Four observation method for orbit determination, useful for asteroids

[David Sims]

If you are a serious amateur astronomer, then there probably will be occasions when you have photographic observations of an asteroid moving through a star field, and you might think that there's a chance that it is one that hasn't been discovered by anyone else. So you will want to calculate the asteroid's orbital elements, both so that you can find it again, and so that you can prove your claim as the discoverer should that be the case. For situations such as this, I've written a program so that you can easily calculate the Keplerian elements of your asteroid's orbit.

The type and manner of input is documented on one of the pages linked below. If you don't own a physical HP Prime calculator and don't wish to buy one, you can download the emulator for free from the Hewlett-Packard company.

 

Determining an Orbit from Four Observations in Right Ascension and Declination

... the math in plain algebra, with a complete worked example

 

HP Prime program to find orbital elements from four observations by the method of Gauss

... source code, with example input/output

 

Freeware app for the HP Prime calculator (20 KB download)

... No charge. Just credit David Sims as author of this code in any derivatives you make based on it.

 

HP Prime Virtual Calculator Emulator

HP Connectivity Kit

... You will needed the Connectivity Kit to transfer files from your computer, either to a physical HP Prime calculator or to an emulator running on your PC. The emulator is, of course, the HP Prime Virtual Calculator Emulator.

 

Acknowledgement to the Russian astronomer Alexander Dmitriyevich Dubyago (Александр Дмитриевич Дубяго), whose book The Determination of Orbits taught me the method used in the program.

Acknowledgement to the French astronomer Jacques Laskar, who supplied the 10-degree polynomial to calculate the obliquity of the ecliptic.

 

Moderators of these forums might want to relocate this post to the "astronomy tools" folder, under a new tool-category name. (Software, Celestial Mechanics, etc., some such thing.)