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The question arose because I wanted to understand the path of the ecliptic after reading about it here: https://community.dur.ac.uk/john.lucey/users/solar_year.html

Sun's path on ecliptic

Is the sinusoidal path due to earth’s axial tilt? Or is it related to mapping the path on a 2D pane? Is there way to visualise this to aid understanding?

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  • $\begingroup$ I tried to add that ecliptic anim to your question, but it doesn't always get displayed, for some reason. But if you click the community.dur.ac.uk/john.lucey/users/solar_year.html link, the anim will get displayed on this page; at least it does on my phone browser. ;) $\endgroup$ – PM 2Ring Feb 18 at 12:00
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Both the equator and the ecliptic are great circles on the celestial sphere. The appearance of each on a map depends on the map projection.

In an equirectangular projection centered on the equator, the equator (brown) is a straight line, and the ecliptic (blue) is a sinusoid.

equator-centered cylindrical projection

If the same projection is centered on the ecliptic instead, the ecliptic is a straight line and the equator is a sinusoid.

ecliptic-centered cylindrical projection

Lucey provides both views too, but his ecliptic-centered map doesn't show the equator. The axes are labeled in ecliptic rather than equatorial coordinates.

ecliptic-centered cylindrical by Lucey

He also provides a stereographic projection centered on the midday zenith at 55°N. Here both equator (red) and ecliptic (green) are mapped as circular arcs.

zenith-centered stereographic by Lucey

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The ecliptic is a plane. It looks like a sine wave because that diagram maps the sky onto a flat plane. On the celestial sphere, the ecliptic is a great circle that crosses the celestial equator at the equinox points and which is tilted to the celestial equator by the same amount as the Earth's axial tilt (currently 23°26′12.0″).

Here's a diagram from Wikipedia that might be helpful:

Celestial sphere

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  • $\begingroup$ Would the path still be sinusoidal if Earth wasn’t tilted? Or would it then be a straight line - similar to this animation? community.dur.ac.uk/john.lucey/users/sun_ecliptic.gif $\endgroup$ – keynes Feb 18 at 13:11
  • $\begingroup$ @keynes Yes, if the Earth's axis wasn't tilted, then the ecliptic would coincide with the equator. $\endgroup$ – PM 2Ring Feb 18 at 13:22

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