 There's a really direct analogy between the Rutherford model for the atom and planetary motion. Having a large planet with moons going around it, mutually attracted by gravity, is very similar to having a large nucleus with electrons going around it, mutually attracted by electromagnetism. Indeed, the strength of a electromagnetic attraction between a positive charge and negative charge goes down this distance squared, just like gravity does. If we try and model the simplest possible atom, we'd have the hydrogen atom, which is simple because it has one positively charged nucleus, and just one electron. So if we imagine that as going around in a circular orbit, then we already know enough to model that orbit. So if we have a radius R, then we know the strength of the attraction between these two charges, it's going to be proportional to each charge. The charge of the electron is just E. The charge on the nucleus is going to be equal and opposite, and we know it's going to be attractive because we've got one positive and one negative, so it's in that direction. And we know it's going to be inversely proportional to the radius squared. And we know what that force is going to do. That force is going to accelerate our electron. Why is our electron having to accelerate? Because it's going around in a circle. If it wasn't accelerating, it would go in a straight line. And we know that if the electron is traveling at velocity V, then the acceleration to make it go around in a circle has to be exactly equal to V squared on R. So the centripetal acceleration is V squared on R, and that acceleration has to be provided by our force. And we know from Newton's Laws that the force is mass times acceleration, and we know from the electromagnetism how strong the force is. What we have is a relationship between the velocity and the radius. We can see that the smaller the radius, the faster electrons go around. It sounds like we're doing a really good job, except we've got a really big problem here, and that problem is this. If you have an accelerating charge, it gives off radiation. So an accelerating charge will give off electromagnetic radiation, which will cause it to lose energy. If it loses energy, then it's going to fall down the potential well, which is the attraction between these two charges. And as it does so, it will speed up. So some of that energy will go into kinetic energy, and some of that energy will go off into light. And what will happen is that will just keep on going. And so the electron would spiral into the nucleus until they collide, and it'll be run out of energy. In other words, if this model were true, atoms wouldn't exist. So all atoms would be unstable in this way. And there'd be a clear signature, because as the electron spiraled into the middle, it would get faster and faster. And so the frequency of the radiation emitted would go up and up. And so it would start off at a low frequency, and then it would chirp up, up, up, up, up, up, up, up. And it's exactly that chirping signal in the emitted radiation that was used to detect gravity waves in 2015. Now in that case, it was two enormous masses larger than our sun spiraling in together after billions of years of slowly emitting gravitational waves to lose energy. But in the case of atoms, that decay process was so fast, that there must be something wrong with the theory.