Abstract
A few years ago it was suggested that the distance to celestial bodies could be computed by tracking their position over about 24 hours and then solving a regression problem. One only needed to use inexpensive telescopes, cameras, and astrometry tools, and the experiment could be done from one's backyard. However, it is not obvious to an amateur what the regression problem is and how to solve it. This paper identifies that problem and shows how to solve it with linear programming. It also takes into account the body's celestial latitude to improve the method's accuracy. The new method is validated both with simulated and actual data to compute distances to asteroids to within 1% of correct values. It can be used as a new tutorial for amateurs to see how consumer-grade astrophotography and free astrometry and optimization tools come together to solve an important problem. It can also be used as a tool in crowdsourced detection of dangerous asteroids.
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