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## 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

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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 -