Re: greater affects?
1) This mass is so small that any General Relativity gravitational effects are totally swamped by gravitational noise your St Bernard dog creates when moving around the house. Indeed, we can use Newtonian gravity to get good results about trajectories of the N-body system under analysis.
2) "Gravitational waves" are very weak (Directly from Jimbo's Dubious Font Of Knowledge: If we use the previous values for the Sun and the Earth, we find that the Earth's orbit shrinks by 1.1×10^−20 meter per second. This is 3.5×10^−13 m per year, which is about 1/300 the diameter of a hydrogen atom. The effect of gravitational radiation on the size of the Earth's orbit is negligible over the age of the universe.). They also propagate at lightspeed, so are soon gone.