Craig A. McLaughlin

Satellite Formation Flying Design and Evolution

Several satellite formation e ying designs and their evolution through time are investigated. Satellite formation e ying designs arederived from the linearized equations of relative motion under two-body dynamics better known as Hill’ s equations (Hill, G. W., “ Researches in the Lunar Theory,”American Journal of Mathematics , Vol. 1, No. 1, 1878, pp. 5‐26). The formations are then propagated forward in time in the presence of realistic perturbations to determine the stability of each design. Formations considered include in-plane, in-track, circular, and projected circular designs. The Draper Semianalytic Satellite Theory is used to propagate mean elements of the satellites. When perturbations disrupt the satellite formations, an effort is made to quantify the cost of formation-keeping maneuvers. The goal of this effort is to provide physical insight into satellite formation e ying design and outline the effects of realistic dynamics on those designs.

TechSat 21: formation design, control, and simulation

The satellite cluster approach to space missions requires science and technology advances in several key areas. Among these challenges is understanding the dynamics of satellites in close proximity to each other so that a formation can be intelligently designed, controlled, and simulated. An overview of on-going research in this area under the TechSat 21 program along with preliminary findings is provided. Included in this overview is the recent progress made in the design of formations including designs for circular formations, projected circular formations, and J/sub 2/ invariant formations. Strategies for formation control are presented as well as the baseline design for the TechSat 21 propulsion system. Fuel expenditure is estimated for various formations using different control strategies. The TechSat 21 mission requires relative position knowledge between satellites to the millimeter level while the radar is transmitting and receiving; concepts for meeting this requirement are also presented. In order to facilitate mission planning and gain confidence in mission success, the Air Force Research Laboratory (AFRL) is building an end to end simulation testbed for the TechSat 21 mission. An overview of the testbed design and functionality is provided. Focus is centered on the dynamics and control module of the testbed. The dynamics and control module utilizes high fidelity orbit propagation as the basis of the simulation of the formation dynamics. Through this simulation control algorithms, relative navigation techniques, and the effects of errors in initial conditions and control forces are investigated.

