Jupiter''s orbital period is approximately 12 years.If it were exactly 12 years,which of the following periods would NOT produce an effective resonance with Jupiter?

Question

Quizplus · Accepted Answer

The effective resonance with Jupiter occurs when the ratio of the orbital periods of two planets is a small integer ratio. For example, if a planet's orbital period is exactly half of Jupiter's, then they are in a 2:1 resonance. Similarly, if a planet's orbital period is a third of Jupiter's, then they are in a 3:1 resonance, and so on. 
In this case, if Jupiter's period is exactly 12 years, then the effective resonances would be with periods of 6.0 years (2:1), 4.0 years (3:1), and 3.0 years (4:1). 
Therefore, options A), B), and D) all have periods that can produce an effective resonance with Jupiter, while C) 5.1 years does not have a small integer ratio with respect to Jupiter's period of 12 years, and thus would not produce an effective resonance.

Jupiter''s Orbital Period Is Approximately 12 Years