Once upon a time in the land of Bohr's atom, scientists tried to explain electrons floating around the nucleus and came up with the magical faerie tale of orbitals. Orbitals are on par with medieval Christian medicine; that is, the physicians explained ailments in terms of demons, curses and sin. Sometimes the physicians got lucky with the diagnosis and treatment, but there was no concrete method to prove when they were wrong, it was just the sinner's disbelief that killed them, not a misdiagnosis. You have just got to love absolute truths. Orbitals are one of those truths.
Orbitals are a faerie tale. A story. A guess. An educated guess perhaps, but a guess all the same. When you describe something as being "90% likely to be located someplace in this region" you are guessing, just like medieval physicians did. They based their guess work on the religion of the Christian God; modern scientists base their guess work on one incorrect theory, which in turn grew to hundreds and thousands of incorrect theories. Or at least, incorrectly based theories.
Let's put a little truth back into those theories. For simplicity's sake we are only going to talk about the "original three" subatomic particles: electrons, protons and neutrons. The remainder of the particles actually fall in line and make much more sense with what I am going to point out. Ready then?
Electron's move in logical, predictable orbits around the nucleus of an atom.
Bold and brash, right? Wrong. Here's the simple understanding of it all.
1) Electrons are influenced by the positive-to-negative electromagnetic pull of the nucleus of the atom. Given this, an electron should get sucked into and become part of the nucleus of the atom (this is why physicists first started to make stuff up).
2) The distance between the source of a given force and an object the force is acting upon changes the strength of that force. Meaning an electron located in North Carolina is not going to get sucked into the nucleus of an atom located in Virginia. Still means that electron is going to get sucked into its own nucleus though.
3) Enter my Hypothesis (I'm about ready to do a nice write up to move this officially to a theory, as well as a slight rewrite to bring it more inline with scientific wording): The faster an object is moving relative to a source of energy/force, the less influence said force exerts upon the object.
You can read my initial write-up entitled Classical Mechanics Rule
to see how this affects an electron. Basically, electrons move too damn fast to allow the electromagnetic pull of the protons to suck it into the nucleus; instead the force gets reduced thanks to the electron's speed and a stable orbit is created.
Based on this first part, a hydrogen atom in a complete void would have an orbital pattern that looks exactly like what everyone thinks an orbit should look like. There is even a mathematical formula for this orbital pattern, because it is the same mathematical formula for any circular orbit. Of course, not all atoms are hydrogen atoms and none reside in a complete void, nor are all hydrogen atoms simple one proton nucleus atoms. This is where things really are complicated. If only there was a mathematical formula that could accurately describe that complicated orbit just as well as one describing a circular orbit, but surely if there was such a mathematical formula someone would have come up with it by now (and won a Nobel Prize as a result).
The good news is there is one. The even better news is that, to my knowledge, no one has won a Nobel Prize for it yet. There might have been, and I just missed it, but given that the world is still using (and teaching) quantum physics, I am fairly certain that no one has released said formula. What is the mathematical formula then? I don't know. Crap, so much for that Nobel Prize.
Alright, that is partially a lie or I wouldn't be bothering to write up an entry about all this. I know almost all the pieces of the formula, or rather I know what all the pieces are and the mathematical formulas for most of those pieces. Being a nice person, and thinking science should be expanded for sciences sake, here are the components that make up the mathematical formula of a stable orbit (planets, electrons, black hole event horizons, etc):
1. The mathematical formula for a standard orbit (Trigonometry, baby).
2. The mathematical formula for force applied based upon distance (available in Physics or Chemistry books incase you don't know it by heart).
3. The mathematical formula for force applied based upon speed (yea, this is the missing one, but can actually be easily figured out. Heck, someone might actually know it already, but if not, there are simple experiments).
4. The mathematical formula for force applied to an object through specific barriers (neutrons are a barrier, as are certain solar phenomena).
5. The constant values of each force for each object.
6. The speed of each object.
Pretty simple right? Number five is a "gotcha" in that not only does a proton pull on an electron and a star pull on a planet, but electrons repel one another and planets have gravitational forces of their own. Number six is an easy one, except when additional energy is applied, but that can be factored in; we do after all know the speed of an electron in a vacuum, and, well, between the electron and the nucleus is a vacuum (pretty clever).
When you throw all this together you can model a complete, stable orbital system. Sooner or later I will get around to producing this formula in its entirety. Of course this will require all the textbooks to be rewritten as well as many of the existing theories (like, because I mentioned them previously, a ton of the stuff on black holes), but that is what science is all about. Change based on new information, and currently the new information is that Orbitals do not exist. Do the math and you will agree.