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DUKSUP: A Computer Program for High Thrust Launch Vehicle Trajectory Design and Optimization

From the late 1960s through 1997, the leadership of NASAs Intermediate and Large class unmanned expendable launch vehicle projects resided at the NASA Lewis (now Glenn) Research Center (LeRC). One of LeRCs primary responsibilities --- trajectory design and performance analysis --- was accomplished by an internally-developed analytic three dimensional computer program called DUKSUP. Because of its Calculus of Variations-based optimization routine, this code was generally more capable of finding optimal solutions than its contemporaries. A derivation of optimal control using the Calculus of Variations is summarized including transversality, intermediate, and final conditions. The two point boundary value problem is explained. A brief summary of the codes operation is provided, including iteration via the Newton-Raphson scheme and integration of variational and motion equations via a 4th order Runge-Kutta scheme. Main subroutines are discussed. The history of the LeRC trajectory design efforts in the early 1960s is explained within the context of supporting the Centaur upper stage program. How the code was constructed based on the operation of the AtlasCentaur launch vehicle, the limits of the computers of that era, the limits of the computer programming languages, and the missions it supported are discussed. The vehicles DUKSUP supported (AtlasCentaur, TitanCentaur, and ShuttleCentaur) are briefly described. The types of missions, including Earth orbital and interplanetary, are described. The roles of flight constraints and their impact on launch operations are detailed (such as jettisoning hardware on heating, Range Safety, ground station tracking, and elliptical parking orbits). The computer main frames on which the code was hosted are described. The applications of the code are detailed, including independent check of contractor analysis, benchmarking, leading edge analysis, and vehicle performance improvement assessments. Several of DUKSUPs many major impacts on launches are discussed including Intelsat, Voyager, Pioneer Venus, HEAO, Galileo, and Cassini.

Launch vehicle performance optimization↗

The Strategy for the Second Phase of Aerobraking Mars Global Surveyor

On February 19, 1999, the Mars Global Surveyor (MGS) spacecraft was able to propulsively establish its mapping orbit. This event followed the completion of the second phase of aerobraking for the MGS spacecraft on February 4, 1999. For the first time, a spacecraft at Mars had successfully employed aerobraking methods in order to reach its desired pre-launch mapping orbit. This was accomplished despite a damaged spacecraft solar array. The MGS spacecraft was launched on November 7, 1996, and after a ten month interplanetary transit was inserted into a highly elliptical capture orbit at Mars on September 12, 1997. Unlike other interplanetary missions, the MGS spacecraft was launched with a planned mission delta-V ((Delta)V) deficit of nearly 1250 m/s. To overcome this AV deficit, aerobraking techniques were employed. However, damage discovered to one of the spacecraft's two solar arrays after launch forced major revisions to the original aerobraking planning of the MGS mission. In order to avoid a complete structural failure of the array, peak dynamic pressure levels for the spacecraft were established at a major spacecraft health review in November 1997. These peak dynamic pressure levels were roughly one-third of the original mission design values. Incorporating the new dynamic pressure limitations into mission replanning efforts resulted in an 'extended' orbit insertion phase for the mission. This 'extended' orbit insertion phase was characterized by two distinct periods of aerobraking separated by an aerobraking hiatus that would last for several months in an intermediate orbit called the "Science Phasing Orbit" (SPO). This paper describes and focuses on the strategy for the second phase of aerobraking for the MGS mission called "Aerobraking Phase 2." This description will include the baseline aerobraking flight profile, the trajectory control methodology, as well as the key trajectory metrics that were monitored in order to successfully "guide' the spacecraft to its desired mapping orbit. Additionally, the actual aerobraking progress is contrasted to the planned aerobraking flight profile. (A separate paper will describe the navigation aspects of MGS aerobraking in detail.) Key to the success of the MGS mission is the delivery of the spacecraft to its final mapping orbit and the synergy the instrument complement provides to its scientific investigators when science data is returned from that orbit. The MGS mapping orbit is characterized as a low altitude, near-circular, near-polar orbit that is Sun-synchronous with the descending equatorial crossing at 2:00 AM local mean solar time (LMST).

Johnston, M. D.↗

Doubly-periodic orbits in the Sun-Earth-Moon system

A series of periodic orbits in the Earth-Moon circular restricted problem of three bodies was found which is ideally suited for exploring the Earth's geomagnetic tail. The mean apsidal motion of the basic highly elliptical Earth orbit was maintained at about one degree per day by a sequence of lunar swingbys, keeping the apogees in the anti-Sun direction. The orbits were periodic in reference frames rotating at both lunar and solar rates. Apogee distances were alternately raised and lowered by the lunar swingby maneuvers. Several categories of these Sun-synchronous double lunar swingby orbits were identified. The strength and flexibility of this trajectory concept was demonstrated with real world simulations.

