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Guidance and trajectory considerations in lunar mass transportation

Flight-mechanics problems associated with large-scale transport of lunar mass to a space colony or manufacturing facility are discussed. The proposed transport method involves launch of payloads from a mass-driver on the lunar surface, onto ballistic trajectories to a passive mass-catcher located near the L2 libration point, with the caught mass subsequently being transported to the colony. Arrival velocities at L2, sensitivities in arrival dispersion due to launch errors, and effects of launch site location are treated, via numerically integrated orbits in the restricted three-body problem. From any launch site it is possible to define a target point reached with zero dispersion due to errors in a selected component of launch velocity. Effects of lunar geometrical librations and of obliquity, as well as the conditions for biasing a trajectory away from L2 so as to reduce stationkeeping costs, are dealt with along with transfer orbits from L2 to the colony. The theory of capture and the theory of resonance lead to a colony orbit, with period approximately two weeks, reached from L2 with velocity increment as low as 9.02 m/sec.

Heppenheimer, T. A.↗

Lunar Flight Study Series: Volume 8. Earth-Moon Transit Studies Based on Ephemeris Data and Using Best Available Computer Program. Part 3: Analysis of Some Lunar Landing Site Problems Utilizing Two Fundamental Principles

This report presents two fundamental properties of lunar trajectories and makes use of these properties to solve various lunar landing site problems. Not only are various problems treated and solved but the properties and methods are established for use in the solution of other problems. This report presents an analysis of lunar landing site problems utilizing the direct mission mode as well as the orbital mission mode. A particular landing site is then specified and different flight profiles are analyzed for getting an exploration vehicle to that landing site. Rendezvous compatible lunar orbits for various stay-times at the landing site are treated. Launch opportunities are discussed for establishing rendezvous compatible lunar orbits without powered plane changes. Then, the minimum required plane changes for rendezvous in the lunar orbit are discussed for launching from earth on any day. On days that afford rendezvous compatible opportunities, there are no powered plane change requirements in the operations from launch at AMR through the rendezvous in lunar orbit, after the stay at the lunar site.

Tucker, W. B.↗

Secondary Payload Opportunities on NASA's Space Launch System (SLS) Enable Science and Deep Space Exploration

For the first time in almost 40 years, a NASA human-rated launch vehicle has completed its Critical Design Review (CDR). With this milestone, NASA's Space Launch System (SLS) and Orion spacecraft are on the path to launch a new era of deep space exploration. This first launch of SLS and the Orion Spacecraft is planned no later than November 2018 and will fly along a trans-lunar trajectory, testing the performance of the SLS and Orion systems for future missions. NASA is making investments to expand the science and exploration capability of the SLS by developing the capability to deploy small satellites during the trans-lunar phase of the mission trajectory. Exploration Mission 1 (EM-1) will include thirteen 6U Cubesat small satellites to be deployed beyond low earth orbit. By providing an earth-escape trajectory, opportunities are created for the advancement of small satellite subsystems, including deep space communications and in-space propulsion. This SLS capability also creates low-cost options for addressing existing Agency strategic knowledge gaps and affordable science missions. A new approach to payload integration and mission assurance is needed to ensure safety of the vehicle, while also maintaining reasonable costs for the small payload developer teams. SLS EM-1 will provide the framework and serve as a test flight, not only for vehicle systems, but also payload accommodations, ground processing, and on-orbit operations. Through developing the requirements and integration processes for EM-1, NASA is outlining the framework for the evolved configuration of secondary payloads on SLS Block upgrades. The lessons learned from the EM-1 mission will be applied to processes and products developed for future block upgrades. In the heavy-lift configuration of SLS, payload accommodations will increase for secondary opportunities including small satellites larger than the traditional Cubesat class payload. The payload mission concept of operations, proposed payload capacity of SLS, and the payload requirements for launch and deployment will be described to provide potential payload users an understanding of this unique exploration capability.

Singer, Jody↗

Trajectory Model of Lunar Dust Particles

The goal of this work was to predict the trajectories of blowing lunar regolith (soil) particles when a spacecraft lands on or launches from the Moon. The blown regolith is known to travel at very high velocity and to damage any hardware located nearby on the Moon. It is important to understand the trajectories so we can develop technologies to mitigate the blast effects for the launch and landing zones at a lunar outpost. A mathematical model was implemented in software to predict the trajectory of a single spherical mass acted on by the gas jet from the nozzle of a lunar lander.

