Gravitational constant = G
Mass of planet A = M1
Mass of planet B = M2 = 3M1
Mass of the probe = m
Radius of the orbit around planet A = R1
Radius of the orbit around planet B = R2 = 2R1
Orbital speed of the space probe around planet A = V1
Orbital speed of the space probe around planet B = V2
Period of orbit around planet A = T1
Period of orbit around planet B = T2
For planet A,
V1T1 = 2R1
The gravitational force between planet A and the space probe provides the required centripetal force for the circular motion of the probe.
Similarly for planet B,
Ratio of the orbital period around planet B to that around planet A = 1.6
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