Farohar, R.↗

Computation of optimal low- and medium-thrust orbit transfers

This paper presents the formulation of the optimal low- and medium-thrust orbit transfer control problem, numerical methods for solution, and numerical solutions of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and 3D noncoplanar nonaligned elliptic terminal orbits. We set up examples to demonstrate the ability of two indirect methods to solve the resulting two point boundary value problems (TPBVP). The methods demonstrated are the multiple point shooting method as formulated in Oberle's (1987) subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are tradeoffs to using either method. We present numerical solutions of planar transfers in which both the initial orbit exit and final orbit entry points have been optimized. These solutions include two- and three-burn transfers. The methods used show an ability to handle thrust down to at least T/W(o) = O(10 exp -3). They also show similar convergence abilities with or without the oblateness and drag terms. We discuss the issue of maximizing with respect to the final time and provide evidence that implies a local optimum at a maximum final time for a given number of burns.

Chuang, C.-H.↗

Transfers from TLI to Lunar Frozen Orbits with Applications to NASA’s CLPS & Artemis Programs

This paper will focus on trajectory transfers from trans-lunar injection (TLI) to lunar frozen orbits with applications to NASA’s Commercial Lunar Payload Services (CLPS) and Artemis Human Landing System (HLS) programs. For a CLPS application, the CS-3 mission is explored, which will deploy a communications relay satellite in lunar elliptical frozen orbit followed by landing a payload on the lunar farside during dawn. Given HLS will land a crew near the lunar south pole with lighting and timing requirements, the effect of varying the Earth-Moon transit duration to influence the approach direction upon landing will be explored.

lunar frozen orbits↗

Theory and computation of optimal low- and medium-thrust transfers

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.

Chuang, C.-H.↗

Multi-Beam Surface Lidar for Lunar and Planetary Mapping

Surface lidar techniques are now being demonstrated in low Earth orbit with a single beam of pulsed laser radiation at 1064 nm that profiles the vertical structure of Earth surface landforms along the nadir track of a spacecraft. In addition, a profiling laser altimeter, called MOLA, is operating in elliptical Martian orbit and returning surface topography data. These instruments form the basis for suggesting an improved lidar instrument that employs multiple beams for extension of sensor capabilities toward the goal of true, 3-dimensional mapping of the Moon or other similar planetary surfaces. In general the lidar waveform acquired with digitization of a laser echo can be used for laser distance measurement (i.e. range-to-the-surface) by time-of-flight measurement and for surface slope and shape measurements by examining the detailed lidar waveform. This is particularly effective when the intended target is the lunar surface or another planetary body free of any atmosphere. The width of the distorted return pulse is a first order measure of the surface incidence angle, a combination of surface slope and laser beam pointing. Assuming an independent and absolute (with respect to inertial space) measurement of laser beam pointing on the spacecraft, it is possible to derive a surface slope with-respect-to the mean planetary surface or its equipotential gravity surface. Higher-order laser pulse distortions can be interpreted in terms of the vertical relief of the surface or reflectivity variations within the area of the laser beam footprint on the surface.

Bufton, Jack L.↗

Proof-of-Concept Trajectory Designs for a Multi-Spacecraft, Low-Thrust Heliocentric Solar Weather Buoy Mission

A new solar weather mission has been proposed, involving a dozen or more small spacecraft spaced at regular, constant intervals in a mutual heliocentric circular orbit between the orbits of Earth and Venus. These solar weather buoys (SWBs) would carry instrumentation to detect and measure the material in solar flares, solar energetic particle events, and coronal mass ejections as they flowed past the buoys, serving both as science probes and as a radiation early warning system for the Earth and interplanetary travelers to Mars. The baseline concept involves placing a mothercraft carrying the SWBs into a staging orbit at the Sun-Earth L1 libration point. The mothercraft departs the L1 orbit at the proper time to execute a trailing-edge lunar flyby near New Moon, injecting it into a heliocentric orbit with its perihelion interior to Earth s orbit. An alternative approach would involve the use of a Double Lunar Swingby (DLS) orbit, rather than the L1 orbit, for staging prior to this flyby. After injection into heliocentric orbit, the mothercraft releases the SWBs-all equipped with low-thrust pulsed plasma thrusters (PPTs)-whereupon each SWB executes a multi-day low-thrust finite bum around perihelion, lowering aphelion such that each achieves an elliptical phasing orbit of different orbital period from its companions. The resulting differences in angular rates of motion cause the spacecraft to separate. While the lead SWB achieves the mission orbit following an insertion burn at its second perihelion passage, the remaining SWBs must complete several revolutions in their respective phasing orbits to establish them in the mission orbit with the desired longitudinal spacing. The complete configuration for a 14 SWB scenario using a single mothercraft is achieved in about 8 years, and the spacing remains stable for at least a further 6 years. Flight operations can be simplified, and mission risk reduced, by employing two mothercraft instead of one. In this scenario: the second mothercraft stays in a libration-point or DLS staging orbit until the first mothercraft has achieved nearly 180 separation from the Earth. The timing of the second mothercraft's subsequent lunar flyby is planned such that this spacecraft will be located 180 from the first mothercraft upon completion of its heliocentric circularization maneuvers. Both groups of satellites then only have to spread out over 180 to obtain full 360 coverage around the Sun.

