As far as I can make out, I used:

v

_{o} = √(m

^{2}G)/mr)

where v

_{o} is the orbital velocity, G is the gravitational constant, m is the mass and r is the radius, obtained from

http://en.wikipedia.org/wiki/Orbital_velocity#Mean_orbital_speedNote that I've omitted the second mass variable in that formula as the mass of the light is assumed to be zero.

The formula for the Schwarzchild radius from

http://en.wikipedia.org/wiki/Schwarzschild_radius#Formula_for_the_Schwarzschild_radiusis:

r

_{s} = 2Gm/c

^{2}so for an Earth sized mass of 5.9736 * 10

^{24} kg the Schwarzchild radius is:

= (2*6.67E-11*5.9736E+024) / (299792458

^{2})

= 7.97E+14 / 8.99E+16

= 0.00886647 metres i.e. just under 9 mm

and the orbital velocity for an Earth sized mass at a radius of 0.00886647 metres is

= √ ((5.9736E+024 * 5.9736E+024) * 6.67E-11) / (5.9736E+024 * 0.00886647)

= √ 2.38E+39 / 5.30E+22

= √ 4.49E+16

= 2.12E+8

which is < speed of light.

It seems that I originally did a spreadsheet to compare the orbital velocities for different masses and it turned out that the orbital velocity at the Schwarzchild radius is always 2.12E+8 for

any mass.

As always though, you'd better check my maths.