The gravitational force between pluto and charon is 3.61 × 1018 n. pluto has a mass of 1.3 × 1022 kg, which is only slightly greater than charon’s mass of 1.6 × 1021 kg.

how far apart are pluto and charon?

2.0 × 107 m
2.4 × 1012 m
3.8 × 1014 m
5.8 × 1024 m

From Newtons law of gravitation we know that the force of gravity between two bodies Fg is Fg=(G*M*m)/r², where G is the gravitational constant, G=6.67*10^-11 m³/(kg s²), M and m are masses and r is the distance between those masses. So to get the distance we need to solve for r:

r²=(G*M*m)/Fg

and when we take the square root:

f=√{(G*M*m)/Fg}.

We input the numbers and get: r=19603832.5 m or in scientific notation: 

r=1.96*10^7 m. So the correct answer is the first one: 2*10^7 m.