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v7	v8
18	18	To get a handle of the resolution where this approximation may break down, I made a few tables of error for some different scenarios. In what follows recall that the kinetic energy at r which would have been acquired from freefall alone is just GM/r.
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20		First, let's consider ke(r) > GM/r. This corresponds to the upper plot. In this plot, the accretion energy (per unit mass) for a freely falling particle from infinity, GM/R, is normalized to 1 and lies exactly on top of the x-axis. This plot shows that particles falling in from r with ke(r) > GM/r, would produce stronger accretion energy than those which would have fallen in from freefall alone. As the speed increases, they would produce greater and greater accretion energies. I am next going to solve the following equations for r given various ke(r)>GM/r at the .01% error level and the 30% level,
	20	First, let's consider ke(r) > GM/r. This corresponds to the upper plot. In this plot, the accretion energy (per unit mass) for a freely falling particle from infinity, GM/R, is normalized to 1 and lies exactly on top of the x-axis. This plot shows that particles falling in from r with ke(r) > GM/r, would produce stronger accretion energy than those which would have fallen in from freefall alone. As the speed increases, they would produce greater and greater accretion energies. I am next going to solve the following equations for r given various ke(r)>GM/r at the .01% error level and the 30% error level,
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