Courses › Computational astrophysics › Module 2: Orbits and gravity › Lesson 4
Lesson 4: Elliptical Orbits
The shape of an orbit and how tides round it off
🎯 Objectives
- Understand what eccentricity measures
- Calculate the periapsis and apoapsis of an orbit
- See in a simulation how tides circularise an orbit and heat it
🧪 Exercise
- Calculate Mercury's periapsis a(1−e) and apoapsis a(1+e) (a = 0.387 AU, e = 0.2056).
- Calculate how many times more light Mercury receives at periapsis than at apoapsis.
- Simulate Proxima b for 4.5 Gyr and watch the eccentricity column.
⚠️ Model limits
- The eccentricity of 0.1 for GJ 1132 b, TRAPPIST-1e, Proxima b and Earth is hypothetical: it is used to show the circularisation process.
- The drawing of the ellipses is Keplerian geometry, not an engine simulation.
- Circularisation uses the Hut (1981) model with constant tidal efficiency; the times are order-of-magnitude.
- HD 80606 b doesn't change in the simulation; its real history probably involves a companion star (Wu and Murray 2003), which the engine doesn't simulate.
📚 References
- Hut (1981), Tidal evolution in close binary systems, A&A 99.
- Naef et al. (2001), HD 80606 b, a planet on an extremely elongated orbit, A&A 375.
- Wu & Murray (2003), Planet migration and binary companions: the case of HD 80606b, ApJ 589.
- Davies & Davies (2010), Earth's surface heat flux, Solid Earth 1.
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