospheric carbon dioxide has increased 4.3 percent per decade. As a result, the density of the thermosphere 90–1000 kilometers above Earth has been decreasing. This trend presents important implications for space mission design, reentry planning, and debris hazard forecasting.

For satellites whose useful mission lifetime is limited by stationkeeping fuel allocation, the decreased density will result in increased orbital lifetimes with the same fuel allocation, or reduced fuel allocation (and spacecraft mass) for the same orbital lifetime.

On the other hand, orbital lifetimes will also increase for debris, increasing the risk of collision. One way to mitigate the increased debris hazard is to plan for collision avoidance maneuvering. This requires additional fuel allocation, which will offset any gains from decreased stationkeeping fuel requirements. It also requires accurate prediction of impending collision and effective operational maneuvers for avoidance. Increased satellite lifetimes will also increase the fuel requirement for end-of-life disposal to ensure reentry within 25 years, as recommended by the Inter-Agency Space Debris Coordination Committee.

The Aerospace Corporation has been reviewing the available data and conducting a series of simulations to quantify the effects of increased orbital lifetimes and the implications for national security space systems.

## Theoretical Basis

Thermospheric temperature reflects the net effect of heating and cooling through a number of processes. The most important are heating caused by the absorption of very short wavelength solar radiation, and cooling caused by molecular diffusion and infrared radiation. Infrared radiation has a cooling effect because the kinetic energy of the gas at the molecular level is transferred to the radiation field and lost to space. Energy is radiated away (escapes) because the emitting gases are tenuous (optically thin), and little radiation is absorbed and reradiated back to where it was emitted; moreover, greenhouse gases that do absorb radiation reemit before they can transfer the absorbed radiation to kinetic energy through collisions. The more infrared emitters (greenhouse gases) there are, the greater the amount of radiation lost—and the greater the cooling. The most important greenhouse gas in the thermosphere is carbon dioxide.

By contrast the troposphere is optically thick. Radiation emitted from the surface is absorbed and reradiated before it can escape. The absorbed radiation is reradiated both upward and downward. The downward radiation warms the lower layers of the atmosphere. The more greenhouse gases there are, the greater the downward flux of radiation—and the greater the warming. The most important greenhouse gas in the troposphere is water vapor, followed by carbon dioxide. The greenhouse effect near Earth’s surface is huge; without it, Earth would be several tens of degrees (Celsius) cooler (this is the total effect, not the incremental effect due to human activity).

Unlike the troposphere, where there is a complicated system of feedback, the thermosphere is a comparatively simple system, and there is general agreement on the magnitude of the effect of increasing levels of greenhouse gases (which causes the thermosphere to cool down).

The resulting cooling of the thermosphere causes it to contract. The expected effect on satellites is to decrease the atmospheric drag—and in fact, this has been observed for a number of space objects that have been studied since 1961. Aerospace has applied the results derived from observations of those space objects to model the future decrease in density and explore the ramifications for spacecraft lifetimes.

## Model Assumptions

The ability to project the future state from available data is complicated by several factors. For example, the increase in carbon dioxide has been fairly linear in the recent decade, but the longer-term trend has been for an accelerating increase. On the other hand, it is also possible that future controls on emissions might substantially decrease the annual rate of increase. Moreover, as greenhouse gases build up, self-absorption effects become increasingly important—clearly, the thermosphere will not disappear in the future, so eventually, self-limiting processes will act to decrease the sensitivity to increases in greenhouse gas concentrations.

A model of the future must also account for the aging of model data prior to the present. The Aerospace study applied NASA’s Mass-Spectrometer-Incoherent-Scatter (MSIS) model, which includes atmospheric data generated over the course of several decades. A precise accounting of data aging is difficult, but an adequate estimate of a reference year would be the midpoint of the years spanned since the earliest data taken to the latest. The earliest data used in the MSIS model is from 1961, so a reasonable midpoint year for the model released in 2000 (MSIS00) is 1980. Thus, January 1, 1980, was selected as the starting point.

