Answer:
[tex]\frac{F_e}{F_m}=285461.75196[/tex]
Explanation:
r = Radius of Earth = [tex]6.371\times 10^6\ m[/tex]
[tex]r_o[/tex] = Radius of Moon = [tex]3.84\times 10^{8}\ m[/tex]
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
Gravitational force on the apple on Earth
[tex]F_e=\frac{GM_em}{r^2}[/tex]
Gravitational force of Moon on the apple
[tex]F_m=\frac{GM_mm}{r_m^2}\\\Rightarrow F=\frac{GM_mm}{(r_o-r)^2}[/tex]
Dividing the two equations
[tex]\frac{F_e}{F_m}=\frac{\frac{GM_em}{r^2}}{\frac{GM_mm}{(r_o-r)^2}}\\\Rightarrow \frac{F_e}{F_m}=\frac{M_e\times (r_0-r^2)}{r^2M_m}\\\Rightarrow \frac{F_e}{F_m}=\frac{5.972\times 10^{24}\times (3.84\times 10^{8}-6.371\times 10^6)^2}{(6.371\times 10^6)^2\times 7.35\times 10^{22}}\\\Rightarrow \frac{F_e}{F_m}=285461.75196[/tex]
The ratio of the force between Earth and the apple to the force between Moon and the apple is [tex]\frac{F_e}{F_m}=285461.75196[/tex]
