  Initial orbit determination (IOD) from line-of-sight (i.e., bearing)
measurements is a classical problem in astrodynamics. Indeed, there are many
well-established methods for performing the IOD task when given three
line-of-sight observations at known times. Interestingly, and in contrast to
these existing methods, concepts from algebraic geometry may be used to produce
a purely geometric solution. This idea is based on the fact that bearings from
observers in general position may be used to directly recover the shape and
orientation of a three-dimensional conic (e.g., a Keplerian orbit) without any
need for knowledge of time. In general, it is shown that five bearings at
unknown times are sufficient to recover the orbit -- without the use of any
type of initial guess and without the need to propagate the orbit. Three
bearings are sufficient for purely geometric IOD if the orbit is known to be
(approximately) circular. The method has been tested over different scenarios,
including one where extra observations make the system of equations
over-determined.
