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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Analysis of error in TOMS total ozone as a function of orbit and attitude parameters

Computer simulations of orbital scenarios were performed to examine the effects of orbital altitude, equator crossing time, attitude uncertainty, and orbital eccentricity on ozone observations by future satellites. These effects were assessed by determining changes in solar and viewing geometry and earth daytime coverage loss. The importance of these changes on ozone retrieval was determined by simulating uncertainties in the TOMS ozone retrieval algorithm. The major findings are as follows: (1) Drift of equator crossing time from local noon would have the largest effect on the quality of ozone derived from TOMS. The most significant effect of this drift is the loss of earth daytime coverage in the winter hemisphere. The loss in coverage increases from 1 degree latitude for + or - 1 hour from noon, 6 degrees for + or - 3 hours from noon, to 53 degrees for + or - 6 hours from noon. An additional effect is the increase in ozone retrieval errors due to high solar zenith angles. (2) To maintain contiguous earth coverage, the maximum scan angle of the sensor must be increased with decreasing orbital altitude. The maximum scan angle required for full coverage at the equator varies from 60 degrees at 600 km altitude to 45 degrees at 1200 km. This produces an increase in spacecraft zenith angle, theta, which decreases the ozone retrieval accuracy. The range in theta was approximately 72 degrees for 600 km to approximately 57 degrees at 1200 km. (3) The effect of elliptical orbits is to create gaps in coverage along the subsatellite track. An elliptical orbit with a 200 km perigee and 1200 km apogee produced a maximum earth coverage gap of about 45 km at the perigee at nadir. (4) An attitude uncertainty of 0.1 degree in each axis (pitch, roll, yaw) produced a maximum scan angle to view the pole, and maximum solar zenith angle).

Gregg, W. W.↗
NASA NTRS1991

Navigation for Muses-A (HITEN) aerobraking in the earth's atmosphere - Preliminary report

Aerobraking phase covariance study results and preliminary joint JPL/ISAS orbit determination findings are presented. Possible explanations for differences in the JPL and ISAS perigee altitude results are discussed. Agreement between predicted and reconstructed values for the altitude and time of perigee passage attests to the accuracy of the JPL orbit solutions.

Kawaguchi, J.↗
NASA NTRS1995

Orbit determination of highly elliptical Earth orbiters using improved Doppler data-processing modes

A navigation error covariance analysis of four highly elliptical Earth orbits is described, with apogee heights ranging from 20,000 to 76,800 km and perigee heights ranging from 1,000 to 5,000 km. This analysis differs from earlier studies in that improved navigation data-processing modes were used to reduce the radio metric data. For this study, X-band (8.4-GHz) Doppler data were assumed to be acquired from two Deep Space Network radio antennas and reconstructed orbit errors propagated over a single day. Doppler measurements were formulated as total-count phase measurements and compared to the traditional formulation of differenced-count frequency measurements. In addition, an enhanced data-filtering strategy was used, which treated the principal ground system calibration errors affecting the data as filter parameters. Results suggest that a 40- to 60-percent accuracy improvement may be achievable over traditional data-processing modes in reconstructed orbit errors, with a substantial reduction in reconstructed velocity errors at perigee. Historically, this has been a regime in which stringent navigation requirements have been difficult to meet by conventional methods.

Estefan, J. A.↗
NASA NTRS1961

A Comparison of Theory and Observation of the Echo I Satellite

Observations of the Echo I balloon satellite have been compared with a theory including the following perturbing effects: (1) solar radiation pressure; (2) lunar and solar gravitation; (3) second, third, and fourth harmonics of the earth's gravitational potential; and (4) atmospheric drag. With a set of orbital elements at the 26th day of the lifetime of the satellite, it was possible to match the observational data to 180 days with root mean square residuals as follows: Delta-a = 17.9 km, Delta-e = 0.0021, Delta-i = 0.0177 deg., Delta-omega = 1.1231 deg., Delta-Omega = 0.4821 deg., Delta-perigee height = 7.50 km. No differential correction has been applied as yet. Values of atmospheric density between 1500 and 930 km, assuming neutral drag effects only, have been inferred from the orbital data. The connection between solar activity and drag is also examined. As the Echo I perigee height continues to oscillate between 900 and 1500 km, more valuable orbital data will be obtained and atmospheric properties will be deduced. Further refinements in the mathematical model, especially in a time-dependent model atmosphere, should bring a substantial reduction in the residuals of the observations.

