Answer:
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Explanation:
[tex]m_e[/tex] = Mass of the Earth = 5.98 × 10²⁴ kg
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
[tex]r_1[/tex] = Distance from the center of the Moon to the center of Earth = 6371000 m
[tex]r_2[/tex] = Distance from the center of the earth center to sun center
[tex]m_m[/tex] = Mass of moon = [tex]7.35\times 10^{22}\ kg[/tex]
M = Mass of sun = [tex]1.989\times 10^{30}\ kg[/tex]
[tex]F_1=G\frac{m_em_m}{r_1^2}\\\Rightarrow F_1=6.67\times 10^{-11}\frac{5.98\times 10^{24}\times 7.35\times 10^{22}}{(384000000)^2}\\\Rightarrow F_1=1.988\times 10^{20}\ N[/tex]
[tex]F_2=G\frac{Mm_e}{r_1^2}\\\Rightarrow F_2=6.67\times 10^{-11}\frac{5.98\times 10^{24}\times 1.989\times 10^{30}}{(149.6\times 10^9+6371000+695.51\times 10^6)^2}\\\Rightarrow F_2=3.511\times 10^{22} N[/tex]
[tex]\frac{F_1}{F_2}=\frac{1.988\times 10^{20}}{3.511\times 10^{22}}\\\Rightarrow \frac{F_1}{F_2}=0.00566\\\Rightarrow F_1=F_20.00566[/tex]
Hence the force of moon on earth is 0.00566 times the force of earth on moon center to center
