Moon effect. Some people believe that the Moon controls their activities. If the

Question

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 percentage 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 × 10^8 m, Earth's radius is 6.37 × 10^6 m, Moon's mass is 7.36 × 10^22 kg, and Earth's mass is 5.98 × 10^24 kg.

I know the answer to part A (6.9%), I just need help with part B.

Explanation / Answer

You need to calculate the force of the moon at the surface of the earth

F = G Mm/d^2

i used d to denote distance

assuming a circular orbit you would have when the moon is on the side of earth you are on

d1 = dc - re

when the moon is on the opposite side of the earth that you are on

d2 = dc + re

===============

F = G Mm/d^2

F1 = G Mm/(dc -re)^2

F2 = G Mm/(dc + re)^2

we can find the ratio

F2/F1 = (G Mm/(dc + re)^2 ) * ((dc - re)^2/GMm)

we see the GMm cancel so we dont need those

F2/F1 = (dc - re)^2/(dc + re)^2

= (3.82*10^8) - 6.37*10^6)^2/(3.82*10^8 + 6.37*10^6)^2

=0.93546

this means that the pull on the far side is 0.9354 times the pull on the close side

by taking the inverse we find

F1 = 1.068 * F2

(a)this means 6.8 percent increase (ans)

=============

(b)

F2/F1 =0.93546

solving for F2

F2 = 0.935 * F1

so the weight would decrease by 0.000684 percent (ans)

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