Marginally Stable Circular Orbits in Schwarzschild Black Hole Surrounded by Quintessence Matter

Marginally stable circular orbits (MSCOs) of a massive test particle are investigated in the spacetime geometry of Schwarzschild black hole surrounded by quintessence. For that matter we consider three important scenarios where the equation of state parameter ${\omega }_q$, has one of the following forms (i) ${\omega }_q=-1$ (ii) ${\omega }_q=-2\mathrm{/}3$ and (iii) ${\omega }_q=-1\mathrm{/}3$. The existence of such marginally stable circular orbits in these scenarios depend on the range of normalization factor $\alpha$. Briefly, we show that in the first case such orbits exist only if $0<\alpha <4\mathrm{/}16875$. Moreover in the second case which is a special Kiselev black hole it is found that MSCOs exist when the value of the normalization factor satisfy $0<\alpha \le 0.00536165238$. In the last case the MSCOs are also shown to exist.