Contrast the solar system model of the atom with Schrodinger's Wave Equation. I wrote this so far: Schrodinger's Wave Equation is that the electrons move around the nucleus as a wave, while the solar system model has problems which are the accelerating electrons giving off light, leading them to spiral into the nucleus very quickly. I need 3 other facts integrated in my answer about either the solar system model or the Schrondinger wave equation.

The solar system model of an atom, usually called the "planetary" model, describes an atom as composed of a single positively charged nucleus and several electrons. The electrons orbit around the nucleus similarly to the planets of the solar system orbiting the Sun, hence the name "planetary." It is important to note that the number of the electrons is such that their total negative charge exactly equals the positive charge of the nucleus, so the atom as a whole is electrically neutral. Also, note that the size of the nucleus is about hundred thousand times smaller than the distance between the nucleus and the orbiting electrons, so the atom itself is mostly filled with empty space (the volume taken up by the electrons is negligible).
This model of an atom works well for some applications, but it is not consistent with the classical theory of electromagnetism. As you have pointed out, the electrons that undergo circular motion around the nucleus are accelerating (because they are constantly changing their velocity), so they will radiate or emit light. This light will carry off their energy, so they will eventually slow down. If the speed of an electron decreases, the radius of its orbit also has to decrease. As a result, the electron will "fall" into the nucleus, and the atom will collapse.
This, of course, does not happen (because then matter as we know it would not exist!) but the classical mechanics of electromagnetism cannot explain the structure of the atom. A different theory, known as quantum mechanics, is needed to explain why the electrons have stable orbits. The Schrodinger equation is the central equation of quantum mechanics. In this theory, each particle, including an electron, is modeled as a wave. The position of each electron at a given moment of time is not known precisely, but it is described as a probability function, called a wave function.These wave functions are characterized by certain integer numbers (called quantum numbers) that describe the energy of the electrons, and each number is associated with what traditionally would be the orbit. (There is an orbit for n = 1, an orbit for n = 2, and so on. The energy of the electron in each orbit depends on n.) In a quantum mechanical model, each electron forms a wave around the nucleus, in the sense that there is a probability that it can be found at a given place on the "orbit" (keep in mind that there is no actual wave-like motion going on). 
Please see the linked article that summarizes the atomic models and discusses the history of the development of the atomic theory.
http://www.abcte.org/files/previews/chemistry/s1_p6.html