What parts of the earth is nearest to the path of the moon? I saw a website saying that the closest part of the earth to the moon is just below the equator, since the earth is shaped like a beach ball instead of a sphere. Is this true? Isn't the path of the moon along the ecliptic plane plus or minus 5 degrees? If so then where exactly does the ecliptic plane fall along the latitudes of the earth? 10 degrees latitude, 20 degrees latitude? Thank you in advance.
You are right to question the claim that the Moon's path is below the equator! And it is also true that the Moon's orbit can be inclined by up to 5 degrees from the ecliptic. And just as the ecliptic does not have a fixed path over the surface of the Earth, neither does the Moon's path. The line on the surface of the Earth that is closest to the Sun changes over the course of the year from 23 degrees North in June to 23 degrees South in December. Imagine that it is June and the Moon's orbit happens to be about the same as the ecliptic - then over the course of the month the path on the Earth closest to the Moon would go in a spiral from 23 degrees North latitude to 23 degrees South latitude and back again as the Moon swings through it's orbit. Every time the Earth rotated it would trace another loop in the spiral, and since the moon takes ~15 days to go from 23-North to 23-South, each loop is separated on the Earth by about (2×23)/15 = 3 degrees latitude. If you looked again in five years, the Moon's path would no longer be in line with the ecliptic (it would be 5 degrees inclined) - and would then swing from 28-North to 28-South latitude and back every month. So then the loops would be separated by (2×28)/15 = 3.7 degrees. Same thing 10 years later would drop from 18-North to 18-South and so the loops would only be separated by (2×18)/15 = 2.4 degrees per night. At the Vernal and Autumnal equinoxes the Sun's path (the ecliptic) stays pretty close to the equator - thus the Moon's path would be within 5 degrees from the equator. And every 9.3 years (when the Moon is aligned with the ecliptic) the Moon's path would also stay fairly close to the equator around the time of the Vernal and Autumnal equinoxes.
I hope this answers your question.