Bryant, R. W.↗
NASA NTRS1961

The Effect of Lift on Entry Corridor Depth and Guidance Requirements for the Return Lunar Flight

Corridors for manned vehicles are defined consistent with requirements for avoiding radiation exposure and for limiting values of peak deceleration. Use of lift increases the depth of the entry corridor. Mid-course guidance requirements appear to be critical only for the flight-path angle. Increasing the energy of the transport orbit increases the required guidance accuracy for the flight-path angle. Corrective thrust applied essentially parallel to the local horizontal produces the maximum change in perigee altitude for a given increment of velocity. Energy required to effect a given change in perigee altitude varies inversely with range measured from the center of the earth.

Wong, Thomas J.↗
NASA NTRS1997

Ion Outflow and Convection in the Polar Cap and Cleft as Measured by Tide, EFI, MFE and Timas

This study examines high-latitude ion outflows and velocities perpendicular to the magnetic field derived from moments of ion distributions measured by the TIDE (Thermal Ion Dynamics Experiment) instrument on the Polar satellite. Hydrogen and oxygen ions are shown to be E X B drifting in the polar cap and cleft regions with a speed of about 5-20 km/s at apogee (approximately 9 Re) and a speed of 1-2 km/s at perigee (approximately 1. 8 Re). E X B drifts are calculated from electric fields measured by EFI (Electric Field Instrument) and magnetic fields measured by MFE (Magnetic Field Experiment) both of which are also on Polar. How convection at Polar's perigee relates to potential patterns of the ionosphere will be discussed. In the cusp/cleft the distribution of hydrogen extends over a large enough range of energy to be measured by both TIDE and the Toroidal Imaging Mass-Angle Spectrograph (TIMAS). Such comparisons will be also be presented.

Elliott, H. A.↗
NASA NTRS1999

Velocity and Density of Low Energy Ions in High-Latitude Magnetosphere

This study examines the characteristics of low energy ions at the polar cap boundary and within the polar cap in relationship to the convection velocity. The source of low energy ions in the magnetosphere could be driven by solar wind/IMF (interplanetary magnetic fields) interactions affecting energization processes of ionospheric ions. The IMF also influences the convection pattern which is in part responsible for determining the path ions take as they leave the ionosphere and contribute to magnetospheric populations. The primary source of data for this study is the Thermal Ion Dynamics Experiment (TIDE) on board the Polar satellite. TIDE can measure 3-D velocities and covers an energy range ideal for examining the polar cap plasma (0-450 eV). Due to certain limitations, this study uses H+ measurements at apogee and O+ measurements at perigee. At apogee H+ is very field-aligned and outflowing, and at perigee O+ is often moving downward in the polar cap proper. The path highly field-aligned flows take across the polar cap are also affected by changes in the magnetic field line topology which varies with geophysical conditions. Convection near the polar cap boundary is of particular interest since often the convection there is highly structured, and convection reversals may play a role in causing ion outflow. This study will examine in particular the density structures of ions in relationship to the convection velocity. Examining such relationships may provide insight into understanding the consequences of the 3-D flow on the density of ions in the polar cap, and transport of ions across the polar cap.

