Consider two planets of mass m and 2m,
respectively, orbiting the same star in circular
orbits. the more massive planet is 4.5 times
as far from the star as the less massive one.
what is the ratio f1 : f2 of the gravita-
tional forces exerted on the star by the two
planets?
what is the ratio v1 : v2 of the speeds of the
two planets?
what is the ratio t1 : t2 of the orbital periods
of the two planets?

Part a)

Part b)

Part c)

Explanation:

Part a)

As we know that the gravitational force is given as

so we will have to find the ratio of force on two planets due to star

so here we have

Part b)

Orbital speed is given as

so the ratio of two orbital speed is given as

Part c)

Time period is given as

so the ratio of two time period is given as

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the force on the thing and the distance the force moves the thing