Prior to going into space, scientists estimated that the neutral gravity point - the location between the earth and moon, where the moon's and the earth's gravitational pull is zero or neutral - was approximately 23,900 miles above the lunar surface. Based on this estimate, the theory of 1/6 lunar gravity was rationalized. However, this is not
accurate because the actual neutral point is located approximately
43,495 from the moon.
Using the actual distance equates to a much higher lunar gravity.
This is from William Brian's book Moongate: Suppressed Findings of the U.S. Space Program. Brian claimed that NASA discovered that the acceleration due to gravity at the lunar surface was actually 0.64g instead of the figure of around 0.165g that is widely held to be accurate, and was known hundreds of years before NASA was even conceived.
Brian arrived at the conclusion that the moon was actually more massive than was previously thought due to discrepancies in the statements of the gravitational "neutral point" -- the point along an imaginary line between the earth and the moon at which the force due to gravity acting on a point mass will be equal from the earth and from the moon. This is, traditionally, roughly one-tenth the distance from the moon to the earth (because the masses of the earth and moon are roughly in the ratio 9<sup>2</sup> : 1). The thing is is that there is a discrepancy in the location of the neutral point even in the traditional sense because there is more than one definition of the neutral point, keep in mind that space is three-dimensional, and not one-dimensional. The definition given above, as it happens, is not useful in navigating spacecraft.
The point at which Apollo spacecraft were considered to enter the moon's "sphere of influence" (a neutral point) was actually ahead of the earth-moon line and was thus a greater distance both from the earth and from the moon.