Elliott, Heather A.↗
NASA NTRS1999

Venus and Beyond Using the Ariane ASAP Launch Capability

The cost of executing planetary missions in the next ten years is expected to decrease significantly. The principle reason is that new technology is reducing spacecraft mass while increasing capability. Another reason is that launch costs are expected to decrease. A move in this direction is to permit important planetary missions to fly as secondary payloads, and this opportunity is now provided by the French on the Ariane 5 using the Ariane Structure for Auxiliary Payloads (ASAP). The ASAP will fly on GEO missions, and can boost up to eight 100 kg (or 200 kg, if paired) payloads into the elliptical geosynchronous transfer orbit (GTO), which delivers large communication satellites to GEO. An efficient multi-burn method has been developed by this author to deliver these small spacecraft from GTO to Mars and other destinations. This method, referred to here as Moon-Earth Gravity Assist (MEGA), requires 3 or more major maneuvers together with close flybys of the earth and moon. An example for a Mars 2003 mission (not to scale) is shown in Figure 1, where, once in GTO, the first burn sends the spacecraft beyond the Moon to a distance of 1.2 million kilometers. At apogee, the second burn targets to an encounter with the Moon such that a swingby returns the spacecraft to the Earth with a 300 km perigee, and with an inclination such that a perigee burn will send the spacecraft off to Mars with the required escape velocity vector. Details of this method, specifically for Mars missions, can be found in Reference 3. A similar strategy works for Venus, with some caveats. This method is required to work for any Ariane 5 launch date over a three month period, to ensure a high probability of getting off the ground. The launch period is provided by fixing the Earth escape date (3rd burn), but allowing the high ellipse (beyond the Moon) period to vary by one or two months, and also allowing a one to two month wait time in GTO (or other orbit) before the first burn is performed. Figure 2 shows the trajectory profiles for the early and late GTO launch dates for a Mars 2003 mission. Venus. which is an inner planet, poses special problems for the MEGA process. The escape direction is reverse that of Earth's motion, and the GTO apogee arrival

Penzo, Paul A.↗
NASA NTRS1999

Local Time Dependence of Jovian Radio Emissions Observed by Galileo

Galileo has been in orbit around Jupiter since December 1995. All the orbits are equatorial and elliptical, with apogees between 60 R(sub J) - 142 R(sub J) and perigees from 8 - 12 R(sub J). Since orbit injection, the plasma wave instrument (PWS) has been collecting data over specific intervals of each of the orbits at all local times and a range of different radial distances. We present the results of a survey of the data for the frequency range 300 kHz to 5.6 MHz, which includes the hectometric (HOM) and low-frequency decametric (DAM) emissions. The results indicate that both the HOM and DAM emission are more intense and occur more frequently in the midnight sector of Jupiter. This is in analogy to Earth and consistent with a magnetic substorm source for a portion of the radio emissions in this frequency range. Another peak in the power levels is observed on the Jovian dayside in the local time range 11 hrs < LT < 12 hrs. This peak does not have a terrestrial counterpart. We speculate that this dayside peak may be a result of sampling near perigee, but we cannot rule out the possibility that this is not the case.

Menietti, J. D.↗
NASA NTRS2002

Orbit Determination Support for the Microwave Anisotropy Probe (MAP)

The Microwave Anisotropy Probe (MAP) is a Medium Class Explorers (MIDEX) mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The main science objective of the MAP mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations anisotropy. MAP was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle at exactly 19:46:46.183 UTC on June 30, 2001. The spacecraft received a nominal direct insertion by the Delta into a 185 km circular orbit. MAP was then maneuvered into a sequence of phasing loops designed to set up a lunar swingby (gravity-assisted acceleration) of the spacecraft onto a transfer trajectory to a Lissajous orbit about the Earth-Sun L2 point. The mission duration is approximately 27 months with 3 to 4 months of transfer time to the final mission orbit about L2. The MAP transfer orbit consisted of 3.5 phasing loops: the first loop has a 7-day period, the second and third loops have a 9-day period, and the last half loop has a 4-day period as illustrated in Figure 1, which also indicates the placement of maneuvers. A Pfinal correction maneuver was performed 18 hours after the last perigee to more closely achieve the targeted lissajous orbit. The lunar encounter or swingby took place approximately 30 days after launch. After the lunar encounter, the spacecraft will cruise for approximately 120 days before it arrives at L2. A Mid-Course Correction (MCC) maneuver was executed seven days after the swingby to further refine the trajectory. Once the MAP satellite is injected into the L2 Lissajous orbit, it will perform occasional stationkeeping maneuvers to maintain the Lissajous orbit for a minimum of two years (and a goal of four years). Because of its complex orbital characteristics, the mission provided a unique challenge to orbit determination (OD) support in many orbital regimes. Extensive trajectory error covariance analysis was performed to predict ephemeris accuracy for the OD process using a Bayesian least-squares technique. The orbit determination error analysis is essential for maneuver planning and maneuver recovery study. Several tracking scenarios were investigated for each phase of the mission. This paper provides a summary of the premission trajectory covariance error analysis, as well as actual real-time OD results. The use and impact of the various tracking stations, systems, and measurements will be discussed. Details of the operational OD support and the inferred OD accuracy will be presented, and the results will be compared to the premission covariance analysis, In addition, there will be a discussion of the challenges presented to OD support including delta-Vs at apogee as well as perigee, and effects due to spacecraft attitude mode, in light of their implications to the OD accuracy and covariance analysis.

