Question:How heavy is Earth's moon?

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I had always heard that the center of gravity of our Earth-moon system was basically on the surface of the earth. If that's the case, then apparently the math works out to say the moon is 1/6th of earth's gravity.

But here's an interesting bit of data:

Houston reports the instant at which we leave the lunar sphere of
influence.  This means simply that despite the fact we are only
thirty-four thousand nautical miles from the moon, and still 
174,000 away from the earth, the earth's pull has become dominant,
and the mathematical equations now recognize that fact.

This says the center of gravity of the earth-moon system is not near the surface of Earth. I forget what that says about the mass of the moon compared to the earth, but perhaps 2/3rds earth's mass.

I quoted that from Google Video: John Lear tells all part 4 of 4.

Video capture below; I don't remember in what book that info is highlighted.

John Lear tells all part 4 of 4, 06:06.png