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So I'd like to ask whether the semi-major axis of planetary orbits are aligned? Logically, they shouldn't be, but many websites act as if they are. If they're not aligned, what's the angle between the reference xy axis and the semi-major axis of the orbits of planets?

Thanks!

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    $\begingroup$ I think those websites assume orbits are nearly circular, and, for circles, any radius is also a semi-major axis. $\endgroup$ – barrycarter Nov 28 '15 at 16:25
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The major axes of the planets are not aligned.

The major axis passes through the perihelion, the solar system barycentre and the aphelion. So by looking up the Longitude of perihelion we can find the direction of the major axis:

planet  Longitude of perihelion 
M       77
V       132
E       103
M       -24
J       15
S       93
U       171
N       45

There is no evidence of alignment.

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The current longitudes of perihelion show no alignment. Furthermore, they change because all the planets have orbital precession - that is, the longitude of perihelion changes by between 0.36 arcseconds/year for Neptune (i.e. the longitude of perhelion goes through the full range of angles in 10,000 years) to 19.5 arcseconds/year for Saturn. So not only is there no alignment, but the relative directions of the semi-major axes change comparatively quickly.

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