Suppose that another moon is discovered orbiting jupiter once 300 days. which of the following values would best estimation of its average distance from jupiter? a 1.30×10^7 km b 1.30×10^4 km c 1.30×10^6 kmd 1.30×10^5 km

The circular force = m*v^2/r
The Gravitation force between Jupiter (mj in this question) = G * m1 * m2/r^2
G = 6.67 * 10^-11
v = 2*pi*r / time
mass jupiter = m2 = mj = 1.898 * 10^27 (wouldn't want to meet the dude in a dark alley).
time = 300 days * 24 hours / day * 3600 seconds / hour
time = 25920000 seconds.
These two forces are equal (Fg = Fc)
.
v = 6.28 * r /2592000
The mass of the sattelite does not matter. It is the same on both sides of the equation.  

m1 v^/r = G*m1*m2 / r^2 multiply both sides by r and cancel out m1
v^2 = G mj / r 
(6.28 * r)^2 * r = 6.67 * 10^-11 * 1.898 * 10^27 * (25920000)^2
39.4 * r^3 = 8.51 * 10^31
r^3 = 8.51 * 10^31/39.4
r^3 = 2.1587 * 10^30 meters. 
r = cube root (2.1587 * 10^30)
r = 1.292 * 10^10 meters which is 1.292 * 10^7 km
The closest answer is A.

No wonder it took so long to get an answer.