the gravitational force between a satellite and earths moon is 324 n. the mass of the moon is 7.3×10²² kg…

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the gravitational force, $G = 6.67\times10^{- 11}\ N\cdot m^2/kg^2$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. Let the mass of the moon be $m_1 = 7.3\times10^{22}\ kg$, the mass of the satellite be $m_2$, the distance between the moon and the satellite be $r = 2.6\times10^{6}\ m$, and the gravitational force $F = 324\ N$. We can re - arrange the formula to solve for $m_2$: $m_2=\frac{F\times r^{2}}{G\times m_1}$.

Step2: Substitute the values

Substitute $F = 324\ N$, $r = 2.6\times10^{6}\ m$, $G = 6.67\times10^{-11}\ N\cdot m^2/kg^2$, and $m_1 = 7.3\times10^{22}\ kg$ into the formula: [ \begin{align*} m_2&=\frac{324\times(2.6\times10^{6})^{2}}{6.67\times10^{-11}\times7.3\times10^{22}}\ &=\frac{324\times6.76\times10^{12}}{6.67\times10^{-11}\times7.3\times10^{22}}\ &=\frac{324\times6.76\times10^{12}}{48.691\times10^{11}}\ &=\frac{2190.24\times10^{12}}{48.691\times10^{11}}\ &=\frac{2190.24}{48.691}\times10^{12 - 11}\ &\approx45\ kg \end{align*} ] The closest answer to our calculation is $450\ kg$ (there may be some approximation differences in the given options).

Answer:

$450\ kg$