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Determination of Rectilinear Orbit for an Object Moving in the Ecliptic Plane

Transactions of IAA RAS, issue 30, 49–56 (2014)

Keywords: two-body problem, rectilinear motion, preliminary orbit determination, ecliptic

Abstract

It is necessary to complete at least three observations in order to find a general form of a rectilinear orbit in the plane of ecliptic. In this case, the process of orbit determinations by the Laplace method takes a form of solving algebraic equations of the 10th degree, which can have up to four solutions. The method of iterative orbit determination from a system of two equations in the form of a Lambert series is proposed for the cases when time intervals between observations are too long. A linear parabolic motion, which can also have up to four possible solutions, is considered to be the initial approximation.

Citation

Text

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RIS

V. B. Kuznetsov. Determination of Rectilinear Orbit for an Object Moving in the Ecliptic Plane // Transactions of IAA RAS. — 2014. — Issue 30. — P. 49–56.

@article{kuznetsov2014,
  abstract = {It is necessary to complete at least three observations in order to find a general form of a rectilinear orbit in the plane of ecliptic. In this case, the process of orbit determinations by the Laplace method takes a form of solving algebraic equations of the 10th degree, which can have up to four solutions. The method of iterative orbit determination from a system of two equations in the form of a Lambert series is proposed for the cases when time intervals between observations are too long. A linear parabolic motion, which can also have up to four possible solutions, is considered to be the initial approximation.},
  author = {V.~B. Kuznetsov},
  issue = {30},
  journal = {Transactions of IAA RAS},
  keyword = {two-body problem, rectilinear motion, preliminary orbit determination, ecliptic},
  pages = {49--56},
  title = {Determination of Rectilinear Orbit for an Object Moving in the Ecliptic Plane},
  url = {http://iaaras.ru/en/library/paper/1025/},
  year = {2014}
}

TY  - JOUR
TI  - Determination of Rectilinear Orbit for an Object Moving in the Ecliptic Plane
AU  - Kuznetsov, V. B.
PY  - 2014
T2  - Transactions of IAA RAS
IS  - 30
SP  - 49
AB  - It is necessary to complete at least three observations in order to
find a general form of a rectilinear orbit in the plane of ecliptic.
In this case, the process of orbit determinations by the Laplace
method takes a form of solving algebraic equations of the 10th
degree, which can have up to four solutions. The method of iterative
orbit determination from a system of two equations in the form of a
Lambert series is proposed for the cases when time intervals between
observations are too long. A linear parabolic motion, which can also
have up to four possible solutions, is considered to be the initial
approximation.
UR  - http://iaaras.ru/en/library/paper/1025/
ER  -