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This merged image shows the angular distance between the moon and Mars at 10 PM (upper part) and the change in the angular distance at 10 PM the following day (lower part).

This merged image shows the angular distance between the moon and Mars at 10 PM (upper part) and the change in the angular distance at 10 PM the following day (lower part).

My understanding is that the moon changes position in the sky by an average of 13 degrees/day because of its orbital motion around the Earth. The direction of this proper motion is eastward, opposite to the moon's apparent motion westward.

So, if the angular distance between the moon and Mars was 10° at one time, it would be around 23° a day later. But planets also have proper motions of their own. Therefore, Mars would move eastward by an average of 0.5°/day, reducing the angular distance between itself and the moon to 22.5° instead of 23°.

Earth also orbits the sun at about 1°/day.

Does Earth's orbital motion affect the value of the angular distance between the moon and a planet over a period of time (24 hours for example)?

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    $\begingroup$ Yes, it does. Without this effect Mars would never move backwards in the sky (Its ecliptical longitude would steadily increase). $\endgroup$
    – Leos Ondra
    Nov 18, 2022 at 9:28
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    $\begingroup$ Yes, This is exactly what your images show. The moon moves a lot (in its orbit around the earth) and Mars moves a little (due to both it's movement around the sun and the Earth's movement around the sun) The two motions are more or less independent. What do you suppose is missing from this description. I find your question unclear, since the answer seems so obviously "yes". $\endgroup$
    – James K
    Nov 18, 2022 at 20:10
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    $\begingroup$ @JamesK I wasn't sure Earth's motion had such influence. Now that I understand that the change in angular distance is determined by the motion of the moon, Mars and Earth. Assuming perfectly circular orbits for planets around the sun and for the moon around earth, and assuming the moon moves 13°/day, Mars moves 0.5°/day, and Earth moves 1°/day, by how many degrees would the value of the moon-Mars angular distance change 24 hours later? $\endgroup$
    – William
    Nov 19, 2022 at 3:41

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