Equation (17.26) describes the coordinate speed of a massive particle orbiting a nonrotating black hole. However, it can be shown that the orbit is not stable unless r≥3RS; any disturbance will cause a particle in a smaller orbit to spiral down to the event horizon.
(a) Find the coordinate speed of a particle in the smallest stable orbit around a 10M⊙ black hole.
(b) Find the orbital period (in coordinate time t) for this smallest stable orbit around a 10M⊙ black hole.