the gravitational force between pluto and charon is 3.61×10^18 n. pluto has a mass of 1.3×10^22 kg, which is…

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. We need to solve for $r$. First, we can re - arrange the formula for $r$: $r^2=G\frac{m_1m_2}{F}$, so $r=\sqrt{G\frac{m_1m_2}{F}}$.

Step2: Substitute the given values

Given $F = 3.61\times10^{18}\ N$, $m_1 = 1.3\times10^{22}\ kg$, $m_2 = 1.6\times10^{21}\ kg$, and $G = 6.67\times10^{-11}\ N\cdot m^2/kg^2$. Substitute these values into the formula for $r$: [ \begin{align*} r&=\sqrt{\frac{6.67\times 10^{-11}\times(1.3\times 10^{22})\times(1.6\times 10^{21})}{3.61\times 10^{18}}}\ &=\sqrt{\frac{6.67\times1.3\times1.6\times10^{-11 + 22+21}}{3.61\times 10^{18}}}\ &=\sqrt{\frac{6.67\times1.3\times1.6\times10^{32}}{3.61\times 10^{18}}}\ &=\sqrt{\frac{6.67\times1.3\times1.6}{3.61}\times10^{32 - 18}}\ &=\sqrt{\frac{13.8176}{3.61}\times10^{14}}\ &=\sqrt{3.83\times10^{14}}\ &\approx2.0\times 10^{7}\ m \end{align*} ]

Answer:

A. $2.0\times 10^{7}\ m$