Classical Physics to Calculate Rotation Periods of Planets and the Sun - Planetary Exploration and Science: Recent Results and Advances - page 254

of imaginary planet which is assumed to be the same as the period of orbital motion,
the classical equation is used:

2
p G.m s C m 0 / r 3=2

T o D

cm ;

(9.28)

where G is the gravitational constant and r cm is a distance between the imaginary
planet and the center of mass of the Sun and the imaginary planet, which is
calculated, r cm D 1.391 10 12 m. Using T o D 28.356 year from Eq. 9.28 ,the
calculation results in T s D 44.5 day. Refer to Park ( 2013 ) for Mathcad calculations
in detail. Considering 10 30 order of astronomical numbers involved in the equations,
the calculated number is considerably close to the observation 25 days. Two main
approximations are involved in the calculation. First, the parameters of imaginary
planet are dominated by Jupiter and Saturn that consist of gas. As shown in the
calculation of the Earth spin, the rigid part having an average density of 5.515 g/cm 3
for the Earth and 3.341 g/cm 3 for the Moon is a major part to decide the spin rate
accurately. The radial point of the imaginary planet to give 25 days of spin on the
equator surface of the Sun is 4.53 10 7 mor0.56 R 0 . Second, the imaginary
planet is assumed to rotate synchronously with its orbital motion as the case of
the Moon. Considering the spin of Mercury and Venus, this assumption may result
in difference between calculation and observation. Nonvanished initial spin of the
Sun which was not driven by the reaction torque may also contribute to the current
spin of the Sun.

9.5 Spins of Mars, Jupiter, Saturn, Uranus, and Neptune

The spin rates of planets Mars, Jupiter, Saturn, Uranus, and Neptune are also
calculated by the same theory and equations as those of the Earth and the Sun with a
slight modification due to the fact that the CMIs locate inside the planets. Although
the spin rates of the planets look irregularly distributed, it is possible to derive them
in a consistent way with considerable accuracies. Refer to Park ( 2013 ) for Mathcad
calculations in detail.
Figure 9.9 takes Jupiter, as an example, to describe a planet system of which
CMI locates inside the planet. The point CMI about which moment of inertia of the
system is symmetric is calculated, approximately, by taking the same volume B as
volume A and assuming that the whole mass of volume C locates in the center O.
The volume A is given by equation

R J r J

3 r J ;

2
3 R J

1

V D (9.29)

where r J is a distance between the center O and CMI. The moment of inertia of
volume C is equal with that of the satellites as