Classical Physics to Calculate Rotation Periods of Planets and the Sun - Planetary Exploration and Science: Recent Results and Advances - page 261

Figure 9.13b shows a possible experiment to measure a 0.3043 nm shift. A
pendulum of 5 m length and a laser beam with multiple reflection mirrors are set
on an optical table. The total path length of laser beam is 5 km. A monitor displays
a shift of laser beam magnified to 152.2 m. The whole system is enclosed by a
chamber to block air flow.

9.7 Conclusion

As the Earth acts a torque to rotate the Moon synchronously with the orbital motion,
there should be a reaction torque on the Earth, and the torque and the reaction torque
should have the same magnitude and direction with respect to CMI. The rate of
the Earth spin can be calculated by almost an exact number using the fundamental
quantities of the Earth-Moon system. The calculated numbers of the Earth spin are
23 h 39 m 2 s

without taking into account the density distribution and 24 h 3 m 5 s

with

taking into account the density distribution.
It is also shown that the Earth spin axis which is inclined by 23.45 ı with respect
to the Earth orbit can be derived from the gravitation of the Sun acting on the Earth.
The ratio of the horizontal component to the vertical component of the spin velocity
approaches to unity. The calculated number, 23.487 ı , is close to the observation,
23.45 ı . The obliquities of planets to their orbits are dominantly dispersed near
23.45 ı and 0 ı which are stable or equilibrium angles.
The spin of the Sun was also calculated by the same way as the Earth by reducing
the many-body system into a two-body system. It is based on the fact that the
weighted collective contributions determine a single value of spin in the equator
area of the Sun, which is assumed to be affected by a single imaginary planet.
The rotation rates of planets Mars, Jupiter, Saturn, Uranus, and Neptune were 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. All the
periods of the spins of the planets were calculated in a very consistent way using the
densities for cores and volumes A and B. Considering 10 2430 order of astronomical
numbers involved in the equations, the calculated values are considerably close to
the observations to validate calculations. Finally, a possible experiment to measure
the reaction torque in the Earth is discussed.

Appendix

Validity of the Initial Velocities Being Zero

The assumption in Eq. 9.4 that initial velocities v 10 , v 20 which had not been driven
by the forces f 1 and f 2 will be damped out may be validated by estimating the time