Well first of all, since the question deals with the relationship of Charon and Pluto, we don't care about their distance from the sun, because that has no effect on the gravitational forces between them.
All we need is Newton's law of universal gravitation:
Gravitational forces = G m₁ m₂ / D² .
' G ' is the gravitational constant ... 6.67 x 10⁻¹¹ newt-m²/kg²
m₁ = either one of the masses ... 1.31 x 10²² kg (Pluto)
m₂ = the other mass ... 1.55 x 10²¹ kg (Charon)
D = the distance between their centers ... 1.96 x 10⁷ meters
Gravitational forces = G m₁ m₂ / D²
= (6.67 x 10⁻¹¹ newt-m²/kg²)
times (1.31 x 10²² kg) times (1.55 x 10²¹ kg)
divided by (1.96 x 10⁷ meters)²
= (6.67 x 1.31 x 1.55 x 10⁻¹¹ ⁺ ²² ⁺ ²¹ ⁻ ¹⁴) / (1.96)²
= (13.54 x 10¹⁸) / (3.84) = 3.53 x 10¹⁸ newtons .
This is the gravitational force of attraction that Pluto exerts
on Charon. It's also the gravitational force of attraction that
Charon exerts on Pluto. The gravitational forces are always
equal and opposite.
