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A number of missions have recently been proposed that aim to take advantage of the growing scientific interest in the region of space near libration points in the Sun-Earth system. In support of missions that include increasingly complex trajectories and incorporate libration point orbits, more efficient techniques and new philosophies for design must be considered.
It is shown that transfer trajectories to the halo orbit exist throughout the year, with a one week closure of the launch window each month because of unfavorable lunar perturbations that cannot be corrected in the case of transfer trajectory insertion errors. The launch window for transfers to large-amplitude Lissajous orbits is virtually the same as that for transfers to the baseline halo orbit. Details of these trajectories are described and questions about groundstation coverage are discussed.
A contingency trajectory analysis was performed for NASA Ames Research Center’s (ARC’s) Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft in case of a missed lunar orbit insertion (LOI) maneuver. Recovery trajectory options are shown to exist for all LADEE launch opportunities throughout a one year period. Recovery ΔV costs primarily depended on the spacecraft’s apogee location on or near the Sun-Earth weak stability boundary (WSB) and the time needed by the spacecraft to recover (e.g. to “wake up” from “safe” mode) to perform an escape prevention maneuver after the missed LOI.
This paper presents a review of lunar transfer trajectories that go beyond three-body theory and the Jacobi integral.
The Lunar IceCube (LIC) mission, a Next Space Technologies for Exploration Partnerships (NSTEP) program selection, was launched as a rideshare onboard Artemis-I on November 16th 2022, and deployed into a high energy lunar flyby trajectory. The final destination of the mission was a polar elliptical lunar orbit from which it could conduct spectroscopy observations of the lunar surface; however, a near rectilinear halo orbit (NRHO) was planned to be used as a staging orbit that divided the lunar transfer and low-thrust spiral phases of the mission. This paper presents the process used to design the LIC transfer trajectory from the high-energy deployment state to a 9:2 synodic resonance NRHO. Additional analyses performed, to assess the critical deployment to lunar flyby phase of the trajectory and to generate recovery trajectories following a loss of contact with the spacecraft, are described as well. Lessons learned from working on the LIC mission are presented to inform the design of similar future CubeSat missions.
Documentation for the User Interface Program for the Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) is provided. The User Interface Program is a separate software package designed to ease the user input requirements when using the MASTRE Trajectory Program. This document supplements documentation on the MASTRE Program that consists of the MASTRE Engineering Manual and the MASTRE Programmers Guide. The User Interface Program provides a series of menus and tables using the VAX Screen Management Guideline (SMG) software. These menus and tables allow the user to modify the MASTRE Program input without the need for learning the various program dependent mnemonics. In addition, the User Interface Program allows the user to modify and/or review additional input Namelist and data files, to build and review command files, to formulate and calculate mass properties related data, and to have a plotting capability.
Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.
Lissajous orbits and approximation of their invariant manifolds are used to generate landing trajectories to the surface of Europa. Each lissajous is discretized into individual revolutions that each resemble a periodic orbit. The unstable manifolds of each individual revolution propagated forward in time generate more surface coverage than manifolds of simple libration point orbits such as halo or Lyapunov orbits. The stable manifolds propagated backwards in time from the individual lissajous revolutions provide direct connections to the last phase of a moon tour. The strategy developed produces ballistic landing trajectories with a wide surface coverage, and allows for the decoupling of the landing and moon tour phase by using the lissajous as an intermediate staging orbit. The multiple revolutions of the lissajous, multiple departure times along each revolution, multiple quasi periodic options at each energy, and multiple energies of the lissajous family provide many degrees of freedom in the design process.
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The Galileo Probe, Pioneer-Venus probes, and SPRITE concept all share a number of common characteristics. They all follow a similar entry and descent sequence, using an aeroshell to protect against entry environments, and parachutes to aid in extrusion and descent speed control of the descent vehicle containing the science instruments. The descent vehicles all contained similar instruments (e.g. mass spectrometers and atmosphere structure sensors), and data was either relayed back to a carrier spacecraft (Galileo Probe, SPRITE) or transmitted direct to Earth (Pioneer-Venus). Based on these similar characteristics, NASA initiated a study to investigate a “common probe' that might be designed to perform similar science in a variety of planetary environments. This concept would leverage a common aeroshell design, and descent vehicle designs that could be made as similar as possible (the primary exception being that Venus will require a pressure vessel due to the extreme pressures and temperatures seen in the lower portion of the descent). To support the Common Probe study, GSFC and JPL performed a series of interplanetary trajectory analyses to help develop the mission designs for Venus, Jupiter, Saturn, Uranus, and Neptune. Primary considerations in the trajectory modeling included: a maximum of 12-year time of flight (for outer planet destinations), generation of both steep and shallow entry trajectories to each destination (where steep and shallow resulted in approximately 150 g and 50 g peak deceleration during entry at each location), and consideration of the data relay. Gravity assists and trajectories with low delta-V requirements (typically much less than 500 m/s) were also incorporated into the design process to enable launch on existing vehicles such as the Atlas V.
Galactic Jupiter probe missions to make interstellar space measurements using Jupiter gravity assisted trajectories, discussing earth- Jupiter transfer orbits and mission parameters
The Galileo mission has been reprogrammed to use a direct earth-Jupiter trajectory with a May 1986 launch date and with arrival at Jupiter occurring in mid-1988. Within the constraints of Shuttle/Centaur launch vehicle capability and total spacecraft mass and performance, optimal broken-plane trajectories are generated, and the region of positive propellant margin in the launch/arrival space is determined. Mission constraints are used to define a launch/arrival strategy. It is also shown that a close flyby of any one of several asteroids or a comet is possible on the interplanetary transfer with minimal impact on mission performance.
