Answer
(a) The force exerted on the person by the moon is $2.40\times 10^{-3}~N$.
(b) The ratio of the force exerted on the person by the moon and the force exerted on the person by the Earth is $3.50\times 10^{-6}$.
Work Step by Step
(a) We can find the force exerted on the person by the moon. Let $M_M$ be the mass of the moon. Let $M_P$ be the mass of the person.
$F = \frac{G~M_M~M_P}{R^2}$
$F = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(7.35\times 10^{22}~kg)(70~kg)}{(3.78\times 10^8~m)^2}$
$F = 2.40\times 10^{-3}~N$
The force exerted on the person by the moon is $2.40\times 10^{-3}~N$.
(b) We can find the ratio of the force exerted on the person by the moon and the force (which is $mg$) exerted on the person by the Earth.
$\frac{2.40\times 10^{-3}~N} {(70~kg)(9.80~m/s^2)}= 3.50\times 10^{-6}$
The ratio of the force exerted on the person by the moon and the force exerted on the person by the Earth is $3.50\times 10^{-6}$.
