If you publish an article with results from this service, please cite the article (will be published).

This service allows you to determine the Keplerian orbit of a binary star or a preliminary orbit of an asteroid satellite from five apparent relative positions.

  This service is under development and testing. Please, send examples of using the service so that the developer can make corrections and improve the service.
(Author: Nikolay Emelyanov, e-mail emelia@sai.msu.ru )

To use this service see following notes.

1. The determination of the orbit is done in two steps.
First, the sector velocity of the orbit is determined. This requires five apparent relative positions.
At the second stage, the parameters of the spatial orbit are determined by the method of Thiele-Innes. To do this, three most suitable observations are selected from the available five observations.

2. The time interval of observations should not exceed the period of relative orbital revolution.
ATTENTION: this condition is not controlled by the system.

3. It is assumed that the topocentric direction to the object does not change over the time interval of observations used. Thus, the movement of an asteroid across the sky is neglected.

4. You need to enter the differences of right ascensions and declinations. The resulting orbit parameters will be expressed in the same coordinate system as the observations.

5. The semi-major axis and the mean motion are determined independently. This allows to determine the total mass of the system by the service. The semi-major axis is first determined in the same units as the observations entered.

6. The obtained parameters are displayed on the results page, as well as in a separate output file in the form of numbers without literal comments.
Additionally, some file (log file) with intermediate results is in output. This file is intended mainly to control the operation of the program by the program developer.

7. On the result page, some rows with a label "debug:" may be displayed. This is intended to control the work of the program by the developer.

8. Observational data may not be sufficient to determine the orbit. The service reports such circumstances.

9. The choice of observations 135 for the method Thiele-Innes is the most appropriate. If there is a method failure, try choosing 125 or 145.

10. Notes to the graphics. The graph shows the apparent orbit. The thick line shows the arc of the orbit covered by the observations. The dots show the observations used. Units of measurement along the axes are the same as for observations. The line through the center means the projection of the line of apses.

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