Course project: tidal locking and length of day fluctuations

Studies of sedimentary rocks in Australia and elsewhere provide solid evidence that the length of the day 620 millon years ago was about 21.9 hours. Indeed, the speed of Earth's rotation about its own axis is slowly decaying over long time-spans. Further evidence is given in our historical records: precise historical accounts of ecclipses can be backtracked to obtain a calibration of how the length of the day has varied over the last 2.5 millennia. These results show that over the last 2740 years the day on Earth has been lengthen by about 1.78 milliseconds per century. But why?

The main mechanism is the interaction between lunar induces tides and Earth's continents: as landmasses get slammed by the seas, Earth loses some rotational momentum. Thus, lunar influence is the principal force behind the decay. In theory, the slowing down will continue until the rotational speed of the Earth is in sync with the orbital period of the Moon (which is about 29.5 days). This phenomenon is called tidal locking. As the rotational speed decreases the moon also moves further away from the Earth. The Moon itself is much more affected by the Earth than the Earth is by the Moon. Indeed, the Moon has already since long reached tidal locking with the Earth, which is why one always sees the same half of the Moon - space journeys are required to observe the opposite side.

On short time-scales, however, the rotation speed of the Earth varies slightly from day to day, usually called length of day fluctuations ($\Delta$LOD). It is caused by many things, for example interior crustal movements, polar cap melting, rainfall, large storms, etcetera. The fluctuations are carefully measured every day by the Earth Orientation Centre Links to an external site. - daily data is available since the 1960s.

In this course project your task is to:

1. Give a combined textual and visual explaination of tidal locking. Here you're encouraged to use Blender, to produce still images or animations illustrating the mechanism. Your focus should be to illustrate, as pedagogically as possible, the mechanism behind tidal locking, with images, possibly animations, accompanied by well-written text and formulae.
2. Present an analysis of the $\Delta$LOD-data. Choose one aspect in the data you want to visualise, and use two (maybe three) visuals for these. Your visuals should be readable, and accessible to the audience (consider the story-telling with data lecture). As an example, one interesting aspect to show is that the measurement error (standard deviation) has decreased with time.

Prepare a report combining both Task A and Task B. It should be a well-formated, nice-looking report where you present and discuss your solution. Preferably, you should create it as a Jupyter notebook and then export it to HTML. In particular, this allows you to include animations (see hint below). Use Markdown to create sections and to include text and formulae. Feel free to use this template Download this template as a starting point. If you don't want to use Jupyter, you can also chose to hand in a more conventional report written in Word (or LaTeX) and exported to PDF.

Resources

Daily LOD-fluctuations data since 1962 Download Daily LOD-fluctuations data since 1962 (the last column contain the measurement error $\sigma$)
NASA about ocean tides Links to an external site.
Wikipedia page on tidal locking Links to an external site.
Wikipedia page on $\Delta$LOD

Hints

• To embed an mp4-animation in Jupyter, create a code cell and write
  
  from IPython.display import Video
  Video('path/to/movie.mp4', embed=True)
  
  where you need to replace 'path/to/movie.mp4' with the path to your movie (if it is in the same folder as your notebook you only need to specify the name). Execute the cell to show the movie. Make sure the movie is visible in the notebook before you export it to an HTML-file.
• In Blender, this is a simple way to add a texture to a UV-sphere (which you might want to illustrate tidal locking between Earth and Moon, you can download good texture images from here Links to an external site.):
  - With the sphere selected, add a new material to it and go to the 'Node Editor' view. You should have two panes: 'Material Output' and 'Principled BSDF'.
  - Add a 'Image Texture' pane by pressing shift-a and then select from the menu. Open your texture file.
  - Add a 'Texture Coordinate' pane by pressing shift-a and then select from the menu.
  - Connect the node 'Generated' from 'Texture Coordinate' to the node 'Vector' on the 'Image Texture' node, then change from 'Flat' to 'Sphere' projection in the 'Image Texture' node.
  - Connect the node 'Color' from the 'Image Texture' node to the 'Base Color' node of the 'Principled BSDF' node.
• Please notice that rendering in Blender takes a lot of time, so make sure that you check your results by first rendering a few still images before you render a whole animation scene. If you want to speed up the rendering, you can specify a lower resolution.

The course project is mandatory and the grading is a score between 0-10 that will be weighted in for your final course grade.

Good luck!