Source record↗

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Lancaster, J. E.↗

Solar Array Disturbances to Spacecraft Pointing During the Lunar Reconnaissance Orbiter (LRO) Mission

The Lunar Reconnaissance Orbiter (LRO), the first spacecraft to support NASA s return to the Moon, launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle. It was initially inserted into a direct trans-lunar trajectory to the Moon. After a five day transit to the Moon, LRO was inserted into the Lunar orbit and successfully lowered to a low altitude elliptical polar orbit for spacecraft commissioning. Successful commissioning was completed in October 2009 when LRO was placed in its near circular mission orbit with an approximate altitude of 50km. LRO will spend at least one year orbiting the Moon, collecting lunar environment science and mapping data, utilizing a suite of seven instruments to enable future human exploration. The objective is to provide key science data necessary to facilitate human return to the Moon as well as identification of opportunities for future science missions. LRO's instrument suite will provide the high resolution imaging data with sub-meter accuracy, highly accurate lunar cartographic maps, mineralogy mapping, amongst other science data of interest. LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing Mode", provides Lunar nadir, off-nadir, and inertial fine pointing for the science data collection and instrument calibration. This controller combines the capability of fine pointing with on-demand large angle full-sky attitude reorientation. It provides simplicity of spacecraft operation as well as additional flexibility for science data collection. A conventional suite of ACS components is employed in the Observing Mode to meet the pointing and control objectives. Actuation is provided by a set of four reaction wheels developed in-house at NASA Goddard Space Flight Center (GSFC). Attitude feedback is provided by a six state Kalman filter which utilizes two SELEX Galileo Star Trackers for attitude updates, and a single Honeywell Miniature Inertial Measurement Unit (MIMU) to provide body rates for attitude propagation. Rate is computed by differentiating accumulated angle provided by the MIMU. The Observing Mode controller is required to maintain fine pointing while a large fully-articulated solar array (SA) maintains its panel normal to the solar incidence. This paper describes the disturbances to the attitude control resulting from the SA articulation. Observing Mode performance in the presence of this disturbance was assessed while the spacecraft was in an initial elliptical low altitude orbit during the commissioning phase, which started about two weeks after launch and lasted for 90 days. LRO demonstrated excellent pointing performance during Observing Mode nadir and inertial attitude target operations during this phase. Transient LRO attitude errors observed during commissioning resulted primarily from three sources, Diviner instrument calibrations, RW zero crossings, and SA articulation. Even during times of considerable disturbance from SA articulation, the attitude errors were maintained below the statistical attitude error requirement level of 15 arc-sec (3 sigma).

Calhoun, Philip↗

Three-Dimensional Lunar Mission Studies

Some three-dimensional lunar trajectories have been calculated by integration of the equations of motion of the classical restricted three-body problem of celestial mechanics. The calculations have been used for analysis of several aspects of lunar flight including requirements for achieving lunar impact and for establishment of a close lunar satellite. The allowable errors in initial conditions for lunar missions are strongly dependent on the values of the initial injection velocity and the injection angle. There can be large differences in results obtained from two-dimensional analyses (in which the vehicle trajectory is assumed to remain always in the earth-moon plane) and those obtained from three-dimensional analyses. Some of the accuracy tolerances can be fairly well estimated by use of a two-body analysis which considers the inclination of the plane of the vehicle trajectory to the earth-moon plane. Satisfactory orbits for a relatively close lunar satellite can be obtained with accuracies in the initial conditions approximately equal to those required for lunar impact.

Michael, William H., Jr.↗

Application of GPS to Enable Launch Vehicle Upper Stage Heliocentric Disposal

To properly dispose of the upper stage of the Space Launch System, the vehicle must perform a burn in Earth orbit to perform a close flyby of the Lunar surface to gain adequate energy to enter into heliocentric space. This architecture was selected to meet NASA requirements to limit orbital debris in the Earth-Moon system. The choice of a flyby for heliocentric disposal was driven by mission and vehicle constraints. This paper describes the SLS mission for Exploration Mission -1, a high level overview of the Block 1 vehicle, and the various disposal options considered. The research focuses on this analysis in terms of the mission design and navigation problem, focusing on the vehicle-level requirements that enable a successful mission. An inertial-only system is shown to be insufficient for heliocentric flyby due to large inertial integration errors from launch through disposal maneuver while on a trans-lunar trajectory. The various options for aiding the navigation system are presented and details are provided on the use of GPS to bound the state errors in orbit to improve the capability for stage disposal. The state estimation algorithm used is described as well as its capability in determination of the vehicle state at the start of the planned maneuver. This data, both dispersions on state and on errors, is then used to develop orbital targets to use for meeting the required Lunar flyby for entering onto a heliocentric trajectory. The effect of guidance and navigation errors on this capability is described as well as the identified constraints for achieving the disposal requirements. Additionally, discussion is provided on continued analysis and identification of system considerations that can drive the ability to integrate onto a vehicle intended for deep space.

