Olga Podvigina
ul. Profsoyuznaya 84/32, 117997 Moscow, Russia
Institute of Earthquake Prediction Theory and Mathematical Geophysics, RAS
Publications:
Podvigina O. M.
Rotation of a Planet in a Threebody System: a Nonresonant Case
2022, Vol. 18, no. 4, pp. 527541
Abstract
We investigate the temporal evolution of the rotation axis of a planet in a system comprised
of the planet (which we call an exoEarth), a star (an exoSun) and a satellite (an exoMoon).
The planet is assumed to be rigid and almost spherical, the difference between the largest and
the smallest principal moments of inertia being a small parameter of the problem. The orbit
of the planet around the star is a Keplerian ellipse. The orbit of the satellite is a Keplerian
ellipse with a constant inclination to the ecliptic, involved in two types of slow precessional
motion, nodal and apsidal. Applying time averaging over the fast variables associated with the
frequencies of the motion of exoEarth and exoMoon, we obtain Hamiltonâ€™s equations for the
evolution of the angular momentum axis of the exoEarth. Using a canonical change of variables,
we show that the equations are integrable. Assuming that the exoEarth is axially symmetric
and its symmetry and rotation axes coincide, we identify possible types of motions of the vector
of angular momentum on the celestial sphere. Also, we calculate the range of the nutation angle
as a function of the initial conditions. (By the range of the nutation angle we mean the difference
between its maximal and minimal values.)
