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

Answer:

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

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, $G = 6.67\times 10^{- 11}\text{ N}\cdot\text{m}^{2}/\text{kg}^{2}$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

Step2: Rearrange the formula for $r$

From $F = G\frac{m_1m_2}{r^{2}}$, we can get $r^{2}=G\frac{m_1m_2}{F}$, and then $r=\sqrt{G\frac{m_1m_2}{F}}$.

Step3: Substitute the given values

Given $F = 3.61\times 10^{18}\text{ N}$, $m_1 = 1.3\times 10^{22}\text{ kg}$, $m_2 = 1.6\times 10^{21}\text{ kg}$, and $G = 6.67\times 10^{-11}\text{ N}\cdot\text{m}^{2}/\text{kg}^{2}$. First, calculate $m_1m_2=(1.3\times 10^{22})\times(1.6\times 10^{21}) = 2.08\times 10^{43}\text{ kg}^2$. Then, $G\frac{m_1m_2}{F}=\frac{6.67\times 10^{-11}\times2.08\times 10^{43}}{3.61\times 10^{18}}$. $6.67\times 10^{-11}\times2.08\times 10^{43}=6.67\times2.08\times 10^{-11 + 43}=13.8736\times 10^{32}=1.38736\times 10^{33}$. $\frac{1.38736\times 10^{33}}{3.61\times 10^{18}}=\frac{1.38736}{3.61}\times10^{33 - 18}\approx0.3843\times 10^{15}=3.843\times 10^{14}$. $r=\sqrt{3.843\times 10^{14}}\approx2.0\times 10^{7}\text{ m}$.