Moon effect. Some people believe that the Moon controls their activities. If the Moon moves from being directly on the opposite side of Earth from you to being directly overhead, by what percent does (a) the Moon's gravitational pull on you increase and (b) your weight (as measured on a scale) decrease? Assume that the Earth-Moon (center-to-center) distance is `3.82 xx 10^8` m and Earth's radius is `6.37 xx 10^6` m.

Explanation

To solve the problem, we need to calculate the gravitational pull of the Moon on a person when the Moon is in two different positions: directly overhead and directly on the opposite side of the Earth. We will denote the gravitational force exerted by the Moon as \( F_1 \) when it is on the opposite side and \( F_2 \) when it is directly overhead.

### Step 1: Calculate the gravitational pull when the Moon is on the opposite side of the Earth

The distance from the Moon to a person standing on the surface of the Earth when the Moon is on the opposite side is given by:
\[ d_1 = R_{ME} + R_E \]
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