Singular perturbations and minimum fuel space trajectories

Perturbation theory for fuel space trajectory optimizatio

User's guide to four-body and three-body trajectory optimization programs

A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time

Libration point rendezvous Final report

Flight mechanics and mass requirements for one-shot lunar missions utilizing rendezvous at libration points in front of and behind moo

Minimum impulse guidance Interim scientific report

Minimum fuel guidance for time-open rendezvous, orbit transfer, and orbit transfer with tangential nominal impulse

Mission Capabilities of Ion Engines. Phase II

Payloads and mission times were calculated for space vehicles propelled by ion rockets using nuclear power supplies having specific weights from 10 t o 50 lb/kw. Included in the study were five missions: low-altitude lunar satellite, low-altitude Venus satellite, solar probe, Saturn probe, and a Jupiter satellite with a circular orbit at the altitude of Jupiter's fourth moon. The variation of payload with the ration of power supply weight to gross weight was studied and the optimum power levels thereby determined. The ion rocket payload capabilities were compared with those of high-thrust vehicles using hydrogen-oxygen rockets and tungsten-core nuclear rockets; in addition the performance of high- and low-thrust systems staged in combination has been investigated. Launch vehicles considered in this study were the Atlas-Centaur, the Saturn C-1, and the Saturn C-5

A users manual for a computer program which calculates time optical geocentric transfers using solar or nuclear electric and high thrust propulsion

This manual is a guide for using a computer program which calculates time optimal trajectories for high-and low-thrust geocentric transfers. Either SEP or NEP may be assumed and a one or two impulse, fixed total delta V, initial high thrust phase may be included. Also a single impulse of specified delta V may be included after the low thrust state. The low thrust phase utilizes equinoctial orbital elements to avoid the classical singularities and Kryloff-Boguliuboff averaging to help insure more rapid computation time. The program is written in FORTRAN 4 in double precision for use on an IBM 360 computer. The manual includes a description of the problem treated, input/output information, examples of runs, and source code listings

Four-body trajectory optimization

A collection of typical three-body trajectories from the L1 libration point on the sun-earth line to the earth is presented. These trajectories in the sun-earth system are grouped into four distinct families which differ in transfer time and delta V requirements. Curves showing the variations of delta V with respect to transfer time, and typical two and three-impulse primer vector histories, are included. The development of a four-body trajectory optimization program to compute fuel optimal trajectories between the earth and a point in the sun-earth-moon system are also discussed. Methods for generating fuel optimal two-impulse trajectories which originate at the earth or a point in space, and fuel optimal three-impulse trajectories between two points in space, are presented. A brief qualitative comparison of these methods is given. An example of a four-body two-impulse transfer from the Li libration point to the earth is included

Mission Capabilities of Ion Engines Using SNAP-8 Power Supplies

Mission performance capabilities of ion engines powered by the 30 kw and 60 kw SNAP-8 power supplies are compared for the following missions: a 24-hr equatorial satellite, a 100 n mi lunar satellite, a 500 n mi Mars satellite, a Mercury probe, and an out-of-the-ecliptic probe. The capabilities of arc- jet engines and chemical engines for the same missions are compared with those of the ion engines. The majority of the comparisons are for 8500-lb spacecraft which are boosted into a 300 n mi orbit by the Atlas-Centaur. Variations in initial orbit altitude, the use of actual launch dates rather than dates based on simplifying assumptions, and the combined use of chemical and electrical propulsion systems were also evaluated in terms of their effect on mission performance

A Simple Targeting Procedure for Lunar Trans-Earth Injection

A simple targeting algorithm for trans-Earth injection is developed. The techniques presented in this paper build on techniques developed for the Apollo program and other lunar and interplanetary missions. Presently, more sophisticated algorithms exist for solving this problem, but the simplicity of this particular algorithm makes it well-suited for on-board use during contingency and abort operations. In order to support a return from any lunar orbit with available fuel on the spacecraft the algorithm chooses between one-, two-, or three-burn return scenarios. The one- and two-burn cases are based on existing theory. For the three-burn case however, the existing theory is modified in order to provide a simple solution. Rather than attempting to create fuel-optimal trajectories, the algorithm presented in this paper focuses on computing a trajectory from low lunar orbit to direct atmospheric Earth entry that does not violate a fuel constraint. The algorithm attempts to use a minimal number of impulses to execute trans-earth injection. The algorithm can also be used to quickly generate good initial guesses for other more sophisticated targeting algorithms that can be used to find minimal fuel trajectories or optimize other parameters. This algorithm has three principle phases. First, an estimate of the hyperbolic excess velocity at the Lunar sphere of influence is generated. Second, a maneuver is computed that will transfer the craft from a lunar circular orbit to the hyperbolic escape asymptote. Finally, the effects of perturbations are eliminated by using linear state transition matrix targeting

Activin enhances skin tumourigenesis and malignant progression by inducing a pro-tumourigenic immune cell response

Activin is an important orchestrator of wound repair, but its potential role in skin carcinogenesis has not been addressed. Here we show using different types of genetically modified mice that enhanced levels of activin in the skin promote skin tumour formation and their malignant progression through induction of a pro-tumourigenic microenvironment. This includes accumulation of tumour-promoting Langerhans cells and regulatory T cells in the epidermis. Furthermore, activin inhibits proliferation of tumour-suppressive epidermal γδ T cells, resulting in their progressive loss during tumour promotion. An increase in activin expression was also found in human cutaneous basal and squamous cell carcinomas when compared with control tissue. These findings highlight the parallels between wound healing and cancer, and suggest inhibition of activin action as a promising strategy for the treatment of cancers overexpressing this factor