Why do planets not radiate EM waves in their orbits?

Despite being overall near-netural, I would expect the individual electrons and proton to radiate long EM waves as we accelerate around the Sun or rotate around our poles. Is the acceleration so small that the radiated energy is miniscule?

Or is it that somehow the macroscopic neutrality prevent radiation? If this is so, what mechanism causes single electrons or nuclei to fail to radiate?

• The acceleration is too small. – velut luna Jul 10 '16 at 4:12
• See, now you given me my favorite soap box: in all the quantitative science scale matters. No one talks about such radiations, not because it doesn't happen but because the expected size of the effect is so vanishingly small that there isn't a hope of even detecting it. This is the kind of problem for which a physicist would first and foremost do a back-of-the-envelope estimate. Then they'd drop the whole thing as a non-issue. – dmckee Jul 10 '16 at 4:34
• Moving in space around a massive body do you feel a acceleration? Of course not and such a movement Is called a geodesic trajectory. Since the attribute acceleration is not applicable to the movement on geodesic paths it is arbitrary emit a particle EM radiation or not. BUT if it emit the particle has to move on a spiral path towards the massive body because it looses energy. What predicted Einsteins GR theory, is the room more bended near massive bodies than Newtons classical theory? If yes this can be an indication that a particle indeed emit EM radiation on geodesic paths – HolgerFiedler Jul 10 '16 at 6:21

The power radiated by a charged particle moving at non relativistic speeds, whose acceleration is $a$ and charge is $q$, is given by the Larmor Formula $$P =\frac{2q^2a^2K}{3c^3}.$$ The product above is nowhere near $c^3$ for planetary motion and hence the radiation emitted is negligibly small.