## 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

`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 -
```