I'd like to ignore neutrons for a moment as the more I'm thinking about it the more it seems that it's not necessary to know their nature in order to humor this theory.
Now I don't know if anyone has measured or even knows how to measure the electrical charge of the earth. From what I understand about it's construction though is that it's made up 3 distinct layers, becoming more dense towards the core. Now what if in one of the layers predominately there is some kind of mass (which I think most scientists agree with this theory and that it is comprised mostly of nickel) with a sizable positive or negative charge? A huge mass of anything, with even a slight charge (compared to its size) would undoubtedly attract us as if we were just small bits of paper or tiny metal shavings.
There are a number of problems with this idea.
When you see small bits sticking to an object it is because some of the electrons of the
surface atoms of the object have been removed, and thus the electrons which surround the nuclei of the outer atoms of the pieces of paper are attracted to them. The object and pieces of paper have to be very close for this to work. This is because the nuclei of the paper's atoms are repelled by the positively charged outer atoms of the object, so it is only when the electrons are much closer to the object than the nuclei that their attraction is enough to overcome the repulsion. What this means is that the net attraction falls off very very quickly as the distance between paper and object increases; much faster than the inverse square that we see with gravity. It also means that it only works if the outer part of the object is positively charged. If they where negatively charged (excess of electrons) they would repel the pieces of paper.
Secondly, It can't explain the mutual attraction between three or more objects.
For example, we have landed men and objects on the Moon where they "stuck" to the surface just like they do on Earth. This means that for your idea to be correct, the Moon would have to have a net positive charge like the Earth. But like charges repel so the Moon and Earth would repel each other and the Earth would not hold the Moon in orbit.
Another example is the famous Cavendish experiment where the attraction between brass spheres was measured. In your model either both spheres would have been attracted to the Earth and repelled by each other or the spheres would have been attracted to each other and one of them repelled by the Earth. Instead both spheres were attracted to each other and the Earth.
Third, it cannot account for the equivalence between gravitational mass and inertial mass. An object could be made heavier or lighter by just adding or removing some electrons. Since electrons constitute only a very small fraction of the mass of an object, there would be no connection between mass and weight. But every experiment done shows that weight and mass are linked.
Consider a vacuum and on one end there is a mass with one extra electron and on the other end a billion miles from it there is an electrically neutral mass. Let's say that there is no separate force of gravity in this universe. I think these two masses would collide over time. What do you think would happen?
If the electrically neutral object were truly neutral (not made up of a equal amount of positively and negatively charged parts) then there would be no attraction at all. If it was made up of such parts, then it would depend on how they where arranged. If it was made of atoms with outer electrons, then it would actually be slightly repelled. If it was made of a central negative mass surrounded by positive masses, then their would be a slight net attraction. However, this attraction would not follow the square of the distance law or be tied to the mass of the object like we see with gravity. There is just no way to make attraction by electrical charge act in an equivalent way to gravity.