From there, the change in thermospheric density was modeled as a linear decrease of 2 percent per decade at 200 kilometers, increasing to 4 percent per decade at 750 kilometers, changing linearly between those limits.

The model was incorporated into the LIFETIME semi- analytic orbit propagation program. Developed at Aerospace, LIFETIME is a software tool designed for the prediction of satellite decay/reentry and orbit-sustenance fuel requirements. It is especially useful for performing long-term orbit propagations of low Earth orbits, accounting for forces such as Earth gravity harmonics, atmospheric drag, sun and moon perturbations, and solar radiation pressure. Recent numerical tests of the latest version of LIFETIME show close agreement (less than 0.7 percent difference in orbit lifetime computation) with the high-precision orbit determination program, TRACE. The atmospheric density scale factor adjustment was applied to the density value returned by the MSIS00 atmospheric model function.

A large population of the low Earth orbit satellites (such as DMSP, POES, and TOPEX) reside in sun-synchronous orbits. Therefore, a sun-synchronous, circular orbit with a 6 a.m. local time at ascending node was selected as the reference orbit.

Initial altitudes of 350 to 850 kilometers, in increments of 50 kilometers, were selected. The lower limit is representative of the minimum altitude needed for basic satellite operation, and includes the orbit of the International Space Station; the upper limit is representative of sun-synchronous weather satellites.

The selected orbits were simulated for launches taking place in 2010, 2020, and 2030. The first is representative of satellites (and debris) presently in orbit, the second is representative of space missions presently in development, and the third is a future projection.

Five ballistic coefficient values were used: 100, 175, 300, 520, and 900 square centimeters per kilogram (cm2/kg). This range of values is representative of many operational and nonoperational human-made space objects. The lowest value, 100 cm2/kg, is representative of the International Space Station, while 300 cm2/kg is representative of many low Earth orbit weather satellites. A higher value implies a higher ratio of surface area to satellite mass.

Every combination of epoch, initial orbit altitude, and ballistic coefficient was simulated in LIFETIME, with and without the modeled reduction in mesosphere density. The simulations were run with a propagation limit of 50 years because the linear model for the carbon-dioxide growth rate may not be valid beyond 50 years from now.

## Results

The simulations show a modest increase in orbital lifetimes—increasing with time—for all initial altitudes up to 500 kilometers. More dramatic lifetime increases are seen from 550 to 750 kilometers for certain combinations of initial altitude and ballistic coefficient. Comparisons above 750 kilometers (and some at even lower altitudes) were not possible because the increased orbital lifetimes exceeded the study’s 50-year propagation limit (there is no arbitrary propagation time limit in the LIFETIME program).

For initial altitudes up to 500 kilometers, the simulations show a steady, linear increase in the duration of orbital lifetime caused by thinning of the upper atmosphere. For a 2010 launch, the increase in orbital lifetime is 5.2–10.5 percent. This rises to 5.3–11.6 percent for a 2020 launch. By 2030, the increase is 5.0–16.6 percent. At this altitude range, the original orbit lifetime is relatively short, less than 10 years, and the accumulated effect on lifetime due to slow density decrease is small.

At 550 kilometers and higher, the lifetime increases are much more dramatic for certain combinations of initial altitude and ballistic coefficient. For a 2010 launch, the orbital lifetimes increase by 6.8–58.7 percent. For a 2020 launch, the increase is 6.9–65.2 percent. For a 2030 launch, the increase is 6.2–67.5 percent.

The magnitude and altitude of maximum effect vary with ballistic coefficient. Higher ballistic coefficients tend to produce the maximum effect at higher initial altitudes; however, this is not a monotonic trend.

From 550 to 750 kilometers, ballistic coefficients of 100 to 300 cm2/kg have the greatest effect. The largest lifetime increases (58.7–67.5 percent) occur with a ballistic coefficient of 300 cm2/kg at an initial altitude of 600 kilometers.

At 550 kilometers, a ballistic coefficient of 175 cm2/kg has the greatest effect for all epochs, starting at 20.9 percent for a 2010 launch and increasing to 31.9 percent for a 2030 launch.