Truong, Son H.↗
NASA NTRS2002

The Maneuver Planning Process for the Microwave Anisotropy Probe (MAP) Mission

The Microwave Anisotropy Probe (MAP) was successfully launched from Kennedy Space Center's Eastern Range on June 30, 2001. MAP will measure the cosmic microwave background as a follow up to NASA's Cosmic Background Explorer (COBE) mission from the early 1990's. MAP will take advantage of its mission orbit about the Sun-Earth/Moon L2 Lagrangian point to produce results with higher resolution, sensitivity, and accuracy than COBE. A strategy comprising highly eccentric phasing loops with a lunar gravity assist was utilized to provide a zero-cost insertion into a lissajous orbit about L2. Maneuvers were executed at the phasing loop perigees to correct for launch vehicle errors and to target the lunar gravity assist so that a suitable orbit at L2 was achieved. This paper will discuss the maneuver planning process for designing, verifying, and executing MAP's maneuvers. A discussion of the tools and how they interacted will also be included. The maneuver planning process was iterative and crossed several disciplines, including trajectory design, attitude control, propulsion, power, thermal, communications, and ground planning. Several commercial, off-the-shelf (COTS) packages were used to design the maneuvers. STK/Astrogator was used as the trajectory design tool. All maneuvers were designed in Astrogator to ensure that the Moon was met at the correct time and orientation to provide the energy needed to achieve an orbit about L2. The Mathworks Matlab product was used to develop a tool for generating command quaternions. The command quaternion table (CQT) was used to drive the attitude during the perigee maneuvers. The MatrixX toolset, originally written by Integrated Systems, Inc., now distributed by Mathworks, was used to create HiFi, a high fidelity simulator of the MAP attitude control system. HiFi was used to test the CQT and to make sure that all attitude requirements were met during the maneuver. In addition, all ACS data plotting and output were generated in MatrixX. A final test used FlatSat, a real-time hardware-in-the-loop simulator, which used identical MAP flight code to simulate operations on the spacecraft. Simulations in FlatSat allowed the MAP team to verify maneuver commands, timing, and spacecraft configuration before the commands were sent up to the spacecraft for execution. The MAP maneuver team successfully pieced together all of these COTS tools for designing MAP's maneuvers and MAP is now collecting data at L2.

Mesarch, Michael A.↗
NASA NTRS2002

An Overview of Trajectory Design Operations for the Microwave Anisotropy Probe Mission

The purpose of this paper is to document the results of the pre-launch trajectory design and the real-time operations for the Microwave Anisotropy Probe (MAP) mission, launched on June 30, 2001. Once MAP was successfully inserted into a highly elliptical phasing orbit, three perigee maneuvers and a final perigee correction maneuver were performed to tailor a lunar encounter on July 30, 2001. MAP achieved its final Lissajous orbit (0.5 deg. by 10.5 deg.) about the Sun-Earth/Moon L2 libration point via this lunar encounter. This paper will show the maneuvers that were designed to arrive at the mission orbit. A further discussion of how the MAP trajectory analysts altered the pre-launch phasing loop maneuvers as well as the lunar encounter to meet all mission constraints, including the constraint of zero lunar shadows is also included.

