  We study real time dynamics of a Dp-brane orbiting a stack of NS5-branes. It
is generally known that a BPS D-brane moving in the vicinity of NS5-branes
becomes unstable due to the presence of tachyonic degree of freedom induced on
the D-brane. Indeed, the D-brane necessarily falls into the fivebranes due to
gravitational attraction and eventually collapses into a pressureless fluid.
Such a decay of the D-brane is known to be closely related to the rolling
tachyon problem. In this paper we show that in special cases the decay of
D-brane caused by gravitational attraction can be avoided. Namely for certain
values of energy and angular momentum the D-brane orbits around the fivebranes,
maintaining certain distance from the fivebranes all the time, and the process
of tachyon condensation is suppressed. We show that the tachyonic degree of
freedom induced on such a D-brane really disappears and the brane returns to a
stable D-brane.