At 750 kilometers, the largest ballistic coefficient of 900 cm2/kg produces the largest lifetime increases at later epochs. For a 2030 launch, the 900 cm2/kg case produced a 35.0 percent increase in orbital lifetime. The response is flatter in earlier epochs, with a 15.1 percent increase for a 2020 launch and a 10.2 percent increase for 2010.

Beyond these observations, it is difficult to draw conclusions for altitudes above 650 kilometers and ballistic coefficients less than 100 cm2/kg because many orbits in these ranges exceeded the study’s 50-year propagation limit. For example, all cases starting at 600 kilometers and below reentered within 50 years, but none of the 850-kilometer cases did. Between these limits, reentry within 50 years varied according to ballistic coefficient. At a ballistic coefficient of 100 cm2/kg, the results and conclusions are valid up to an initial altitude of 600 kilometers. At 300 cm2/kg, the results are valid up to 700 kilometers initial altitude. At 900 cm2/kg, the results are valid up to 750 kilometers.

The lack of valid results for the orbital lifetimes exceeding 50 years does not imply that the effect of mesospheric thinning is not significant. Indeed, the effect may be even greater for orbits that naturally have longer lifetimes. Such effects were not quantified in the Aerospace simulations, but merit further study, especially for long-term debris hazard studies. The importance of atmospheric thinning above 650 kilometers should not be dismissed for lack of valid results from this study.

## Conclusion

The change in orbit lifetimes has important and interrelated implications for mission design, fuel allocation, space operations, and debris hazard assessment. The increased orbit lifetimes present the possibility of longer satellite operational lifetimes, at the cost of increasing debris hazard. Aerospace continues to study the available data to support guidelines and recommendations for future system design.

* Further Reading *

R. Akmaev and V. Fomichev, “Cooling of the Mesosphere and Lower Thermosphere Due to Doubling of CO2,” *Annales Geophysicae*, Vol. 16, pp. 1501–1512 (1998).

C. Chao, *Applied Orbit Perturbation and Maintenance* (The Aerospace Press/AIAA, El Segundo, CA, and Reston, VA, 2005).

C. Chao and M. Platt, “An Accurate and Efficient Tool for Orbit Lifetime Predictions,” *AAS Paper 91-134, AAS/AIAA Spacecraft Mechanics Meeting* (Houston, Feb. 11–13, 1991).

J. Emmert, J. Picone, S. Lean, and S. Knowles, “Global Change in the Thermosphere: Compelling Evidence of a Secular Decrease in Density,” *Journal of Geophysical Research*, Vol. 109, No. A02301 (2004); doi:10.1029/2003JA010176.

J. Emmert, J. Picone, and R. Meier, “Thermospheric Global Average Density Trends, 1967–2007, Derived from Orbits of 5000 Near-Earth Objects,” *Geophysical Research Letters*, Vol. 35, pp. L05101 (2008); doi:10.1029/2007GL032809.

J. Liu and R. Alford, “Semianalytic Theory for a Closed-Earth Artificial Satellite,” *Journal of Guidance and Control*, Vol. 3, No. 4 (July–Aug. 1980).

National Oceanic and Atmospheric Administration, Global Monitoring Division, *Trends in Carbon Dioxide* (NOAA 2010); www.esrl.noaa.gov/gmd/ccgg/trends (as of Mar. 15, 2011).

J. Picone, A. Hedin, D. Drob, and A. Aikin, “NRLMSISE-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues,” *Journal of Geophysical Research*, Vol. 107, No. A12, p. 1468 (2002); doi:10.1029/2002JA009430.

L. Qian, R. Roble, S. Solomon, and T. Kane, “Calculated and Observed Climate Change in the Thermosphere, and a Prediction for Solar Cycle 24,” *Geophysical Research Letters*, Vol. 33, p. L23705 (2006); doi:10.1029/2006GL027185.

R. Roble and R. Dickinson, “How Will Changes in Carbon Dioxide and Methane Modify the Mean Structure of the Mesosphere and Thermosphere?” *Geophysical Research Letters*, Vol. 16, No. 12, pp. 1441–1444 (1989).

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