Mesarch, Michael A.↗
NASA NTRS2003

The O+ Density Trough at 5000 km Altitude in the Polar Cap

At altitudes near 5000 km over the Southern polar cap region of the terrestrial magnetospherehonosphere, the Thermal Ion Dynamics Experiment (TIDE) onboard the Polar satellite has observed O+ ion density trough regions, in which the O+ densities were at least one order of magnitude lower than the surrounding O+ densities. In the O+ demify trough regions, the estimated O+ densities were generally lower than 0.01 per cc. The boundaries between normal density level regions and the trough density regions were usually abrupt transitions. From December 1, 1997 to November 30, 1998, polar cap O+ troughs in Polar/TIDE observations occurred at a frequency of about 48%. Statistical examination of the Polar perigee observations from December 1 , 1997 to November 30, 1998 shows that the Polar perigee passes evenly covered the southern polar cap region, while the O+ density trough was always located on the nightside portion of the polar cap magnetospherehonosphere, and that invariant latitude spans of such troughs could be as large as 230 in extent. The trough occurrence displayed strong seasonal dependence; in the winter season (e.g. for July in the southern hemisphere) the O+ ion density trough occurrence frequency ranged up to 92%, while in the summer season (e.g. for January in the southern hemisphere) it decreased to as infrequent as 15%. The O+ ion density trough occurrence appeared relatively independent of the geomagnetic Kp index, and IMF Bz, By conditions. However, as suggested by the seasonal dependence, the O+ ion density trough occurrence was strongly related to the solar zenith angle (SZA). In the SZA range 500 to 1250, the trough occurrence increased monotonically with SZA. Also, case-by-case examinations of near-simultaneous O+ densities and vertical velocities observed by the DMSP satellite group orbiting at 840 km altitude indicate that the O+ density troughs observed at 5000 km altitude exhibit moderate correlation or anti-correlation with topside ionosphere density or velocity features at 840 km altitude for approximately half of the near-conjunction cases examined.

Zeng, W.↗
NASA NTRS2004

The O(+) Density Trough at 5000 km Altitude in the Polar Cap

At altitudes near 5000 km over the southern polar cap region of the terrestrial magnetosphere/ionosphere, the Thermal Ion Dynamics Experiment (TIDE) on board the Polar satellite has observed O(+) ion density trough regions, in which the densities were at least one order of magnitude lower than the surrounding O(+) densities. In the 0" density trough regions, the estimated O+ densities were generally lower than 0.01 per cc. The boundaries between normal density level regions and the trough density regions were usually abrupt transitions. From 1 December 1997 to 30 November 1998, polar cap O(+) troughs in Polar/TIDE observations occurred at a frequency of about 48%. Statistical examination of the Polar perigee observations from 1 December 1997 to 30 November 1998 shows that the Polar perigee passes evenly covered the southern polar cap region, while the O(+) density trough was always located on the nightside portion of the polar cap magnetosphere/ionosphere, and that invariant latitude spans of such troughs could be as large as 23 deg. in extent. The trough occurrence displayed a strong seasonal dependence; in the winter season (e.g., for July in the Southern Hemisphere) the O(+) ion density trough occurrence frequency ranged up to 92%, while in the summer season (e.g., for January in the Southern Hemisphere) it decreased to as low as 15%. Our statistical results show that the trough occurrence was generally anticorrelated with solar wind dynamic pressure in the solar wind dynamic pressure range 0.8 - 2.6 nanopascal. The O(+) ion density trough occurrence appeared relatively independent of the geomagnetic Kp index, IMF Bz, and By conditions. However, as suggested by the seasonal dependence, the O(+) ion density trough occurrence was strongly related to the solar zenith angle (SZA). In the SZA range 50 deg. to 125 deg., the trough occurrence increased monotonically with SZA. In addition, we sought to determine consistent density and velocity signatures at lower altitudes associated the O(+) ion density trough at 5000 km by examining the near-simultaneous O(+) densities and vertical velocities observed by the DMSP satellite group orbiting at 840 km altitude. However, consistent correlations between the dual altitudes were not reliably established from the present examinations.

Zeng, W.↗
NASA NTRS2004

Qualification of Laser Diode Arrays for Mercury Laser Altimeter Mission

NASA's requirements for high reliability, high performance satellite laser instruments have driven the investigation of many critical components; specifically, 808 nm laser diode array (LDA) pump devices. The MESSENGER mission is flying the Mercury Laser Altimeter (MLA) which is a diode-pumped Nd:YAG laser instrument designed to map the topography of Mercury. The environment imposed on the instrument by the orbital dynamics places special requirements on the laser diode arrays. In order to limit the radiative heating of the satellite from the surface of Mercury, the satellite is designed to have a highly elliptical orbit. The satellite will heat near perigee and cool near apogee. The laser power is cycled during these orbits so that the laser is on for only 30 minutes (perigee) in a 12 hour orbit. The laser heats 10 C while powered up and cools while powered down. In order to simulate these operational conditions, we designed a test to measure the LDA performance while being temperature and power cycled. Though the mission requirements are specific to NASA and performance requirements are derived from unique operating conditions, the results are general and widely applicable. We present results on the performance of twelve LDAs operating for several hundred million pulses. The arrays are 100 watt, quasi-CW, conductively-cooled, 808 nm devices. Prior to testing, we fully characterize each device to establish a baseline for individual array performance and status. Details of this characterization can be found in reference. Arrays are divided into four groups and subjected to the temperature and power cycling matrix are shown.

