## Geometric method for determination of parabolic orbits

Transactions of IAA RAS, issue 26, 28–33 (2012)

**Keywords**:
orbit determination, two body problem, Comets, parabolic orbit

### Abstract

A modification of geometric Kuryshev Perov method for determination preliminary parabolic orbit from four observations is presented. Use of of the geometric relationships between heliocentric distances for object on parabolic orbit (two conditions of coplanarity and expression of semiparameter via two heliocentric vectors) allowis rigorous system of two algebraic equations relatively two geocentric distances to be obtain. In these equations the intervals of times between the observations are not used. The method may be used at any intervals of time between the observations, but is unusable for orbits nearby ecliptic. As an example the orbit of long-periodic comet 153P/Ikeya-Zhang has been computed. Five solutions have been obtained and analyzed

### Citation

`V. Kuznetsov. Geometric method for determination of parabolic orbits // Transactions of IAA RAS. — 2012. — Issue 26. — P. 28–33.`

```
@article{kuznetsov2012,
abstract = {A modification of geometric Kuryshev Perov method for determination preliminary parabolic orbit from four observations is presented. Use of of the geometric relationships between heliocentric distances for object on parabolic orbit (two conditions of coplanarity and expression of semiparameter via two heliocentric vectors) allowis rigorous system of two algebraic equations relatively two geocentric distances to be obtain. In these equations the intervals of times between the observations are not used. The method may be used at any intervals of time between the observations, but is unusable for orbits nearby ecliptic. As an example the orbit of long-periodic comet 153P/Ikeya-Zhang has been computed. Five solutions have been obtained and analyzed},
author = {V. Kuznetsov},
issue = {26},
journal = {Transactions of IAA RAS},
keyword = {orbit determination, two body problem, Comets, parabolic orbit},
pages = {28--33},
title = {Geometric method for determination of parabolic orbits},
url = {http://iaaras.ru/en/library/paper/894/},
year = {2012}
}
```

```
TY - JOUR
TI - Geometric method for determination of parabolic orbits
AU - Kuznetsov, V.
PY - 2012
T2 - Transactions of IAA RAS
IS - 26
SP - 28
AB - A modification of geometric Kuryshev Perov method for determination
preliminary parabolic orbit from four observations is presented. Use
of of the geometric relationships between heliocentric distances for
object on parabolic orbit (two conditions of coplanarity and
expression of semiparameter via two heliocentric vectors) allowis
rigorous system of two algebraic equations relatively two geocentric
distances to be obtain. In these equations the intervals of times
between the observations are not used. The method may be used at any
intervals of time between the observations, but is unusable for
orbits nearby ecliptic. As an example the orbit of long-periodic
comet 153P/Ikeya-Zhang has been computed. Five solutions have been
obtained and analyzed
UR - http://iaaras.ru/en/library/paper/894/
ER -
```