/sci/ - Science & Math

Why is the attraction between two electric charged object irrelevant at a Earth-Moon distance when gravity is not?

Suppose the following experiment:
>Rub a balloon with a cloth
>Put balloon near ceiling
>Balloon is attracted to ceiling and sticks to it, meaning electrostatic force is greater than Earth's force of gravity
>take the same balloon to space (distance between Earth and Moon)
>balloon doesn't get attracted towards that ceiling (electrostatic force is too little) anymore, but it still is under the influence of Earth's gravity and it will fall towards it.

Why that happens if both Coulomb's Law and the Gravitational Law are inversely proportional to the distance squared?

Consider that in the first part of the experiment,
F(electrostatic) > F(gravity)

being:
F(electrostatic) = (k*q1*q2)/(d^2)
F(gravity) = (G*m1*m2)/(d^2)

The numerator values on both formulas stays constant no matter if the balloon is close to the ceiling or at a Earth-Moon distance (meaning that k, q1, q2 and G, m1, m2 won't change). The only single parameter that differs is the distance in the denominator.

Why does integration feels so much harder than differentiation in most cases?