Do bodies radiate energy by emitting gravitons? As gravitons are formulated in current theories, are bodies supposed to radiate energy as they emit gravitons?
I thought that if bodies radiate energy, for big bodies this would be difficult to measure, as they emit a lot more energy in the form of heath, and smaller bodies in their orbits would get the energy back by feeling the gravity of the big ones. But what would happen to a small shard of ice projected by a collision between comets far from the gravitational pull of any star? Is it supposed to evaporate?
Furthermore let's suppose we have a sphere of a very dense material, it is attached to a probe, but by a long arm, so long that the gravity radiated by the probe reaching the sphere is far less than the gravity radiated by the sphere. Let's suppose that the probe is travelling along the path of the pioneer far away from the sun. At a certain point the sphere could radiate more gravity than it receives, should there be any detectable effect?
 A: Yes bodies radiating gravitons do radiate energy. That's why we were able to detect gravitational waves a few years ago, as you can see from the Wikipedia article on gravitational waves:

On 11 February 2016, the LIGO collaboration announced the first observation of gravitational waves, from a signal detected at 09:50:45 GMT on 14 September 2015 of two black holes with masses of 29 and 36 solar masses merging about 1.3 billion light-years away. During the final fraction of a second of the merger, it released more than 50 times the power of all the stars in the observable universe combined. The signal increased in frequency from 35 to 250 Hz over 10 cycles (5 orbits) as it rose in strength for a period of 0.2 second. The mass of the new merged black hole was 62 solar masses. Energy equivalent to three solar masses was emitted as gravitational waves.

However simply existing will not radiate gravitational waves; you need to accelerate, and in the situations you describe there is no acceleration.
