Classical Physics to Calculate Rotation Periods of Planets and the Sun - Planetary Exploration and Science: Recent Results and Advances - page 244

were gradually accreted into a planetary core on the order of 15 Earth masses. Such
a massive core could then attract a large amount of hydrogen and helium from the
surrounding disk to form a gas giant planet, marked by runaway gas accretion,
starting when the solid and gas masses are about equal. The other scenario, disk
instability hypothesis, argues that the gas disk itself was unstable and that density
fluctuations became large enough that some portion of the disk collapsed under its
own gravity. This collapsing clump would eventually evolve into a gas giant planet.
Some of the solids that were in the gas would eventually settle into a core, but
that core is expected to be small, on the order of a few Earth masses (Boss 2000 ;
Stevenson 2006 ; Giampieri et al. 2006 ).
Here it is shown that planetary spins including the spin of the Sun can be
calculated accurately from an extension of classical Newtonian physics into the
planetary rotations especially between a planet and its satellites (Park 2008 , 2013 ).
A planet acts as a torque on its satellites to rotate them synchronously. There should
be a reaction torque on the planet, of which magnitude and direction with respect
to the center of moment of inertia (CMI) are the same as those of the torque,
which is analogous to Newton's third law in the linear motion. The spins of the
Earth and the Moon are driven by the torque and the reaction torque in such a way
that the rotation period of the Earth can be calculated by almost exact accuracy
from the fundamental quantities of the Earth and Moon system. It is also shown that
the Earth spin axis which is tilted by 23.45 ı with respect to the Earth orbit can be
derived from the gravitation of the Sun acting on the Earth in a similar way that the
gravitation of the Earth acts on the Moon to rotate it synchronously. The rotation
period of the Sun is also calculated by the same way as the Earth by reducing
the many-body system into a two-body system. The theory and equations can also
be applied to the planets, Mars, Jupiter, Saturn, Uranus, and Neptune, which have
satellites and rotate fast, to calculate the periods of their spins in a very consistent
way. Planets including the Sun take two different kinds of rotations. One is the near
synchronous rotations by the influence of the gravitation of the Sun. The other is the
fast rotations which are driven by the planet and its satellites. All spins in the latter
can be calculated accurately and consistently by the theory and equations in this
article. Finally, a possible experiment to measure the reaction torque on the Earth is
discussed.

9.2 The Rotation Period of the Earth

It is well known in mechanical physics that there is a good correspondence
in quantities and equations between linear motions and angular motions, mass
and moment of inertia, velocity and angular velocity, acceleration and angular
acceleration, force and torque, etc. The correspondence works for the first and
second Newton's laws; a body rotating with a certain velocity tends to keep rotating
with the same velocity if there is no torque acted on the body, and a torque acted