## A Method for Determination of Preliminary Elliptical Orbits from Two Short CCD Series of Observations

Transactions of IAA RAS, issue 39, 8–16 (2016)

**Keywords**:
preliminary orbit, asteroids, numerical method.

### Abstract

A method for determination of preliminary elliptical orbits is proposed. This method can be applied if the spherical coordinates (α, δ) and their first derivatives (𝑎̇ , δ) are known at two moments. The integral of areas and the integral of energy are used to obtain four nonlinear equations. A numerical solution of these equations gives a value of the topocentric distance and its first derivative. Elements of an asteroid orbit can be calculated from these data.

### Citation

`T.A. Vinogradova. A Method for Determination of Preliminary Elliptical Orbits from Two Short CCD Series of Observations // Transactions of IAA RAS. — 2016. — Issue 39. — P. 8–16.`

```
@article{vinogradova2016,
abstract = {A method for determination of preliminary elliptical orbits is proposed. This method can be applied if the spherical coordinates (α, δ) and their first derivatives (𝑎̇ , δ) are known at two moments. The integral of areas and the integral of energy are used to obtain four nonlinear equations. A numerical solution of these equations gives a value of the topocentric distance and its first derivative. Elements of an asteroid orbit can be calculated from these data.},
author = {T.~A. Vinogradova},
issue = {39},
journal = {Transactions of IAA RAS},
keyword = {preliminary orbit, asteroids, numerical method},
pages = {8--16},
title = {A Method for Determination of Preliminary Elliptical Orbits from Two Short CCD Series of Observations},
url = {http://iaaras.ru/en/library/paper/1647/},
year = {2016}
}
```

```
TY - JOUR
TI - A Method for Determination of Preliminary Elliptical Orbits from Two Short CCD Series of Observations
AU - Vinogradova, T. A.
PY - 2016
T2 - Transactions of IAA RAS
IS - 39
SP - 8
AB - A method for determination of preliminary elliptical orbits is
proposed. This method can be applied if the spherical coordinates (α,
δ) and their first derivatives (𝑎̇ , δ) are known at two moments.
The integral of areas and the integral of energy are used to obtain
four nonlinear equations. A numerical solution of these equations
gives a value of the topocentric distance and its first derivative.
Elements of an asteroid orbit can be calculated from these data.
UR - http://iaaras.ru/en/library/paper/1647/
ER -
```