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The design of solar sail trajectories is treated, along with the associated thrust vector control history that transfers a solar-sail-propelled spacecraft, or sailcraft, from the Earth/Sun L1 libration point to a sub-L1 retion nearer the Sun.
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Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.
A baseline configuration for the dual-aircraft platform (DAP) concept is described and evaluated in a physics-based flight dynamics simulations for two month-long missions as a communications relay in the lower stratosphere above central Florida, within 150-miles of downtown Orlando.The DAP configuration features two large glider-like (130 ft wing span) unmanned aerial vehicles connected via a long adjustable cable (total extendible length of 3000 ft) which effectively sail without propulsion using available wind shear. Use of onboard LiDAR wind profilers to forecast wind distributions are found to be necessary to enable the platform to efficiently adjust flight conditions to remain sailing by finding sufficient wind shear across the platform. The aircraft derive power from solar cells, like a conventional solar aircraft, but also extract wind power using the propeller as a turbine when there is an excess of wind shear available.Month-long atmospheric profiles (at 3-5 min intervals) in the vicinity of 60,000-ft are derived from archived data measured by the 50-Mhz Doppler Radar Wind Profiler at Cape Canaveral and used in the DAP flight simulations. A cursory evaluation of these datasets show that sufficient wind shear for DAP sailing is persistent, suggesting that DAP could potentially sail over 90% of the month-long durations even when limited by modest ascent/descent rates.DAP's novel guidance software uses a non-linear constrained optimization technique to define waypoints such that sailing mode of flight is maintained where possible, and minimal thrust is required where sailing is not practical. A set of constraints are identified which result in waypoints that enable efficient flight (i.e., minimal use of propulsion) over the two month-long flight simulations. Waypoint solutions may need to be tabulated for a wide range of potential atmospheric conditions and stored onboard for quick retrieval on a real DAP.DAP's flight control software uses an unconventional mixture of spacecraft and aircraft control techniques. Flight simulations confirms that this controls approach enables the platform to consistently reach successive waypoints over the month-long flight simulations.The ability of DAP to transition between the sailing mode (i.e., cable tension is high) and standard formation flight (i.e., cable tension is low) is a vital capability (e.g., to enable intermittent turns while stationkeeping). A new method to perform these transitions has been identified and characterized with flight simulation which requires special aircraft modifications.The energy-usage of the DAP configuration during two month-long stationkeeping missions over central Florida (i.e., stationkeeping over Orlando) is evaluated and compared to that of a pure solar aircraft of the same weight and aerodynamic performance. DAP is shown to consistently reduce net propulsion usage while simultaneously increasing solar energy capture.A baseline 700 GHz communications system is described and its performance evaluated for the proposed mission over central Florida. It is found that the variable roll orientation of the aircraft would increase the power required to maintain coverage over the stationkeeping radius of 150 miles (e.g., by as much as 100% when DAP is 150 miles from Orlando), compared to level flight. This effect can be mitigated via additional antenna design complexity or a more restricted stationkeeping radius.
The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.
The Lunar Reconnaissance Orbiter (LRO) will be the first mission under NASA's Vision for Space Exploration. LRO will fly in a low 50 km mean altitude lunar polar orbit. LRO will utilize a direct minimum energy lunar transfer and have a launch window of three days every two weeks. The launch window is defined by lunar orbit beta angle at times of extreme lighting conditions. This paper will define the LRO launch window and the science and engineering constraints that drive it. After lunar orbit insertion, LRO will be placed into a commissioning orbit for up to 60 days. This commissioning orbit will be a low altitude quasi-frozen orbit that minimizes stationkeeping costs during commissioning phase. LRO will use a repeating stationkeeping cycle with a pair of maneuvers every lunar sidereal period. The stationkeeping algorithm will bound LRO altitude, maintain ground station contact during maneuvers, and equally distribute periselene between northern and southern hemispheres. Orbit determination for LRO will be at the 50 m level with updated lunar gravity models. This paper will address the quasi-frozen orbit design, stationkeeping algorithms and low lunar orbit determination.
The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. In July 2009, a series of orbit-raising maneuvers began the proper orbit phasing of the two spacecraft for the first lunar flybys. Over subsequent months, additional propulsive maneuvers and gravity assists will be performed to move each spacecraft though the Sun-Earth weak stability regions and eventually into Earth-Moon libration point orbits. We will present the overall orbit designs for the two ARTEMIS spacecraft and provide analysis results of the 3/4-body dynamics, and the sensitivities of the trajectory design to both · maneuver errors and orbit determination errors. We will present results from the. initial orbit-raising maneuvers.
