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I have a simple question : on the following figure:

enter image description here

I don't understand on the right figure why there is a progressive shift on the right when we start from step 1) to step 9). I guess there is an angle between the rotation plane of Mars and the rotation plane of Earth. Otherwise, we could'nt see clearly the recessing movement if the 2 planes were identical, could we ? We would just draw in the sky a simple line which would be the projection of the curve (on right figure) on a single Oy axis.

Anyone could explain me if this difference in two rotation planes is the cause of the shape of this curve (which is also due to the relative position of Mars from Earth) ?

Any help is welcome.

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  • $\begingroup$ Is it due to the inclination of the Earth's axis? So the ecliptic appears to oscillate North to South over a year as seen from any point on Earth. $\endgroup$
    – Steve Linton
    Jul 3, 2020 at 19:18
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    $\begingroup$ According to en.wikipedia.org/wiki/Mars the angle between the orbital planes of Earth & Mars (the inclination to the ecliptic) is 1.850°. That's small, but certainly noticeable: in comparison, the angular diameter of the Moon is about half a degree. $\endgroup$
    – PM 2Ring
    Jul 4, 2020 at 5:29
  • $\begingroup$ Just another question : why doesn't figure on the left is not rotated by an angle of -90 degrees to be more representative ?. the motions are almost horizontal and not vertical when we look at at planets in the the sky Any precision is welcome. Regards $\endgroup$
    – user16492
    Mar 17, 2021 at 8:53

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You are right. If Mars orbited in exactly the same plane as the Earth, instead of an S or a loop, we would see Mars moving prograde relative for the stars along the ecliptic, then slowing and stopping, moving retrograde for a few months, as Earth overtakes it, still on the ecliptic, then moving prograde again.

But Mars doesn't orbit in the same plane, so it has some motion perpendicular to the ecliptic. when these motions are combined, the usual effect is a "loop" or sometimes an "S".

(note that the axial tilt of the Earth is not relevant here)

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  • $\begingroup$ Thanks for your quick answer. Nevertheless, the remark of @Steve Linton is interesting : why don't we take into account of the changing of inclination of the Earth's axis ? Indeed, this one is about 23 degree but planet Mars has alo an inclination roughly equal to 25 degree : so both are similar (difference of 2 degree) ? Is there a compensation effect or anything else since difference between the orbital planes between Earth and Mars is only 1.850° as pointed by @PM 2Ring ? this is the same order of values. $\endgroup$
    – user16492
    Jul 4, 2020 at 10:57
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    $\begingroup$ Because the position of Mars on the celestial sphere is independent of your location on Earth, or the time of day, or the inclination of the Earth. Steve's comment is incorrect. The position in the sky of the ecliptic changes over the year. But it is the position of Mars on the ecliptic that creates the "S" and not the position of the ecliptic on the sky. $\endgroup$
    – James K
    Jul 4, 2020 at 13:22

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