Classical Physics to Calculate Rotation Periods of Planets and the Sun - Planetary Exploration and Science: Recent Results and Advances - page 263

periods. It proves that if their initial spins were much faster than the synchronous
spins, kinetic energy losses of satellites due to gravitations of mother planets were
large enough for the spins of the satellites to decrease to the synchronous spins. If
it is the same for the planets, the remaining initial spins of the planets are, at most,
smaller than the synchronous spins.
Influence of the Fast Rotating Planets on the Spin of the Sun
If the Sun acts torques on the fast rotating planets, Earth, Mars, Jupiter, Saturn,
Uranus, Neptune, in the direction to decrease the speeds of spins, the reaction
torques would make the Sun rotate faster than the planets in the opposite direction
to the current spin of the Sun. A possible reason why it does not happen may be
explained by a small or negligible magnitude of the torques being acted by the Sun.
With reference to Fig. 9.2 , for the gravitation of the Sun to make a torque on the
Earth, the volume of increased radius must be in a certain angle between 0 ı and 90 ı
or 90 ı with respect to the line connecting two centers of the Sun and the Earth. As
the Earth rotates so fast, the increased radius may appear in an angle of ineffective
direction or the volume of increased radius may spread over all 360 ı , due to the
retarded response of the Earth materials. In this case, the Sun would not make a
realistic torque on the Earth, which would be the same with the other fast rotating
planets.
To explain the reaction torque on the Sun to hold the current spin of the Sun, the
fast rotating planets would have some elliptic shape of orbital trajectories with their
own satellites due to the tidal forces of the Sun. As the planets rotate around the
Sun, the long axis of the elliptic orbit would always direct toward the Sun just as the
synchronous rotation of the Moon. If the long axis of elliptic orbit deflects from the
line connecting two centers of the Sun and the planet, then the gravitational force
of the Sun would act a torque to make the elliptic orbit rotate synchronously with
the orbital motion of the planet around the Sun. From this torque, there should be a
reaction torque on the Sun to hold the current spin.
References
Allen CW (1973) Astrophysical quantities, 3rd edn. Athlone Press, London
Boss AP (2000) Possible rapid gas giant planet formation in the solar nebular and other
protoplanetary disks. Astrophys J 536:L101-L104
Chamberlin TC (1897) A group of hypotheses bearing on climate change. J Geol 5:653-683
Dones L, Tremaine S (1993) Why does the Earth spin forward? Science 259:350-354
Giampieri G, Dougherty MK, Smith EJ, Russell CT (2006) A regular period for Saturn's magnetic
field that may track its internal rotation. Nature 441:62-64
Giuli RT (1968) On the rotation of the Earth produced by gravitational accretion of particles. Icarus
8:301-323