A planet in circular orbit around a star is a stable system. No energy change takes place. With an elliptical orbit, there is some interchange between potential and kinetic energy, but the total is conserved. A satellite orbiting earth has some atmosphere to deal with, so their orbits decay.

An electron orbiting a nucleus has no atmosphere to deal with. However, the time-varying electric field associated with its motion should induce a magnetic field, and result in energy being lost to the emitted electromagnetic wave. But now add the quantum constraint that the length of the orbit must be an integral multiple of the wavelength of the electron's wavefunction. That means the orbit can't experience continuous decay. Instead, an electron can drop from a higher energy orbit to a lower one, emitting in the process a photon whose energy is the energy difference between the two orbits. This accounts for the discrete emission spectrum of elements.

Exactly what happens while the electron is 'waiting' to drop to that lower energy orbit is beyond my understanding of quantum mechanics.A planet in circular orbit around a star is a stable system. No energy change takes place. With an elliptical orbit, there is some interchange between potential and kinetic energy, but the total is conserved. A satellite orbiting earth has some atmosphere to deal with, so their orbits decay.

An electron orbiting a nucleus has no atmosphere to deal with. However, the time-varying electric field associated with its motion should induce a magnetic field, and result in energy being lost to the emitted electromagnetic wave. But now add the quantum constraint that the length of the orbit must be an integral multiple of the wavelength of the electron's wavefunction. That means the orbit can't experience continuous decay. Instead, an electron can drop from a higher energy orbit to a lower one, emitting in the process a photon whose energy is the energy difference between the two orbits. This accounts for the discrete emission spectrum of elements.

Exactly what happens while the electron is 'waiting' to drop to that lower energy orbit is beyond my understanding of quantum mechanics.