Muller, Ronald↗

Trending of SNPP Ephemeris and Its Implications on VIIRS Geometric Performance

This paper describes trends in the Suomi National Polar-orbiting Partnership (SNPP) spacecraft ephemeris data over the four and half years of on-orbit operations. It then discusses the implications of these trends on the geometric performance of the Visible Infrared Imaging Radiometer Suite (VIIRS), one of the instruments onboard SNPP. The SNPP ephemeris data includes time stamped spacecraft positions and velocities that are used to calculate the spacecraft altitude and sub-satellite locations. Through drag make-up maneuvers (DMUs) the orbital mean altitude (spacecraft altitude averaged over an orbit) has been maintained at 838.8 kilometers to within plus or minus 0.2 kilometers and the orbital period at 101.5 minutes to within plus or minus 0.2 seconds. The corresponding orbital mean velocity in the terrestrial frame of reference has been maintained at 7524 meters per second to within plus or minus 0.5 meters per second. Within an orbit, the altitude varies from 828 kilometers near 15 degrees North latitude to 856 kilometers near the South Pole. Inclination adjust maneuvers (IAMs) have maintained the orbit inclination angle at 98.67 degrees to within plus or minus 0.07 degrees and the sun-synchronous local time at ascending node (LTAN) at 13:28 to within plus or minus 5 minutes. Besides these trends, it is interesting to observe that the orbit's elliptic shape has its major axis linking the perigee and apogee shorter than the line linking the ascending node and the descending node. This effect is caused by the Earth's oblate spheroid shape and deviates from a Keplerian orbit theory in which the two orbiting bodies are point masses. VIIRS has 5 imagery resolution bands, 16 moderate resolution bands and a day-night band, with 32, 16 and 16 detectors, respectively, aligned in the spacecraft flight (also known as track) direction. For each band's sample within a scan, the detectors sample the Earth's surface simultaneously in the track direction in the Earth Centered Inertial frame of reference. The distance between the center of the area sensed by the trailing detectors of one scan and the leading detectors of the next includes a component caused by earth rotation. This earth rotation component is relatively small (approximately 70 meters per second) for an orbit like SNPP, but must be taken into account in the design of low-Earth orbit scanning sensors similar to VIIRS to ensure contiguous coverage at nadir.

SNPP↗

NASA tracking and data acquisition in the 1990s - High earth orbit and planetary spacecraft support

It is pointed out that during the decade of the 1980's the Deep Space Network (DSN) and the ground stations of the Ground Spaceflight Tracking Data Network (GSTDN) will have been consolidated into one ground-based network to provide services for tracking and data acquisition for NASA deep space probes and highly elliptical earth orbiters. The Tracking and Data Relay Satellite System (TDRSS) will have been implemented to handle low earth orbiters. Anticipated solar system exploration missions of the 1990's are discussed, and a description is presented of the new tracking and data acquisition requirements for supporting these missions. The technology options needed to meet these new requirements are identified, and the impact of these technology options on the consolidated DSN is discussed. Attention is given to the evolution of the DSN of the 1980's into the DSN of the year 2000.

Smith, J. G.↗

TRAP/SEE Code Users Manual for Predicting Trapped Radiation Environments

TRAP/SEE is a PC-based computer code with a user-friendly interface which predicts the ionizing radiation exposure of spacecraft having orbits in the Earth's trapped radiation belts. The code incorporates the standard AP8 and AE8 trapped proton and electron models but also allows application of an improved database interpolation method. The code treats low-Earth as well as highly-elliptical Earth orbits, taking into account trajectory perturbations due to gravitational forces from the Moon and Sun, atmospheric drag, and solar radiation pressure. Orbit-average spectra, peak spectra per orbit, and instantaneous spectra at points along the orbit trajectory are calculated. Described in this report are the features, models, model limitations and uncertainties, input and output descriptions, and example calculations and applications for the TRAP/SEE code.

