No, because this process is so inefficient. Although the mass of every body includes the energy stored in
its gravitational field, the only way to get a body to loose energy
by gravity is by way of gravitational radiation. General Relativity theory says that gravity waves and radiation
are produced by accelerating the body. However, in order for a body
to lose mass this way, you need to accelerate the body enormously
because gravity waves are so weak. The acceleration felt by two dense neutron stars orbiting around
each other every minute at a distance of a few hundred kilometers
is the most extreme acceleration known. It is not very effective in
causing the bodies to loose much mass compared to the feeble mass
lost by the electromagnetic radiation leaving their surfaces.
For example, our sun emits 4x10^33 ergs/sec of electromagnetic energy.
From E=mc^2 this is equal to a mass loss of
4x10^33/(3x10^10)^2 = 4.4 million metric tons of mass every second. During its 4.5 billion years of life, it has lost
6.2x10^23 metric tons of mass...but its physical mass consists of 2x10^27 metric tons, so it has only lost
0.003 of its mass by radiation.
Gravity is even less efficient than this because the sun is only weakly being accelerated by its planets and the rest of the stars in the Milky Way.
Return to Dr. Odenwald's Gravity
page at the Astronomy Cafe Blog.