Stephen, Mark↗
NASA NTRS2005

Visualization of Space-Time Ambiguities to be Explored by the NASA GEC Mission with a Critique of Synthesized Measurements for Different GEC Mission Scenarios

The objective of this grant was to study how a multi-satellite mission configuration can be optimized for maximum exploratory scientific return. NASA's Solar Terrestrial Probe (STP) concept mission Geospace Electrodynamic Connections (GEC) was the target mission for this pilot study. GEC prime mission characteristics were two fold: (i) a series of three satellites in the same orbit plane with differential spacing, and (ii) a deep-dipping phase in which these satellites could dip to altitudes as low as 130 km to explore the lower ionosphere and thermosphere. Each satellite would carry a full suite of plasma and neutral in-situ sensors and have the same dipping capability. This latter aspect would be envisaged as a series, up to 10, of deep-dipping campaigns, each lasting 10 days during which the perigee would be lowered to the desired probing depth. The challenge in optimization is to establish the scientific problems that can best be addressed by varying or selecting satellite spacing during a two-year mission while also interspersing, in this two year time frame, the deep-dipping campaigns. Although this sounds like a straightforward trade-off situation, it is complicated by the orbit precession in local time, the location of perigee, and that even the dipping campaigns will have preferred satellite spacing requirements.

Sojka, Jan J.↗
NASA NTRS2005

Fluctuations in Conjunction Miss Distance Projections as Time Approaches Time of Closest Approach

A responsibility of the Trajectory Operations Officer is to ensure that the International Space Station (ISS) avoids colliding with debris. United States Space Command (USSPACECOM) tracks and catalogs a portion of the debris in Earth orbit, but only objects with a perigee less than 600 km and a radar cross section (RCS) greater than 10 cm-objects that, in fact, represent only a small fraction of the objects in Earth orbit. To accommodate for this, the ISS uses shielding to protect against collisions with smaller objects. This study provides a better understanding of how quickly, and to what degree, USSPACECOM projections tend to converge to the final, true miss distance. The information included is formulated to better predict the behavior of miss distance data during real-time operations. It was determined that the driving components, in order of impact on miss distance fluctuations, are energy dissipation rate (EDR), RCS, and inclination. Data used in this analysis, calculations made, and conclusions drawn are stored in Microsoft Excel log sheets. A separate log sheet, created for each conjunction, contains information such as predicted miss distances, apogee and perigee of debris orbit, EDR, RCS, inclination, tracks and observations, statistical data, and other evaluation/orbital parameters.

Christian, John A., III↗
NASA NTRS2006

MXER Simulation Study (Appendix A)

In this study, we consider the dynamics of a spinning tether system in an elliptical orbit in application to the Momentum Exchange Electrodynamic Reboost system. Momentum exchange tether systems have been studied in a variety of applications since Hans Moravec's early publication. It has recently been suggested that momentum exchange systems can be enhanced with electrodynamic reboost between payload transfers. The Momentum Exchange Electrodynamic Reboost system (MXER) has a projected tether span of up to 100 km, and spins rapidly with a period of 6-7 min. It is placed in an orbit with a low perigee of about 400 km and a high apogee of about 8000 km. To capture a payload at a perigee rendezvous, within a window of a few seconds, the motion of the system has to be predicted with very high precision, having acceptable position errors on the order of 1 m. While this level of precision is routinely achieved today for conventional (non-tethered) satellites, it is much more difficult to achieve for a 100 km long flexible tether system. It is the goal of this study to investigate theoretical aspects of the dynamics and offer a practical approach to high precision dynamic modeling of a typical momentum exchange tether system.

Levin, E. M.↗