Question

Moon effect. Some people believe that the Moon controls their activities. The Moon moves from being directly on the opposite side of Earth from you to be being directly overhead. Assume that the Earth-Moon (center-to-center) distance is 3.82 108 m and Earth's radius is 6.37 106 m. (a) By what percent does the Moon's gravitational pull on you increase

Answer 1

Answer:

6.9%

Explanation:

We are given that

Distance between Earth and Moon=d=$3.82\times 10^8$ m

Radius of Earth=r=$6.37\times 10^6 m$

a.Initially gravitational pull

$F=\frac{GmM}{(r+d)^2}$.....(1)

After changing

Gravitational pull

$F'=\frac{GmM}{(d-r)^2}$.....(2)

Equation (2) divided by equation (1)

$\frac{F'}{F}=\frac{(r+d)^2}{(d-r)^2}$

$\frac{F'}{F}=\frac{(3.82\times 10^8+6.37\times 10^6)^2}{(3.82\times 10^8-6.37\times 10^6)^2}=1.069$

Increases in gravitational pull=$\frac{F_2}{F_1}-1=1.069-1=0.069\times 100=6.9$%