The orbit of the moon disqualifies Heliocentricity?

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The orbit of the moon disqualifies Heliocentricity?
As most know, the main reason given for the moon always showing the same face towards the Earth, is that its rotational speed matches its orbital speed. This excuse hinges on one BIG faulty assumption : That the orbit of the moon around the Earth is circular.

However, for some reason, likely to do with constructing argumentation for seasons (as is the case of all the planets orbits around the sun), the orbit of the moon around planet Earth had to be elliptical. – How else was the apparent …