question 6 of 15 the evil team of ms. moonstruck and mr. luny intend to deflect the moon from its orbit…

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula is $F = G\frac{Mm}{r^{2}}$, where $F$ is the gravitational force, $G = 6.67\times10^{- 11}\ m^{3}\ kg^{-1}\ s^{-2}$ is the gravitational constant, $M$ is the mass of one object, $m$ is the mass of the other object, and $r$ is the distance between the centers of the two objects. We know $F = 8310\ N$, $M = 7.36\times10^{22}\ kg$, $r = 5390\ km=5.39\times10^{6}\ m$, and we need to solve for $m$.

Step2: Rearrange the formula for $m$

Starting from $F = G\frac{Mm}{r^{2}}$, we can solve for $m$: [m=\frac{F\times r^{2}}{G\times M}]

Step3: Substitute the given values

Substitute $F = 8310\ N$, $G = 6.67\times10^{-11}\ m^{3}\ kg^{-1}\ s^{-2}$, $M = 7.36\times10^{22}\ kg$, and $r = 5.39\times10^{6}\ m$ into the formula for $m$: [m=\frac{8310\times(5.39\times10^{6})^{2}}{6.67\times10^{-11}\times7.36\times10^{22}}] First, calculate $(5.39\times10^{6})^{2}=5.39^{2}\times10^{12}=29.0521\times10^{12}$. Then, $8310\times29.0521\times10^{12}=8310\times2.90521\times10^{13}=241422.951\times10^{13}=2.41422951\times10^{18}$. Next, $6.67\times10^{-11}\times7.36\times10^{22}=6.67\times7.36\times10^{-11 + 22}=49.1912\times10^{11}=4.91912\times10^{12}$. Finally, $m=\frac{2.41422951\times10^{18}}{4.91912\times10^{12}}\approx4.91\times10^{5}\ kg$.

Answer:

$4.91\times10^{5}$