The new baseline for the Galileo Mission is a 1989 Venus-earth-earth gravity-assist (VEEGA) trajectory, which utilizes three gravity-assist planetary flybys in order to reduce launch energy requirements significantly compared to other earth-Jupiter transfer modes. The launch period occurs during October-November 1989. The total flight time is about 6 years, with November 1995 as the most likely choice for arrival at Jupiter. Optimal 1989 VEEGA trajectories have been generated for a wide range of earth launch dates and Jupiter arrival dates. Launch/arrival space contour plots are presented for various trajectory parameters, including propellant margin, which is used to measure mission performance. The accessible region of the launch/arrival space is defined by propellant margin and launch energy constraints; the available launch period is approximately 1.5 months long.
The Lunar Lander Ascent Module (LLAM) will leave the lunar surface and actively rendezvous in lunar orbit with the Crew Exploration Vehicle (CEV). For initial LLAM vehicle sizing efforts, a nominal trajectory, along with required delta-V and a few key sensitivities, is very useful. A nominal lunar ascent and rendezvous trajectory is shown, along with rationale and discussion of the trajectory shaping. Also included are ascent delta-V sensitivities to changes in target orbit and design thrust-to-weight of the vehicle. A sample launch window for a particular launch site has been completed and is included. The launch window shows that budgeting enough delta-V for two missed launch opportunities may be reasonable. A comparison between yaw steering and on-orbit plane change maneuvers is included. The comparison shows that for large plane changes, which are potentially necessary for an anytime return from mid-latitude locations, an on-orbit maneuver is much more efficient than ascent yaw steering. For a planned return, small amounts of yaw steering may be necessary during ascent and must be accounted for in the ascent delta-V budget. The delta-V cost of ascent yaw steering is shown, along with sensitivity to launch site latitude. Some discussion of off-nominal scenarios is also included. In particular, in the case of a failed Powered Descent Initiation burn, the requirements for subsequent rendezvous with the Orion vehicle are outlined.
The impact of aircraft emissions and contrails on the environment adds an additional aspect to aircraft trajectory optimization. This study developed a three-dimensional trajectory optimization algorithm for trans-Atlantic flights in cruise to generate aircraft trajectories that minimize environmental impacts due to CO2 emissions and contrails in the presence of winds. The climate-optimal trajectory is developed using dynamic programming that adjusts a wind-optimal aircraft heading while determining the optimal locations, altitudes and times for en-route step climbs. Flying wind-optimal routes minimize aircraft travel time, fuel burn and associated emissions during cruise while adjusting aircraft heading and en-route step climbs at the optimal locations and times minimize climate impact of contrails. This capability integrates an air traffic management simulation with aircraft fuel burn and emissions models, contrail formation and dispersion models, simplified climate response models, and a common climate metric. A study was conducted to evaluate the potential cost and benefits of flying climate-optimal routes in North Atlantic Airspace and their impacts to the Organized Track System design based on the trans-Atlantic air traffic during a day, July 12, 2012. Results show eastbound flights achieved a larger environmental benefit with less additional fuel burn than westbound flights that operated in strong headwinds that caused more additional fuel burn and aircraft emissions to avoid traversing contrails favorable regions.
When designing a mission, the addition of a maneuver at the right spot often improves the utility of an otherwise mediocre trajectory. However, the additional degrees of freedom of finding the best maneuver location can severely complicate automated broad-search algorithms. A computationally-efficient formulation that reduces the maneuver design space to a single dimension is presented, where the efficacy of additional maneuvers along previously computed transfers is calculated explicitly via Lawden's "primer vector." Examples include leveraging maneuvers to ease capture at Europa, phasing maneuvers to enable resonant-hopping among Saturn's moons, and broken-plane maneuvers on transfers to Mars.
In order to achieve the Artemis I mission objectives to human-rate the Orion spacecraft even under off-nominal conditions, trajectories were developed to handle contingency scenarios: alternate missions for contingencies before or during the Trans-Lunar Injection burn, recoveries to return Orion to the nominal trajectory after a delayed or partial burn, and abort trajectories to return the spacecraft to Earth after a critical failure. In addition, disposal trajectories were generated for situations where recovery was not an option. Details are given on the trajectory characteristics, solution families, the generation of the trajectories, and operations considerations.
The information required by a programmer using the Minimum Hamiltonian AScent Trajectory Evaluation (MASTRE) Program is provided. This document enables the programmer to either modify the program or convert the program to computers other than the VAX computer. Documentation for each subroutine or function based on providing the definitions of the variables and a source listing are included. Questions concerning the equations, techniques, or input requirements should be answered by either the Engineering or User's manuals. Three appendices are also included which provide a listing of the Root-Sum-Square (RSS) program, a listing of subroutine names and definitions used in the MASTRE User Friendly Interface Program, and listing of the subroutine names and definitions used in the Mass Properties Program. The RSS Program is used to aid in the performance of dispersion analyses. The RSS program reads a file generated by the MASTRE Program, calculates dispersion parameters, and generates output tables and output plot files. UFI Program provides a screen user interface to aid the user in providing input to the model. The Mass Properties Program defines the mass properties data for the MASTRE program through the use of user interface software.