2.6.9. Find the force of gravitational attraction acting on you from the Earth, Moon, and Sun.
Solution
By Newton's law gravitation: $F=G\frac{m_1 m_2}{r^2}$ where $m_1$ is my mass, $m_2$ is the mass of the celestial body, and $r$ is the distance between the center of the body and me Using $G=6.674×10^{-11}\frac{Nm^2}{kg^2}$ For me and Earth: $m_1=70kg$ $m_{Earth}=5.972×10^{24}kg$ $r_{Earth}=6.371×10^6m$ (that's Earth's radius, assuming that I'm at sea level) and calculating $F_{Earth}\approx 686N$ (this is equeal to my weight!, $mg=70kg×9.8\frac{m}{s^2}$) For me and the Moon: $m_{Moon}=7.342×10^{22}kg$ Average Earth–Moon distance: $r=3.844×10^8m$ and calculating $F_{Moon}\approx 2.4×10^{-3}N$ For me and the Sun: $m_{Sun}=1.989×10^{30}kg$ Average Earth–Sun distance: $r=1.496×10^{11}m$ and calculating $F_{Sun}\approx 0.414N$