Answer:
[tex]M = \frac{R^3 \times \omega^2}{G}[/tex]
M is mass of pluto
Explanation:
we know that gravitational force between moon and Pluto can be derived by using the given relation
[tex]F_{gravitational} = \frac{GMm}{r^2}[/tex]
here
G-gravitational constant =[tex] 6.67408 \times 10^{-11} m^3 kg^{-1} s^{-2}[/tex]
M- mass of pluto
m - mass of moon [tex]= 7.34767309 \times 10^{22} kg[/tex]
r - radius of moon - 1737.1 km
F_{gravitational} = centripetal force [tex]= \frac{m v^2}{R}[/tex]
where [tex]v = \omega \times r[/tex]
[tex]\omega[/tex] - angular speed of moon [tex]= 2.7 \times 10^{-6} /s[/tex]
plugging all value in the above equation to get the mass of Pluto
[tex] \frac{m (\omega\times r)^2}{R} = \frac{GMm}{r^2}[/tex]
[tex]M = \frac{R^3 \times \omega^2}{G}[/tex]
M is mass of pluto
