In this article it says:
The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics. The Bohr model of an atom was based upon Planck's quantum theory of radiation.
My question is: how can this be if it is actually impossible? Any accelerating point charge should emit radiation, as explained here, for example. It is not like I can posit the existence of an orbit where the electron is stable, just out of mid air. What am I missing here?