Rotational Period of the Planet Mercury
Abstract
IN a recent communication by S. J. Peale and T. Gold^{1} the rotational period of Mercury, determined from radar Dopplerspread measurements to be 59 +/ 5 days^{2}, has been explained in terms of a solar tidal torque effect, taking into account the large eccentricity of Mercury's orbit, and the 1/r^{6} dependence of the tidal friction (r being the Sunplanet distance). They conclude from a very brief discussion that after slowing down from a higher direct angular velocity, the planet will have a final period of rotation between 56 and 88 days, depending on the assumed form of the dissipation function. However, from their discussion it is by no means clear why permanent deformations would imply a period of 88 days as a final rotation state after a slowingdown process. A very nearly uniform rotational motion of 58.65 siderealday period, that is 2/3 of the orbital period, may indeed be a stable periodic solution. This rotational motion could have the axis of minimum moments of inertia nearly aligned with the SunMercury radius vector at every perihelion passage. The orbital angular velocity at perihelion (2φ/56.6 days) is close to 2φ/58.65 days, leading to an approximate alignment of the axis of minimum moment of inertia with the radius vector in an arc around perihelion where the interaction is strongest. The axial asymmetry of Mercury's inertia ellipsoid may result in a torque that counterbalances the tidal torque, giving a stable motion with this orientation and with a period twothirds of the orbital period. It would therefore be possible for Mercury to have a higher permanent rigidity than that permitted by Peale and Gold.
 Publication:

Nature
 Pub Date:
 November 1965
 DOI:
 10.1038/208575a0
 Bibcode:
 1965Natur.208..575C