Search
• Papers

## 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
BibTeX
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 -