Precision Orbit Derived Total Density

O PERATIONAL orbit determination and orbit prediction experience suggests that the extreme upper atmosphere is more variable than the factors included in atmospheric density models commonly used in orbit propagation. Unmodeled atmospheric density variations can greatly impact the orbit determination process and add kilometers of error to orbit predictions. The motivation for this research is to improve orbit determination and prediction by improving density models and to better measure and understand thermospheric and exospheric density variations, especially variations with time scales shorter than those of the empirical models typically used for atmospheric drag calculations. This paper represents afirst step toward those long-term goals, which will process precision orbit data from multiple satellites simultaneously. Atmospheric density modeling has long been one of the greatest uncertainties in the dynamics of low-Earth-orbit satellites. Accurate density calculations are required to provide meaningful estimates of the atmospheric drag perturbing satellite motion. These effects increase with lower altitude orbits, higher effective area, and lower mass satellites. McLaughlin [1] gave an introduction to the neutral atmosphere and the time varying effects on the density of the thermosphere and exosphere. The effects include diurnal variations, solar rotation, the solar cycle, winds and tides, gravity waves, long-term climate change, and magnetic storms and substorms. The authors hope to increase understanding of the variations in neutral density that are important for satellite drag. Vallado [2] gave an introduction to the basic density variations and to the density models most commonly used in orbit determination. A more comprehensive introduction to the space environment and the neutral atmosphere can be found in Hargreaves [3]. Sabol and Luu [4] gave a summary of the drivers of atmospheric density variations and some of the problems associated with the temporal resolution of various proxies used in empirical density models. Marcos et al. [5] presented an overview of ongoing research to address the inaccuracies in satellite drag modeling. There are two major types of research ongoing to address these problems. The first is dynamic calibration of the atmosphere (DCA) and the second is use of satellites with accelerometers to measure the nonconservative accelerations, including drag. DCA involves estimating density corrections to a given atmospheric density model based upon the observed motion of satellites. The work of Storz et al. [6] and Bowman et al. [7,8] on the High Accuracy Satellite Drag Model (HASDM), Cefola et al. [9], Yurasov et al. [10,11], andWilkins et al. [12,13] are all examples of approaches to provide corrections to atmospheric density models. In each case, the observations from a group of satellites are used to estimate large-scale corrections to an existing atmospheric density model. The approaches have shown the ability to provide a general improvement to a baseline atmospheric density model. The DCA approaches have several disadvantages, however. First, the approaches are designed to run internal to a particular orbit determination scheme. This means that users of other orbit determination schemes have to rely on that system to provide atmospheric density correction updates. In addition, the atmospheric density corrections are only applicable to a certain point in time. Thus, one must have access to the entire archive of density corrections applicable to a given problem. A second limitation of DCA approaches to date is that the corrections have limited spatial and temporal resolution. The corrections do allow the models to better represent effects with temporal resolution of several hours to days, but not temporal effects with shorter time scales.Most dynamic atmospheric density models use a daily solar flux and averaged 3 h geomagnetic indices as input values to address solar and geomagnetic activity. Using these values limits the ability of the models to represent changes in the atmosphere that occur within the averaging interval of the input data. Although the original Russian DCAwork used radar observations, most current DCA approaches use two-line element sets of a large number of low-Earth-orbit objects as observations to develop atmospheric corrections in a DCA scheme. Unfortunately, relying on two-line element sets reduces the accuracy of the corrections and provides limited temporal resolution. HASDM [6–8] relies on the actual radar observations of low-Earthorbit satellites, but even this accuracy is lower than that available from precision orbit ephemerides (POEs) or satellite laser ranging (SLR). In addition, the radar observations are not generally available. The second major type of research related to improving atmospheric density knowledge is using satellites with accelerometers to measure nonconservative forces, which can then be used to estimate density. This represents the opposite extreme from using two-line element sets in terms of accuracy and total data availability. The accelerometer data provide a way to separate the gravitational forces from the nonconservative forces such as drag, solar radiation pressure, and Earth radiation pressure. Then by using accurate radiation pressure models, the drag acceleration can be determined Presented as Paper 2009-6951 at theAIAA/AASAstrodynamics Specialist Conference, Honolulu, HI, 18–21 August 2008; received 12 October 2009; revision received 22 June 2010; accepted for publication 31 July 2010. Copyright

Comparing Physical Drag Coefficients Computed Using Different Gas-Surface Interaction Models

Drag coefficient is a major source of uncertainty in calculating the aerodynamic forces on satellites in low Earth orbit. Closed-form solutions are available for simple geometries under the assumption of free molecular flow; however,mostsatelliteshavecomplexgeometries,andamoresophisticatedmethodofcalculatingthedragcoefficient is needed. This work builds toward modeling physical drag coefficients using the direct simulation Monte Carlo method capable of accurately modeling flow shadowing and concave geometries. The direct simulation threedimensional visual program and the direct simulation Monte Carlo analysis code are used to compare the effects of two separate gas–surface interaction models: diffuse reflection with incomplete accommodation and quasi-specular Cercignani–Lampis–Lordmodels.Resultsshowthatthetwogas–surfaceinteractionmodelscomparewellataltitudes below ∼500 km during solar maximum conditions and below ∼400 km during solar minimum conditions. The differenceindragcoefficientofasphereat ∼800 kmcalculated usingthetwogas–surfaceinteractionmodels is ∼6% during solar maximum and increases to ∼10% during solar minimum. The difference in drag coefficient of the GRACE satellite computed using the two gas–surface interaction models at ∼500 km differs by ∼15% during solar minimum conditions and by ∼2–3% during solar maximum conditions.

Altimeter sampling characteristics using a single satellite

Altimetric satellites have characteristic sampling patterns in both space and time based on their repeat period and orbit inclination. Aliased phenomena measured by altimetric measurements can appear as propagating waves with both wavelength and direction of propagation different from the underlying phenomena. All signals that contribute to the altimetric measurement can be aliased and produce such patterns, not just tidal signals. For example, mesoscale energy will be aliased as will unmodeled atmospheric variations. Past discussions of aliasing have only considered spatially homogeneous signals. This paper extends this work to phenomena with finite wavelengths and considers both the north-south and east-west components of the resulting aliases.

