Moons in Resonance

Teacher Notes 

Answers to Questions:

1) Once every Europa orbit.

2) 1,070,000 km X (421,600 km/M.U.) = 2.54 M.U.

(2.54 MU)3 µ (Orb)2

16.39 MU µ (Orb)2

Ö16.39 MU µ (Orb)

4.05 MU µ Orb

3) It takes Ganymede almost four times as long as Io to complete an orbit around Jupiter, and twice as long as Europa.

Explain to students that the ratio of orbital periods in simple whole numbers (1:2:4) is called orbital resonance. As you saw in the kinesthetic activity, the periodic alignment of the moons creates interesting interactions in the gravitational pull of each moon on the others. The mechanism for producing orbital resonance is not well understood, and may not be very simple. As a simplified analogy, you may wish to demonstrate the resonance of strings on a musical instrument, where striking one string causes another one that is tuned to the same frequency to vibrate.

4) Yes. Once every Ganymede orbit. The combined gravitational forces of Europa and Ganymede pull the orbit of Io slightly outward, which results in greater tidal flexing.

A good analogy for the effects of combined gravitational forces is the difference between Spring tides and Neap tides on Earth.

5) Europa's orbital period is 3.54 Earth days. Ganymede's orbital period is 7.16 Earth days.

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Top Level "Bringing Jupiter to Earth"

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