hi sammys,
thanks for the warm welcome
f_g = g*m_1*m_2/r^2 (law of gravitation)
v = sqrt(g*m/r) (circular orbit)
v = 2*pi*r/t
t = 2*pi*r/v = 2*pi*r*sqrt(r/(g*m)) = 2*pi*r^(3/2)/sqrt(g*m) (circular orbit)
g is the gravitational constant 6.67e-11 m^3*kg^-1*s^-2
titan, a moon of saturn, has a 16 day orbital period and an orbital radius of 1,222,000 km. what is the mass of saturn?
my attempt:
t = 2*pi*r^(3/2)/sqrt(g*m)
t = 16 days = 1,382,400 s
r = 1,222,000/2 km = 611,000,000 m
1,382,400 = 2*pi*611,000,000^(3/2)/sqrt(6.67e-11*m) => m =...