Question

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?

a.2.0 × 107 m
b.2.4 × 1012 m
c.3.8 × 1014 m
d.5.8 × 1024 m

Answer 1

Gravitational force:
F = G * m1 * m2 / r²
And gravitational constant: G = 6.67 * 10^(-11) m³/kgs²
Therefore:
r = sqrt ( G * m1 * m2 / F ) =
= sqrt ( 6.67 * 10^(-11) m³/kgs² * 1.3 * 10^(22) kg * 1.6 * 10^(21) / 3.61 * 10^(18) N ) =
= sqrt ( 3.84 * 10^(14) ) = 1.96 * 10^(7) m ≈ 2 * 10^(7) m
Answer:
A ) 2.0 * 10^(7) m