This paper presents the results of a high-fidelity simulation of spacecraft orbit determination in a near rectilinear halo orbit (NRHO). Others in the literature have examined this problem with linear covariance analysis, but the highly-nonlinear dynamics of this orbit challenge the assumptions underlying such analyses. The present work builds on similar analysis performed by other authors to contribute a fuller understanding of the operational requirements for NRHO navigation. The present work serves as a check to the assumptions of previous studies and an independent verification of those results. The results from the literature are extended by quantifying the space of orbital states from which a spacecraft with given control authority can safely return to the nominal path. Spacecraft state uncertainty estimates are evaluated as a function of time. Simulated range and range-rate measurements with the Deep Space Network (DSN) ground stations are used to model orbit determination accuracy. Orbit maintenance maneuvers are performed using both short-horizon and long-horizon stationkeeping targeting. Monte Carlo analysis of orbit determination and stationkeeping is performed. This paper quantifies the achievable state uncertainty with deep space network (DSN)-only range and range-rate observations. This paper also addresses requirements on the frequency of DSN observation periods and correlates ground contact frequency with navigation accuracy. The results of several related studies are presented and discussed: the effect of missing ground station passes, the effect of missing stationkeeping maneuvers, the sensitivity of the spacecraft state estimate to realistic error sources, and stationkeeping propellant budget.
Tradeoffs between electric propulsion system mass ratio and transfer time from LEO to GEO were conducted parametrically for various thruster efficiency, specific impulse, and other propulsion parameters. A computer model was developed for performing orbit transfer calculations which included the effects of aerodynamic drag, radiation degradation, and occultation. The tradeoff results showed that thruster technology areas for integrated propulsion should be directed towards improving primary thruster efficiency in the range from 1500 to 2500 seconds, and be continued towards reducing specific mass. Comparison of auxiliary propulsion systems showed large total propellant mass savings with integrated electric auxiliary propulsion. Stationkeeping is the most demanding on orbit propulsion requirement. At area densities above 0.5 sq m/kg, East-West stationkeeping requirements from solar pressure exceed North-South stationkeeping requirements from gravitational forces. A solar array pointing strategy was developed to minimize the effects of atmospheric drag at low altitude, enabling electric propulsion to initiate orbit transfer at Shuttle's maximum cargo carrying altitude. Gravity gradient torques are used during ascent to sustain the spacecraft roll motion required for optimum solar array illumination. A near optimum cover glass thickness of 6 mils was established for LEO to GEO transfer.
It is pointed out that a large class of future spacecraft, referred to as large space structures (LSS), will require advanced stationkeeping thrust subsystems. The present investigation is concerned with the performance requirements of such advanced stationkeeping thrust subsystems. An analytical model is employed to evaluate the sensitivity of the total stationkeeping thrust-system mass, for geosynchronous spacecraft, to variations in the mission parameters and thrust-system performance, taking into account ion propulsion thrust systems. The model is formulated for geosynchronous missions and considers only the N-S orbit perturbations due to sun-moon forces and the E-W orbit perturbations due to solar pressure, since these are the dominant orbit perturbations of LSS missions. The thrust system is scaled in relation to the performance capabilities of the existing 8- and 30-cm diameter ion-thruster technology and consists of separate N-S and E-W thrusters.
Solar electric propulsion (SEP) technology is already being used for geostationary satellite stationkeeping to increase payload mass. By using this same technology to perform part of the orbit transfer additional increases in payload mass can be achieved. Advanced chemical and N2H4 arcjet systems are used to increase the payload mass by performing stationkeeping and part of the orbit transfer. Four mission options are analyzed which show the impact of either sharing the orbit transfer between chemical and SEP systems or having either complete the transfer alone. Results show that for an Atlas 2AS payload increases in net mass (geostationary satellite mass less wet propulsion system mass) of up to 100 kg can be achieved using advanced chemical for the transfer and advanced N2H4 arcjets for stationkeeping. An additional 100 kg can be added using advanced N2H4 arcjets for part of a 40 day orbit transfer.
