system
Given the following post, respond as if you're commenting on Reddit:
human
Since electromagnetism is so much stronger than gravity, why doesn't it have more of an effect on large celestial bodies?

Since bodies like Earth, Jupiter and the Sun all have powerful magnetic fields, why do we not see the orbits of large bodies shifted by the magnetic fields of one another? Indeed, *do* we see this at all?

After all, even a tiny magnet can defy the gravity of an entire planet by lifting a kilogram weight off a table, and an  electromagnet in a scrap yard can lift an entire car. Why, then, does this apparently-more-powerful force not propagate out into space more effectively than gravity?
gpt
Excellent question. The fundamental reason is because there is no such thing as negative mass. Let me explain. Electric charge can come either as positive or negative, and opposites attract. This means that free positive charges will tend to attract free negative charges until they bind to form neutral atoms and molecules (or more exotic composite objects). When bound together, the electric and positive charge are so close to each other that for the most part they cancel each other's effects. To a first approximation, a system with an equal amount of positive and negative electric charge acts like an electric dipole. The electric field of an electric dipole dies off with distance according to 1/r^3 . In contrast, the electric field of a bare electric charge dies off with distance according to 1/r^2 . On astronomical scales, r is huge, so that that the electric field due to a dipole (and by an extension, a neutral molecule) is far weaker than the electric field due to a bare charge. Since opposites attract, most of the electric charge on a planet is bound up in neutral atoms/molecules. For molecules that have a weak dipole moment, the electric field falls off even faster than 1/r^3 . The situation is even worse for magnets. Magnetic poles *always* come in pairs, so that the magnetic field of a magnetic object always dies off as 1/r^3 or faster (as long as you are sufficiently external to the object - inside magnetic objects/systems you can get all sorts of fields).

Now let's turn to gravity. Since there is no negative mass, there is nothing to partially cancel the gravitational field of positive mass. Therefore, the strength of gravity of a localized mass always dies off dominantly as 1/r^2. 

In summary, electromagnetism is stronger than gravity, and they both fundamentally die off with distance at the same rate (1/r^2 ), but due to the existence of negative charges/South magnetic poles and not negative mass, in most practical situations, electromagnetic fields die off much quicker with distance than gravity. The distances involved on astronomical scales are so large that gravity dominates. 

In principle, if we could make an entire planet out of just electrons (if we found someway to turn off their mutual repulsion), the electric field of this planet on astronomical scales would be immensely strong, far stronger than gravity.