Armstrong, T. W.↗

Atmospheric environment during maneuvering descent from Martian orbit

This paper presents an analysis of the atmospheric maneuvering capability of a vehicle designated to land on the Martian surface, together with an analysis of the entry environment encountered by the vehicle. A maximum lift/drag ratio of 2.3 was used for all trajectory calculations. The maximum achievable lateral ranges varied from about 3400 km to 2500 km for entry velocities of 5 km/s (from a highly elliptical Martian orbit) and 3.5 km/s (from a low-altitude lower-speed orbit), respectively. It is shown that the peak decelerations are an order of magnitude higher for the 5-km/s entries than for the 3.5-km/s entries. The vehicle entering at 3.5 km/s along a gliding trajectory encountered a much more benign atmospheric environment. In addition, the glider's peak deceleration was found to be only about 0.7 earth g, making the shallow flight path ideal for manned vehicles whose crews might be physically weakened by the long voyage to Mars.

Tauber, Michael E.↗

High-Latitude Communications Satellite (HILACS)

The Naval Postgraduate School in the AE 4871 Advanced Spacecraft Design course designed a communications satellite (HILACS) that will provide a continuous UHF communications link between stations located north of the region covered by geosynchronous communications satellites. The communications payload will operate only for that portion of the orbit necessary to provide specific coverage. The satellite orbit is elliptic with perigee at 1204 km in the Southern Hemisphere and an apogee at 14,930 km with 63.4 degrees inclination. Analysis and design of each of the subsystems was done to the extent possible within the constraints of an eleven week quarter and the design and analysis tools available. Work was completed in orbital analysis, the reaction control system, attitude control subsystem, electric power subsystem, telemetry, tracking, and control, thermal control subsystem, and the structures subsystem. The design team consisted of 12 students. Additional support was provided by the Jet Propulsion Laboratory and the Naval Research Laboratory.

Source record↗

Optimizing Mars Sphere of Influence Maneuvers for NASA's Evolvable Mars Campaign

NASA's Human Spaceflight Architecture Team is refining human exploration architectures that will extend human presence to the Martian surface. For both Mars orbital and surface missions, NASA's Evolvable Mars Campaign assumes that cargo and crew can be delivered repeatedly to the same destination. Up to this point, interplanetary trajectories have been optimized to minimize the total propulsive requirements of the in-space transportation systems, while the pre-deployed assets and surface systems are optimized to minimize their respective propulsive requirements separate from the in-space transportation system. There is a need to investigate the coupled problem of optimizing the interplanetary trajectory and optimizing the maneuvers within Mars's sphere of influence. This paper provides a description of the ongoing method development, analysis and initial results of the effort to resolve the discontinuity between the interplanetary trajectory and the Mars sphere of influence trajectories. Assessment of Phobos and Deimos orbital missions shows the in-space transportation and crew taxi allocations are adequate for missions in the 2030s. Because the surface site has yet to be selected, the transportation elements must be sized to provide enough capability to provide surface access to all landing sites under consideration. Analysis shows access to sites from elliptical parking orbits with a lander that is designed for sub-periapsis landing location is either infeasible or requires expensive orbital maneuvers for many latitude ranges. In this case the locus of potential arrival perigee vectors identifies the potential maximum north or south latitudes accessible. Higher arrival velocities can decrease reorientation costs and increase landing site availability. Utilizing hyperbolic arrival and departure vectors in the optimization scheme will increase transportation site accessibility and provide more optimal solutions.

Merrill, Raymond G.↗

Perturbed Equations of Motion for Formation Flight Near the Sun-Earth L2 Point

This Memorandum Report consists of a compilation of three individual reports, of increasing complexity, describing investigations of formation flight of spacecraft in the vicinity of the L2 Sun-Earth 1ibration point. The individual reports form the following parts of this compilation: - Introduction to the relative motion of spacecraft about the Sun-Earth L2 Point - Linear and quadratic modelling and solution of the relative motion - Modelling the Perturbations - Elliptical Earth Orbit, Lunar Gravity, Solar Radiation Pressure, Thrusters. The three parts are self-contained, with somewhat, varying notation and terminology. After fair1y significant literature searches: this new work (of Parts 2 and 3) is deemed to be unique because it describes the primary perturbations to the description of relative motion between nearby spacecraft. The effect of the elliptical motion of the Earth about the Sun was verified to be the dominant perturbation to the circular restricted three body problem. Contributions due to lunar gravity and solar radiation pressure are seen to have much smaller effect.

Segerman, Alan M.↗

Trajectory Design for a Spacecraft Capable of Deploying Probes to the Martian Surface en Route to Low Mars Orbit

The presented trajectory design and analysis was performed for the Aeolus spacecraft mission concept. The Aeolus spacecraft consists of an orbiter (i.e., “mothership”) with the goal of transferring from Earth to low Mars orbit via propulsive and/or atmospheric braking (i.e., aerobraking). During various phases of flight from hyperbolic approach of Mars through low Mars Orbit, the Aeolus orbiter will deploy multiple probes which are targeted to land on the Martian surface with the goal of achieving global surface coverage.

Mars hyperbolic approach↗