Phobos, the larger of Marsβ two moons, orbits 5.99Γ10 3 km above the planet surface.
Given that the mass of Mars is 6.42Γ10 23 kg and the radius of Mars is 3.39Γ10 3 km, what are
the orbital speed and period of Phobos?
1
Expert's answer
2020-05-12T09:57:02-0400
Let denote the height at which Phobos is revolving from the surface of the Mars h .Radius of Mars is R, mass of Mars and Phobos are M&m respectively,v is the orbital velocity of Phobos and T is the orbital period of Phobos.
Now, we know that from Newton's law of Gravitation, The gravitational force(centripetal force)of Mars is the only force which responsible for revolution of Phobos around Mars,thus
Force between Mars and Phobos is
F=G(R+h)2Mmβ(1)
where, R+h is the distance from center of Mars to Phobos.hence, the same force F can also be written as
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