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Plotting positions of solar system objects


This page provides software to display the positions of solar system objects at regular intervals, given their 6 orbital elements. The plot is unusual because it shows the objects relative to a fixed sun and earth, as an aid to seeing how size and visual magnitude may vary due to distance. The plotted paths are not conic sections because they result from the combined motion of the earth and each object.

Against each plotted position of an object is shown the date, the object's z coordinate (above or below the plane of the earth's orbit), its radius r from the sun and distance delta from the earth. All distances are in astronomical units (1 a.u. is the mean distance of the earth from the sun).

The calculation is done as script within an SVG page so that a browser will execute it without the need for any other software, such as a compiler. However, the browser must be capable of displaying SVG (see Internet Explorer and Firefox can do it with the aid of an SVG plug-in obtainable free from It does work fine in Internet Explorer but Firefox seems to have difficulty with the script. Users of other browsers please tell me (graham dot relf at fsmail dot net) how well it works.

The calculation scheme is based on theory given in "Orbital Motion" (3rd edn) by A.E.Roy, Institute of Physics Publishing, UK, 2002, ISBN 0-85274-229-0. The solution of Kepler's equation for the eccentric anomaly uses code from which is gratefully acknowledged. See that page for details of how the solution works.

The software is available here. Clicking that link in a suitable browser will display the plot. However, do also save the target as a file and examine it in a text editor to see how you can change it to plot other comets, asteroids, etc, by making small changes. Modifiable sections are clearly indicated by comments in the code.

At the moment (early January 2008) there are no fewer than 3 periodic comets which should be photographable with simple equipment (especially if you take a series of photos and use my GRIP application to combine them). The current version of the plotting software available from this page shows those three periodic comets: 17P/Holmes, 9P/Tuttle and 46P/Wirtanen. I am hoping to photograph them all myself soon but there has not been a clear evening at my home for more than 2 weeks. That's ever since I bought myself a proper motorised equatorial mount for the camera.

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