Answer
Yes, the speed of a satellite in circular orbit around a planet depends on the mass of the planet.
Work Step by Step
Yes, the speed of a satellite in circular orbit around a planet depends on the mass of the planet.
We can find the gravitational force on the satellite:
$F_g = \frac{G~M_p~M_s}{r^2}$
We can find the centripetal force on the satellite:
$F_c = \frac{M_s~v^2}{r}$
Since the centripetal force is provided by the gravitational force, we can equate the two force equations:
$F_g = F_c$
$\frac{G~M_p~M_s}{r^2} = \frac{M_s~v^2}{r}$
$\frac{G~M_p}{r^2} = \frac{v^2}{r}$
$v^2 = \frac{G~M_p}{r}$
$v = \sqrt{\frac{G~M_p}{r}}$
We can see that the satellite's speed depends on the mass of the planet.
