Wednesday, November 16, 2016

astronomy - Axial tilt and precession rate of exoplanets


The Earth's axis is 23.5 degrees away from othogonality to the ecliptic, and it takes about 26 000 years for it to precess fully. I have neither an intuitive sense nor the formula for precession frequency in front of me for how the latter depends on the former (and other things). So...




  1. What is the general formula for gyroscopic precession? I remember working it out as a function of moment of inertia and torque, but it was fiddly and grad mechanics was seven years ago.





  2. What is the formula substituting gravity for the force and a reasonable moment of inertia for a planet?




  3. Is a uniform density sphere a good enough approximation for B?




  4. Do you know of any empirical measurements of any of the above, for any exoplanets? Particularly, any really fast precessors?




  5. Any bigger conclusions we can draw from the above? See Is it easier to learn more about the seasonal changes in an exoplanet's atmosphere when the exoplanet orbits a binary star system?







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classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...