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 km

D 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.