Courses › Computational astrophysics › Module 3: Rotation and tides › Lesson 6
Lesson 6: Tides and Resonances
When orbits agree with each other
🎯 Objectives
- Recognise an orbital resonance from the periods
- Verify TRAPPIST-1's resonant chain with an N-body simulation
- Connect resonances and tides to Io's volcanism
🧪 Exercise
- Calculate P(g) / P(f) from the periods in the lesson and identify the resonance.
- Calculate P(Mars) / P(Earth): is it close to a simple fraction?
- Explain in your own words why Io has volcanoes and the Moon doesn't.
⚠️ Model limits
- The TRAPPIST-1 simulation starts with chosen phases and almost circular orbits, not the real positions on a given date; that is why it doesn't show the fine libration of the resonance.
- The Galilean moons' periods are calculated with Kepler's third law from their distances, not with N-body.
- Io's heat (~100 TW) is a measured value (Lainey et al. 2009), not a result of this simulation.
📚 References
- Agol et al. (2021), Refining the transit-timing and photometric analysis of TRAPPIST-1, PSJ 2, 1.
- Gillon et al. (2017), Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1, Nature 542.
- Lainey et al. (2009), Strong tidal dissipation in Io and Jupiter from astrometric observations, Nature 459.
- Peale, Cassen & Reynolds (1979), Melting of Io by tidal dissipation, Science 203.
Want to go further?
The free version is enough for the whole course. MHD-INT STANDARD adds 300 planets, guided labs and reports; PRO adds 8 advanced modes.
See versions