Gravitational Orbit Decay

So the detection of gravitational waves was announced yesterday. Its quite an amazing detection and will usher in a new age of astronomy. The waves were detected from the collision of two black holes, as they spiraled in towards each other they emitted the energy equivalent of about 3 solar masses of gravitational radiation. We know that black holes and neutron stars in binary systems will one day spiral inwards and undergo a collision, but what about our solar system? Obviously the solar system's lifetime will not permit any planet or satellite of a planet to undergo orbital decay from gravitational forces. The lifetime of our solar system is on the order of 10 billion years. However, what if the Sun was a black hole and we ignored any external forces, how long would it take some of the planets to undergo gravitational orbital decay? From Einstein's field equations we can get an simple formula that predicts how long it takes for a two body system to collide. I calculated the lifetime of the orbits of Mercury, Venus and Earth as well as the power Each planet emits due to gravitational radiation. Currently the Earth emits just 200W of gravitational radiation compared to the 200 PW (Petawatts 10^15) which is emitted in the form of electromagnetic radiation. 

Orbital time decay and gravitational radiation radiated

Another note is that Mercury and Venus will cross paths likely leading to a collision with each other before they spiral into the Sun. But the most astounding aspect of this is the gargantuan timescales. The horizontal axis is in the order of trillions of billions of years. Basically for the Earth to collide with the Sun the equivalent time of the current age of the universe must pass a quadrillion times. Needless to say this is not going to happen, the only element stable enough in these timescales is Tellurium-128, which has a half life of 2.2*10^24 years. About 22x longer than the orbital decay timescale of the Earth.  This was an interesting calculation, got to see how weak gravity really is.