On the procedure of selecting orbits for spacecrafts of astrophysical systems D.V.Kovkov TsNIIMash V.V.Malyshev, A.V.Fedorov Moscow Aviation Institute ( The paper submits the procedures of
selecting orbit parameters for spacecrafts on high elliptical orbit (HEO) and
high circular orbit (HCO) according to a criterion that reflects the required
character of orbital constellation evolution without making orbital
adjustments. The procedure consists in forming the optimality criterion
reflecting the desired character of spacecraft orbit parameter evolution and
its minimization with the help of numerical methods of nonlinear programming.
Besides, a set of optimization criteria is proposed, which reflects the desired
character of constellation orbit parameter evolution or a radio interferometer
base; a method to form a generic criterion of optimality is submitted. Using
the proposed procedures, solutions of applied problems have been obtained concerning
the critical inclination definition, initial conditions of a constant
inclination orbit and initial conditions of an orbit with a specified rate of
inclination change. Space research in the field of extra-atmospheric astronomy is directed
towards solving the fundamental problems of stars and galaxies, cosmology, power
engineering and the nature of gravitation. The main trends of extra-atmospheric
astronomy are as follows: -
research of the Universe evolution
early stages; -
detection of "dark substance" and
"dark energy" nature; -
research of processes in the
vicinity of galaxies' nuclei; -
research of processes of stars and
planetary systems formation. To solve
the above-mentioned problems, the space means carrying various scientific
instruments are developed and deployed. Spectr-R
spacecraft was launched into orbit in July 2011 to become an element of a
gigantic space radio interferometer. Radio telescopes in A space
astrophysical complex normally uses terrestrial and extra-atmospheric
instruments, which observe deep space objects in different frequency ranges. The
analysis of global trends of developments in this domain shows that it is a
single spacecraft with a terrestrial radio telescope that is usually used. It is of
certain importance to create a method to solve a technical problem of synthesis
of a ballistic structure of a radio interferometer space section. The task is
to define the number of satellites, their initial orbit parameters and the date
of deployment to achieve the maximal efficiency of the complex. One
criterion characterizes an astrophysical complex with a single radio
interferometer in outer space. This is a sector of coelosphere observed by the
radio interferometer. The optimization means the search for such initial
conditions of spacecraft movement for which the radio interferometer's orbit
plane, during the active operation, turns, due to the Moon's gravitation, by an
angle which provides the maximal criterion value. This
paper submits an approach based on criterion reflecting the desired pattern of
change (evolution) of spacecraft orbit parameters, or parameters of relative
movement, for example, a radio interferometer's base as a distance between
spacecrafts. A
program complex has been designed to solve the problems, formulated in research. The core
of the complex is an applied program, which implements the user interface. It
provides the user's access to the services, implemented by a number of modules,
namely: - the
module of simulation of the constellation's disturbed motion, which supports
the integration of Newton-Cowell equations for each constellation spacecraft at
given initial conditions and disturbing factors. A user can choose from the
library of four numerical integration methods; - the
initial data preparation module supports the interactive mode, while defining
the constellation composition, integration and recording parameters, initial
conditions, disturbances composition, etc.; - the
optimization module supports the interactive preparation of initial data for an
optimization problem: composition of
unknown parameters, initial approximation, optimality criterion, optimization
method and its parameters. There are 7 zero-level algorithms in the library of
methods library; - the
base of calculated versions contains the information about all the problems that
had been set and solved by a PC user, forming the information sphere for
decision making; - the
visualization module displays the simulation results: construction of routes,
zones of radio coverage as 2D or 3D images, and also the diagrams plotted by log
files and introduction of them into reports prepared using MS Office. A number
of abstract classes have been designed for the complex: planet, satellite
(spacecraft), atmosphere of a planet, planet's time service, gravitation field
service, model to predict the movement of a planet (celestial body). The
abstract classes serve as an initial point of appropriate specific concepts,
such as: the Earth, numerical (tabular) model of the Earth's atmosphere, Earth
upper atmosphere, Earth dynamic atmosphere, "planet" Sun, "planet" Moon, model
of gravitation potential, non-disturbed movement of a spacecraft, C20-type
model of a disturbed
movement, complete Newton-Cowell model of disturbed movement of a spacecraft. The
applied program, developed in When
using Newton-Cowell differential equations as spacecraft movement models, it is
possible to apply any of 5 numerical methods, proposed by the program (see
original full printed paper). References 1.
D.V.Kovkov, V.V.Malyshev, A.V.Fedorov. The study of
the future astrophysical complexes space segment orbits evolution, MAI
bulletin, vol. 17, No. 1, 2010, 62-71. 2.
D.V.Kovkov, V.V.Malyshev, A.V.Fedorov.
The evolution and stability of the future astrophysical complexes space segment
orbits, Cosmonautics and Rocket Production, No.1 (58), 2010, 111-123. 3.
D.V.Kovkov, V.V.Malyshev, A.V.Fedorov. The analysis of
stability of space radio interferometer high-apogee orbits, Cosmonautics and
Rocket Production, No. 2 (59), 2010, pp. 117-122. 4.
Kovkov D.V. The evolution and stability of the future
astrophysical complexes orbits, The reports theses digest of the 15th
International Conference "The System Analysis, Control and Navigation", 5.
D.V.Kovkov, V.V.Malyshev, A.V.Fedorov. The study of
the stability of high-apogee orbits with the Moon gravitation accounting, The
reports theses digest of the 9th International Conference "Aviation
and Cosmonautics George Vladimirovich Kovkov, First Deputy Director General of FSUE TsNIIMash, sphere of scientific
interests: design of space systems. Veniamin
Vasilyevich Malyshev, Honored
scientist of the Russian Federation, Doctor of Engineering Sciences, Professor,
member of the International Academy of Astronautics, K.E.Tsiolkovsky Academy of
Astronautics, International Academy of the Higher School, International Academy
of Nonlinear Sciences, member of the Scientific Council of Roscosmos, Chairman
of Specialized Doctoral Thesis Committee, Chairman of the organizing committee
of the international conference "System Analysis, Control and Navigation",
Laureate of the Prize of the Council of Ministers of the USSR, the Prize for
the best research works instituted by the Ministry of Higher Education of the
USSR, three prizes named after the 25th anniversary of MAI. For his
creative contribution to implementation of space programs and projects he was
awarded the Medals of Yu.A.Gagarin, academicians N.A.Pilyugin, V.N.Chelomey,
and the Badge of S.P.Korolev. He has a patent for invention. For many years he
has been a chairman of the session of the scientific council of RAS on the
problems of motion control and navigation, and a member of the editorial board
of the journal "Izvestiya RAN. Teoriya i sistemy uprav-leniya" (Proceedings of
the Alexander Victorovich Fedorov, Associate Professor of Department No.604 (since 1988), Candidate of
Engineering Sciences (1977). Graduated from MAI, Department No.604. Specializes
in applied theory of optimal control and development of software for design and
control of complex systems. Main fields of research: development of ballistic
support for space systems of communication and navigation, development of
algorithms and software for statistical analysis of controlled motion,
trajectory optimization and motion control, design and control of space
systems. Published over 120 scientific and educational works, including: Sputnikoviye
systemy monitoringa. Analiz, sintez i upravleniye (Analysis, synthesis and
control. Satellite systems for monitoring), MAI, 2000. Laureate of the Prize of
the Council of Ministers of the |
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