1.3.13 Moons data
This downloadable PDF takes you to a table of data for the moons of all the planets plus Pluto. You may find this a useful source of reference as you progress through the course. However we would like you to consult it now to look a little further into orbital resonances. The only column of data that you need to look at for this purpose is the one listing orbital periods.
The table lists the orbital periods of Io, Europa and Ganymede as 1.769, 3.551 and 7.155 days. To verify that these are resonant orbits, you need to divide one period by another. For example the ratio between Europa’s and Io’s period is 3.551/1.769. If you use a calculator this works out at 2.00734878. The final digits are meaningless, and this number rounds down to 2.0. Similarly dividing Ganymede’s period by Io’s period 7.155/1.769 works out at 4.0.
But what about Callisto? Its orbital period is 16.689 days. Does this share an orbital resonance with the others?
Try dividing its orbital period by Ganymede’s, and see what you get.
Dividing Callisto’s 16.689 day orbital period by Ganymede’s 7.155 day orbital period works out at 2.33249, or 2.3. This shows that Callisto’s orbit is not resonant with Ganymede’s.
To finish off, go back to the table and take a quick look at Saturn’s satellites. Can you find any orbital resonances there? (Hint: you may have to look beyond a moon’s immediate neighbour.)