Anzalone, Evan J.↗

Exploration of Low-Thrust Lunar Swingby Escape Trajectories

Spiral escape trajectories enable a spacecraft to escape Earth’s gravity and travel into inter-planetary space under its own power. This analysis demonstrates how to design spiral escape trajectories that leverage single and double Lunar gravity assists and compares the effectiveness of each trajectory type. The trajectories are constructed by combining backwards propagated Q-Law and a perturbed Sims-Flanagan transcription to design the spiral and interplanetary phases, respectively. We demonstrate that these mission types result in significant propellant savings when compared to a conventional, no Lunar swingby spiral escape, and are highly beneficial for the interplanetary rideshare mission concept.

Jackson L Shannon↗

Space Launch System Launch Window and Day of Launch Processes

Lunar missions benefit from varying the launch azimuth as a function of launch time to allow longer launch windows with minimum performance impacts. This variable azimuth approach allows the vehicle to track the Moon’s apparent motion due to Earth’s rotation . The Space Launch System (SLS) Block 1 vehicle design requires the mission to launch into an elliptical parking orbit to provide sufficient energy to insert Orion into a trans-lunar trajectory. The primary benefit of varying the launch azimuth, and as a result the parking orbit inclination, allows the SLS Interim Cryogenic Propulsion Stage (ICPS) to perform its Trans-Lunar Injection (TLI) burn closer to perigee and take advantage of performing a burn in a location where the burn will primarily raise apogee.

A. S. Craig↗

Trajectory Design of the Lunar Impactor Mission Concept

The National Aeronautics and Space Administration (NASA) solicited proposals in 2006 for an opportunity to include a small secondary payload with the launch of the Lunar Reconnaissance Orbiter (LRO) scheduled for October 2008. The cost cap of the proposal was between $50 and $80M, and the mass cap was 1,000 kilograms. JPL proposed a Lunar Impactor (LI) concept for this solicitation. The mission objective of LI was to impact the permanently shadowed region of a South polar crater ultimately to detect the presence of water. The detection of water ice would prove to be an important factor on future lunar exploration. NASA Ames Research Center also proposed a similar concept, the Lunar Crater observation and Sensing Satellite (LCROSS), which was selected by NASA for the mission. However, in this paper, the trajectory design of the LI proposed by JPL is considered. Since the LI spacecraft was to be launched on the LRO launch vehicle as a secondary payload, its initial trajectory must be diverted at some later time from the LRO trans-lunar trajectory for the subsequent impact. Several such trajectories have been considered, where each trajectory option fields some specific values for the mission parameters. The mission parameters include the availability of LRO instruments at the time of impact for the observation by LRO, the mission duration, the impact velocity, the impact angle, etc. It is possible for the LI to be deflected with a relatively low delta-V to impact a South polar crater at a reasonable impact velocity and impact angle directly with no delay. However, the instruments on-board LRO may not be ready for observation. Thus, several delayed trajectory options have been considered further. The lunar phase at the time of impact may also play an important factor for observation, especially from Earth. Several lunar flyby trajectory maneuvers have been identified to arrive at the Moon for impact at the desired lunar phase. By using a combination of these successive lunar flyby maneuvers, the impact lunar phase may be adjusted to the desired location. A few such trajectories have been suggested. Also, some attempts have been made to maximize the impact velocity by converting the impact trajectory into a retrograde orbit with respect to Earth. Since these types of trajectories take advantage of the Sun-Earth three-body region to minimize the delta-V, the mission duration is relatively long. A few such trajectories are suggested. Also, an attempt has been made to adjust the lunar impact within a desired time period for the optimum Earth observation for the above trajectories. The mission parameters resulting from each trajectory option above are considered and weighed against the cost and robustness of the mission in a brief summary.

trajectory design↗

Low-cost unmanned lunar lander

Two student groups designed unmanned landers to deliver 200 kilogram payloads to the lunar surface. Payloads could include astronomical telescopes, small lunar rovers, and experiments related to future human exploration. Requirements include the use of existing hardware where possible, use of a medium-class launch vehicle, an unobstructed view of the sky for the payload, and access to the lunar surface for the payload. The projects were modeled after Artemis, a project that the NASA Office of Exploration is pursuing with a planned first launch in 1996. The Lunar Scout design uses a Delta 2 launch vehicle with a Star 48 motor for insertion into the trans-lunar trajectory. During the transfer, the solar panels will be folded inward and the spacecraft will be powered by rechargeable nickel-cadmium batteries. The lander will use a combination of a solid rocket motor and hydrazine thrusters for the descent to the lunar surface. The solar arrays will be deployed after landing. The lander will provide power for operations to the payload during the lunar day; batteries will provide 'stay-alive' power during the lunar night. A horn antenna on the lander will provide communications between the payload and the earth.

Daniel, Walter K.↗