Answer:
[tex]M=2.84\times 10^{19}\ kg[/tex]
Explanation:
It is given that,
Radius of the circular path, r = 410 km = 410000 m
Speed of the planet X, v = 68 m/s
As the captain of a spaceship orbiting planet X, the centripetal force is balanced by the gravitational force between planet and the captain such that,
[tex]\dfrac{mv^2}{r}=\dfrac{GMm}{r^2}[/tex]
Where
M is the mass of planet X
m is the mass of planet
[tex]M=\dfrac{v^2 r}{G}[/tex]
[tex]M=\dfrac{(68)^2 \times 410000}{6.67\times 10^{-11}}[/tex]
[tex]M=2.84\times 10^{19}\ kg[/tex]
So, the mass of planet X is [tex]2.84\times 10^{19}\ kg[/tex]. Hence, this is the required solution.
