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 × 10⁸ m, Earth's radius is 6.37 × 10⁶ m, Moon's mass is 7.36 × 10²² kg, and Earth's mass is 5.98 × 10²⁴ kg.

(a)

Number

Enter your answer for part (a) in accordance to the question statement

Units

Choose the answer for part (a) from the menu in accordance to the question statement g (gravity)kg/satomskm/h^2rev/minmegatonsft·lbhpdollarshits/satmL/minpercentcm^-3 or /cm^3s/hsmu/ylines/mmcentsuphotons/sphotons/s·m^2ktonm^-3 or 1/m^3kg/minN-s/mN/storr or mm Hgmg/sμm

(b)

Number

Enter your answer for part (b) in accordance to the question statement

Units

Choose the answer for part (b) from the menu in accordance to the question statement g (gravity)kg/satomskm/h^2rev/minmegatonsft·lbhpdollarshits/satmL/minpercentcm^-3 or /cm^3s/hsmu/ylines/mmcentsuphotons/sphotons/s·m^2ktonm^-3 or 1/m^3kg/minN-s/mN/storr or mm Hgmg/sμm

Answer 1

a )

given

d_ce = the Earth–Moon (center-to-center) distance is 3.82 x 10⁸ m

radius of earth R = 6.37 x 10⁶ m  

using F = G M m / d²

d = d_ce + R , then

F_oppo = G M m / (d_ce + R)²  

and

at moon's gravitational pull is directly on overhead

d = d_ce - R

F_over = G M m / (d_ce - R)²

now percentage of increase = (F_over - F_oppo ) x 100 / F_opp

= ( (G M m / (d_ce - R)²) - (G M m / (d_ce + R)²) x 100 / G M m / (d_ce + R)²

= ( (d_ce + R)²) - (d_ce - R)²) x 100 / (d_ce - R)²

= ( ( 382 + 6.37 )² - ( 382 - 6.37 )²) x 100 / ( 382 + 6.37 )²

now percentage of increase = 6.890 %

b )

now percentage of decrease = (F_over - F_oppo ) x 100 / F_R²

= ( (G M m / (d_ce - R)²) - (G M m / (d_ce + R)²) x 100 / G M m / R²

= R²( (d_ce + R)²) - (d_ce - R)²) x 100 x ( M/M_e) / (d_ce - R)² x (d_ce + R)²

= 6.37² (( 382 + 6.37)² - ( 382 - 6.37 )²)x100x(7.36x10²²/5.98x10²⁴)/(3.82-6.37)² / ( 3.82 + 6.37 )²

percentage of decrease = 2.280 x 10^-5 %