CU sea level system at Platform Harvest

Calibration data for the TOPEX/Poseidon altimeter was collected at Texacos Platform Harvest off the coast of southern California. The CU sea level system, containing two Paros depth sensors, was designed and installed at Platform Harvest to collect submerged pressure data. Corrections for instrument bias, water density, and atmospheric pressure were applied to each depth sensor and sea level obtained relative to an established benchmark on the platform. Estimates of H 1/3 were determined to characterize the sea state during the 2‐h period surrounding each overflight using classical theory. To test the validity of these assumptions, the ratio between spectra measurements from the upper and lower depth sensors was normalized by the expected theoretical ratio. The results differ from theory by ∼1% with a standard deviation of ∼2%. The weighted mean frequency as a function of H 1/3 was calculated during several overflight periods. Results indicate that the frequency content tends to be bimodal for H 1/3 valu...

Drag Coefficient Estimation in Orbit Determination

Drag modeling is the greatest uncertainty in the dynamics of low Earth satellite orbits where ballistic coefficient and density errors dominate drag errors. This paper examines fitted drag coefficients found as part of a precision orbit determination process for Stella, Starlette, and the GEOSAT Follow-On satellites from 2000 to 2005. The drag coefficients for the spherical Stella and Starlette satellites are assumed to be highly correlated with density model error. The results using MSIS-86, NRLMSISE-00, and NRLMSISE-00 with dynamic calibration of the atmosphere (DCA) density corrections are compared. The DCA corrections were formulated for altitudes of 200–600 km and are found to be inappropriate when applied at 800 km. The yearly mean fitted drag coefficients are calculated for each satellite for each year studied. The yearly mean drag coefficients are higher for Starlette than Stella, where Starlette is at a higher altitude. The yearly mean fitted drag coefficients for all three satellites decrease as solar activity decreases after solar maximum.

Comparison of Density Estimation for CHAMP and GRACE Satellites

This paper compares atmospheric density estimates obtained from precision orbit ephemerides (POE) for the CHAMP and GRACE satellites. GRACE-A and CHAMP POE data are used to derive atmospheric densities which are calibrated with densities derived from the onboard accelerometers of these satellites. The resulting calibrations are compared between the two satellites for many time periods at differing levels of solar and geomagnetic activity. An overall comparison of calibration for the two satellites is performed. In addition, three particular time periods are examined in greater detail for both satellites. Density is estimated as a correction to an existing baseline density model. The corrections to the Jacchia family of models are found to produce better calibration results with accelerometer data than the corrections to the MSIS family of models. The calibration for GRACE density estimation is found to be consistent regardless of solar and geomagnetic activity and matches the calibration for CHAMP density estimation during low activity times and differs only slightly during more active times.

Calibrating Precision Orbit Derived Total Density

Atmospheric density modeling is the greatest uncertainty in the dynamics of low Earth satellite orbits. Accurate density calculations are required to provide meaningful estimates of the atmospheric drag perturbing satellite motion. This paper uses precision satellite orbits from the Challenging Minisatellite Payload (CHAMP) as measurements in an optimal orbit determination process to estimate total atmospheric density. The accuracy of the precision orbit derived density is compared to CHAMP accelerometer derived density for various filter/smoother settings to calibrate the precision orbit derived densities. Settings studied include the half-lives of the ballistic coefficient and density Gauss-Markov processes, solution spans, and baseline density models. The precision orbit derived densities are shown to more closely match the accelerometer derived densities than either empirical models or dynamic calibration of the atmosphere.

Relative Motion of Two Spacecraft near the Earth -Moon Triangular Libration Points

Formation flying missions to the libration points are becoming common avenues of research. While nearly all of the literature explores the dynamics, navigation, and control of formations near the Sun -Earth/Moon L2, little attention has been paid to the triangular libration points. This paper explores the dynamics of relative motion near the Earth -Moon L4 point within the circular restricted three -body problem . T his research is intended to provide a baseline for and serve as a precursor to more detailed investigation of formation design, control, and navigation at the triangular libration points.