PTYS206_activity_Saturnresonances
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University Of Arizona *
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Course
206
Subject
Astronomy
Date
Apr 3, 2024
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PTYS 206 Activity: Moons of Saturn The table below provides the orbital periods of the 8 major regular satellites of Saturn, as well as the ratios between every possible pairing (the blank entries in the lower triangle would simply be one divided by the entries in the upper triangle). The second row of the table gives the orbital period of each moon in days. Each entry in the table gives the ratio between the orbital period of the moon straight above it, to the orbital period of the moon to the left of it. For example, the ratio between the orbital period of Rhea and the orbital period of Enceladus is 3.297 (= 4.518 days / 1.370 days). Notice the “1”s down the diagonal, which are there because the ratio between the orbital period of Mimas and the orbital period of Mimas is 1. Which moon pairs have orbital period ratios that are within about 1% of a whole number ratio (e.g., 2:1, 3:2, 3:1, etc.)? Write each moon pair and ratio. Mimas Enceladus Tethys Dione Rhea Titan Hyperion Iapetus (Period-days) (0.942) (1.370) (1.888) (2.737) (4.518) (15.945) (21.277) (79.330) Mimas 1.00 1.454 2.004 2.906 4.796 16.927 22.587 84.214 Enceladus 1.000 1.378 1.998 3.297 11.638 15.531 57.905 Tethys 1.000 1.450 2.393 8.445 11.270 42.018 Dione 1.000 1.650 5.826 7.774 28.984 Rhea 1.000 3.529 4.709 17.559 Titan 1.000 1.334 4.975 Hyperion 1.000 3.728 Iapetus 1.000 Lower numbers in the ratios equate to stronger resonances (e.g., 2:1 is stronger than 17:9). Which of these pairs of moons have the strongest resonances? A resonant interaction is a bit like a shoving match – the smaller moon gets pushed around the most. On the playground, getting pushed around leads to bruises and a bruised ego. In orbital dynamics, getting pushed around leads to a higher eccentricity and more tidal heating. Of the strongest resonances you identified above, which moon should have the most tidal heating, based on the list of moon masses below? Moon Mass | Moon Mass
Mimas 0.4
´
10
20
kg | Rhea 23
´
10
20
kg Enceladus 1.1
´
10
20
kg | Titan 1350
´
10
20
kg Tethys 6.2
´
10
20
kg | Hyperion 0.05
´
10
20
kg Dione 11
´
10
20
kg | Iapetus 18
´
10
20
kg What would you look for in images to confirm your prediction?
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