SCHOOL OF AERONAUTICAL SCIENCE
DEPARTMENT OF AEROSPACE ENGINEERING
toA Numerical Method Reference
Trajectories for Optimization Methods
Support Low-Thrust Mission Design
Generate
to
to
Low thrust trajectory is defined as
trajectory computed by different numerical
methods on the basis of orbital mechanics
reduce the fuel consumption of the
space craft/ satellite &rockets.
selecting
tool
A method for generating a wide array of initial guesses and
one that best fits a set of preferred criteria is desirable because it
would expand the range of possible low-thrust trajectories. One
that shows promise for developing initial guesses for low-thrust
trajectories is the theory of invariant manifolds
In astrodynamics, invariant manifolds can be thought of as
structures that show the natural flow of gravitational forces about a
periodic orbit. The manifolds of low-thrust periodic orbits are likely
helpful for producing a range of detailed initial guesses for
low-thrust trajectories. The proposed investigation will study how
the manifolds of low-thrust periodic
orbits can be used to produce improved initial guesses for
low-thrust spacecraft trajectories.
be tested in a higher fidelity model.
gained from visualization and categorization will be applied
to low-thrust mission design. A number of realistic missions
employed to understand manifold behaviours, these include
need to be the final destination of a spacecraft in order for this
mission design method to be of use. The proposed scheme for
categorizing manifold behaviour. Understanding
desired regions of space. Next, the method will calculate the
manifolds which provide the preferred trajectory
transfers from the Earth-Moon system to other bodies. It is
important to note that a spacecraft can leverage the
gained from these visualizations will be used to develop a the
orbit. Therefore, a low-thrust periodic orbit does not mission
optimization technique. Finally, the resulting solution will
Poincare maps and three-dimensional plots. The intuition
scenarios will be tested, including pole sitting orbits and
manifolds of a low-thrust periodic orbit without entering
characteristics at the lowest cost. The result of this
determination will be used as an initial guess in an
The study will begin by computing low-thrust periodic orbits
and obtaining the manifolds of these orbits. Following this, a
variety of visualization methods will be
design method will first identify low-thrust periodic orbits
whose manifolds provide access to the
This entire process will be made as
autonomous as possible to allow for
ease of use by mission designers.
The improved initial guesses generated by this method will produce
superior locally optimal trajectories, which could entail fuel or time
The potential of low-thrust spacecraft has only begun to be realized.
savings for spacecraft. Therefore, mission design strategies produced
by this study could yield innovative trajectories that would reduce
mission cost and increase scientific return. Furthermore, this research
will yield methods for understanding the stability of low-thrust
enabled periodic orbits.
Investment in astrodynamics research will expand the space attainable
by these spacecraft, opening up new regions of space for science and
exploration by NASA and its partners.
INTRODUCTION Applications
The NASA’s Artemis spacecraft trajectory follows an heteroclinic
connection between the two Lagrangian points. In this way, it is
desirable to construct maps of heteroclinic and homoclinic connections
between the invariant objects around the collinear equilibrium points.
That maps can give a general idea of the characteristics of the different
kind of possible connections (time of transfer, loops around the small
primary, levels of energy, etc).
The solutions of the linear CRTBP equations of motion around a collinear
liberation point are
Station keeping at a liberation
point orbit
avfreutral for the CRTED, as well as the line ty stable one, produce
departures from the fierce nominal droit.
The mic purpose of station-keeping to maintain a spacectalt within a
predefined neighborhood about a nominal path Roughly speaking.
consecutive maneuver At a given enor the position and velocity of a
spacecraft can only be estimated using tracking which, due to the
orrals gives acccximated values for both magnitudes However, in the
eat situation and for long time interval, satre modes that
station-keeping is defined as a control procedure that to minimi some
combination of the destation of the spacecraft from the nomina
trajectory and the total maneuver cost, eventually subjected to
constrains que as the minimum time interval between two
Studies of the CATBP, in particular, the Sun-Earth-Moon
system, have stimulated an enormous number of
These maneuvers will insert the spacecraft into the
stable manifold of the nominal orbit
This kind of motion has drawn some attention as it is
performed by co-orbital satellites of Saturn, like Janus
and Epimetheus, or by near Earth asteroids as Cruithne
(an asteroid in 1:1 motion resonant with the Earth) or
asteroid 2002 AA29.
advances in physics and mathematics, including space
manifold or chaotic dynamics in the Solar System.
These (and other) topics are not exclusive of the
classical celestial mechanics.
Done by
I. Surya Prabhas -21103100
Jerry Oliver - 21103089
Govind Menon - 21103077
Adnan Sayeed - 21103112
Poun Raj - 21103123
References
http://www.scholarpedia.org/article/Space_Manifold_dynamics
https://www.nasa.gov/directorates/spacetech/strg/nstrf2016/Reference_Trajectories/
