Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.ipa.nw.ru/conference/2002/sovet/PS/BATRAKOV.PS Дата изменения: Mon Aug 19 15:46:58 2002 Дата индексирования: Tue Oct 2 07:40:40 2012 Кодировка: Поисковые слова: m 8

IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Orbits with osculation of higher orders and their use
in celestial mechanics
Yu. V. Batrakov
Institute of Applied Astronomy, St. Petersburg, Russia
The idea of the generalized or intermediate orbits with osculation of the second
and third order was proposed and considered rigorously in 1981 [1]. The motion
along these orbits is a combination of the non--perturbed motion of a particle
about a non­changeable fictitious point mass and the motion of the fictitious
mass, or an attracting centre, itself. The latter is considered to have a constant
velocity vector or to be non--moving. These orbits can be constructed for any point
of the actual perturbed trajectory. The position, velocity, and acceleration vectors
and even the time derivatives of the acceleration, if the third order osculation is
dealt with, are the same as in the real motion.
The idea of [1] was used in [2], and it was found that the generalized orbits
with high order osculation show sensible advantage when being used as the ref­
erence ones in the Encke method. Another family of the generalized orbits was
proposed in [3]. The fictitious mass is placed in one of the real attracting bodies
(major planets), and it was considered to be changeable with time according to
the Gylden­Meshchersky law. The motion of a particle around this variable mass
is not a Keplerian one. These orbits are computed easily and they are also ef­
fective as the reference ones. So, the rather wide range of the new, effective and
simple reference orbits have been proposed for computing the perturbed trajec­
tories by the Encke method. Attempts of solving the classical problem of orbit
determination from two known heliocentric positions of a particle, if the orbit is
the generalized one [4], are also of certain interest.
The further steps in developing the theory of the osculation of higher order
have been made in [5,6]. The equations of the perturbed motion in the elements
of the generalized (intermediate) orbits were derived for the first time in [5,6].
They are quite similar to the known Newton--Euler (N--E) equations for the usual
osculating elements ( osculation of the first order ). The difference between them
is in the number of variables ( six in N--E and nine in [5] ) and in the form of
the perturbation forces (the force components in N--E and their time derivatives
in [5]; the coefficients at the forces are also different). Testing these equations for
24

the efficiency in practice is now carried out. The work was partly supported by
the RFBR grant No. 01­02­17078.
References
1. Batrakov Yu. V. Intermediate orbits approximating the initial part of the
perturbed motion. Bull. ITA, 1981, 15, 1--5 (in Russian).
2. Batrakov Yu. V., Mirmakhmudov E. R. On effectiveness of using the in­
termediate orbits for computing the perturbed motion. First Spain--USSR
Workshop on Positional Astronomy and Celestial Mechanics. Univ. de Va­
lencia Observ. Astronomico, 1999, 71--76.
3. Shefer V. A. Superosculating intermediate orbits and their application in
the problem of investigation of the motion of asteroids and comets. In:
B. A. Steves and A. E. Roy (eds.) The Dynamics of Small Bodies in the
Solar System. Kluwer Acad. Pubs., Netherland, 1999, 71--76.
4. Sokolov V. G. Determining the intermediate orbit from two positions. In:
A. G. Sokolsky(ed.). The Asteroid Hazard. Conference in ITA in 1995. ITA,
St. Petersburg, 1995, 39--41 (in Russian).
5. Batrakov Yu. V. Second Order Osculation Orbits and Equations for their
Perturbed Elements. IAA Trans., 2000, 5, 230--246 (in Russian).
6. Batrakov Yu. V. Second Order Osculation Intermediate Orbits of Hyperbolic
Type and Equations for their Perturbed Elements. IAA Trans., 2001, 6, 300--
317 (in Russian).
25