Geometric Initial Orbit Determination From Bearing Measurements
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Abstract
Initial orbit determination (IOD) from only bearing measurements is a classical problem in
astrodynamics. The classical solutions of Gauss, Laplace, and others can solve this problem
with three bearing measurements collected at known times. In this work, we apply concepts
from algebraic geometry to investigate purely geometric solutions to this same problem. It is
shown that five optical sightings at unknown times may be used to determine the orbit of an
unknown spacecraft. The solution only requires knowledge that the spacecraft is following a
conic orbit, with no need for any orbit propagation as part of the IOD process.
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2022-08
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