### projected semi-major axis

(semi-major axis projected onto line-of-sight or plane of the sky)

There are two **projected semi-major axes** of orbits commonly
encountered in astronomy: the projection on the plane of the sky, e.g.,
when viewing a visual binary or direct imaging an extra-solar planet,
and projection on the line-of-sight, when working out the orbit
from radial velocity measurements over time. It is of note
that given the geometry of rotation in three dimensions, the
projection of the ellipse's semi-major axis is not merely the
(apparent) longest distance between two points on the projection.
The actual orbit (and projected and actual semi-major axes) can be
worked out with sufficient data on the position of the host in
relation to the projection, and/or on the projected orbital speed
throughout the orbit. In cases sufficiently near the instruments'
precision-limits, such a derived orbit is a rough approximation.

(*orbits,celestial mechanics,measure*)
**Further reading:**

https://astronomy.swin.edu.au/cosmos/P/Projected+Semi-major+Axis

http://spiff.rit.edu/classes/phys440/lectures/fix_tilt/fix_tilt.html

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