Tracking and Data Relay Satellite (TDRS) orbit determination and prediction are supported by the Flight Dynamics Facility (FDF) of the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). TDRS System (TDRSS)-user satellites require predicted TDRS ephemerides that are up to 10 weeks in length. Previously, long-term ephemerides generated by the FDF included predictions from the White Sands Complex (WSC), which plans and executes TDRS maneuvers. TDRSs typically have monthly stationkeeping maneuvers, and predicted postmaneuver state vectors are received from WSC up to a month in advance. This paper presents the results of an analysis performed in the FDF to investigate more accurate and economical long-term ephemerides for the TDRSs. As a result of this analysis, two new methods for generating long-term TDRS ephemeris predictions have been implemented by the FDF. The Center-of-Box (COB) method models a TDRS as fixed at the center of its stationkeeping box. Using this method, long-term ephemeris updates are made semiannually instead of weekly. The impulse method is used to model more maneuvers. The impulse method yields better short-term accuracy than the COB method, especially for larger stationkeeping boxes. The accuracy of the impulse method depends primarily on the accuracy of maneuver date forecasting.
The main science objective of the Microwave Anisotropy Probe (MAP) mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations - anisotropy. MAP will collect these measurements from a lissajous orbit about the Sun-Earth/Moon L2 Lagrange Point. The NASA Goddard Space Flight Center (GSFC) Flight Dynamics Analysis Branch provided mission analysis, maneuver planning and maneuver calibration for the MAP spacecraft. This paper will provide an overview of the MAP trajectory design, a summary of the maneuvers executed. Differences from the pre-launch nominal plan will also be discussed. During the MAP phasing loops, MAP performed three calibration maneuvers in order to characterize the performance of the primary sets of thrusters - +X, +Z, and -Z. The calibration maneuvers were designed to minimize their impact on the trajectory. Four maneuvers were performed to set up the gravity assist of the Moon - required to propel MAP out to its orbit about L2. These maneuvers were performed at the three phasing loop perigees and at 18 hours after the final perigee. It became necessary to alter some of the perigee maneuvers in order to shape the gravity assist. This shaping was done to help meet some mission goals. In particular, the gravity assist was changed slightly in order to remove lunar shadows in both the cruise out to L2 and in the first revolution about L2. This amounted to a change in the phasing loop AV of less than 1 m/s. After the gravity assist, two mid-course correction (MCC) maneuvers were performed in order to fine-tune the trajectory. MCC1 was used to clean up and errors which resulted from the gravity assist. MCC2 was performed in order to mitigate a large stationkeeping maneuver following a crucial instrument calibration period during the cruise phase. MAP executed it's first stationkeeping maneuver in January 16th and is ready for a second calibration period during late Winter / early Spring. Further information concerning subsequent stationkeeping maneuver will be added as they become available.
The Wide-Field Infrared Survey Telescope (WFIRST), a NASA observatory designed to investigate dark energy and astrophysics, is planned for a launch in 2025 to orbit the Sun-Earth L2 (SEL2) Libration Point. Due to the instability of the SEL2 environment, WFIRST must perform maneuvers to remain in its mission orbit. This paper investigates how different error sources affect the resulting stationkeeping delta v for WFIRST. We study how Solar Radiation Pressure (SRP) modeling affects WFIRST's orbital motion and stability, and how SRP combined with Orbit Determination (OD) errors drive the stationkeeping maneuver magnitudes. Our goal is to determine the best way to model WFIRST's SRP so that we minimize its impact on total stationkeeping delta v required over the mission lifetime.
Stationkeeping problems and guidance technique for control of stationkeeping maneuver between orbiting vehicles
The purpose of the spacecraft is to space qualify a number of components for the next generation of communications satellites. The state of development of ion thrusters has reached a point where at least three types of engine may be considered for integration on spacecraft. The proposed methods of stationkeeping require that the thruster operate with a duty cycle of somewhat less than 12 hours in a 24 hour period. Several possible mounting positions for the thrusters were considered during the conceptual design phase. It is concluded that an experimental ion thruster subsystem may be incorporated in the communication satellite and used to demonstrate, at a minimum, north-south stationkeeping of the spacecraft in synchronous orbit.
An ion engine subsystem intended for satellite stationkeeping tasks is described. Ion thrusters are chosen to perform the task because the specific impulse is at least an order of magnitude higher than the commonly used reaction control jets. The higher the value of specific impulse, the greater the total impulse that can be attained for a given weight of propellant, hence cost benefits result. The integration, subsystem testing, and the operating plans for the ion engine experiment to be flown in 1975 on the Canadian Communications Technology Satellite (CTS) are described. The subsystem is designed to demonstrate north-south stationkeeping, attitude control by means of thrust vectoring, long-term space storage and restart capability, and compatibility with a high powered communications transponder.