Astrophysics (Index)About

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. However it does yield information regarding a lower-bound to the semi-major axis. Sometimes, a likely semi-major axis is cited based upon the average of possible semi-major axes, assuming a randomly positioned orbital plane positioning and some knowledge of the observational error distribution. 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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