I was always taught that any accelerating charge produces radiation, but I don't think this condition is sufficient condition. For instance, any free charge on Earth is accelerated due to Earth orbiting the Sun but it doesn't produce radiation.
In fact, an electric charge at rest on the Earth's surface is accelerated and this actually poses a challenge to the idea that uniformly accelerated charge radiates. I believe this is still an open question. For example:
One of the most familiar propositions of elementary classical electrodynamics is that "an accelerating charge radiates". In fact, the power (energy per time) of electromagnetic radiation emitted by a charged particle is often said to be strictly a function of the acceleration of that particle. However, if we accept the strong Equivalence Principle (i.e., the equivalence between gravity and acceleration), the simple idea that radiation is a function of acceleration becomes problematic, because in this context an object can be both stationary and accelerating. For example, a charged object at rest on the Earth's surface is stationary, and yet it's also subject to a (gravitational) acceleration of about 9.8 m/sec2. It seems safe to say (and it is evidently a matter of fact) that such an object does not radiate electromagnetic energy, at least from the point of view of co-stationary observers. If it did, we would have a perpetual source of free energy. Since the upward force holding the object in place at the Earth's surface does not act through any distance, the work done by this force is zero. Therefore, no energy is being put into the object, so if the object is radiating electromagnetic energy (and assuming the internal energy of the object remains constant) we have a violation of energy conservation.
A paper here proposes that uniformly accelerated charge does radiate but that the radiation is "beyond the horizon" for co-moving observers.
We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.
The charge accelerated by the Earth gravity does not emit any radiation,follows from transforming to a frame of reference in which the charge is stationary and applying relativistic requirement that the behavior of the charge including whether or not it radiates,cannot depend on the frame of reference from which it is viewed.