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Does Earth's orbit around the sun significantly alter the eccentricity of the moon's orbit? I wouldn't think so.
Evection (Latin for carrying away), in astronomy, is the largest inequality produced by the action of the Sun in the monthly revolution of the Moon around the Earth. ... It can be considered as arising from an approximately 6-monthly periodic variation of the eccentricity of the Moon's orbit and a libration of similar period in the position of the Moon's perigee, caused by the action of the Sun