Geoscience Reference
In-Depth Information
Chapter 9
Classical Physics to Calculate Rotation Periods
of Planets and the Sun
Sahnggi Park
Abstract
The rotation period of the Earth was calculated from the fundamental
quantities, mass, distance, and radius, of the Earth-Moon system by almost an exact
number 24
h
3
m
5
s
. The rotation periods of Mars, Jupiter, Saturn, Uranus, Neptune,
and the Sun were also calculated by the same equation. The Earth spin axis which is
inclined by 23.45
ı
with respect to the Earth orbit was derived from the gravitation of
the Sun acting on the Earth and calculated by almost an exact number, 23.487
ı
.An
optical experiment to measure the reaction torque on the Earth acted by the Moon
is proposed and discussed.
Keywords
Planetary rotation Spin Earth's rotation Reaction torque
9.1
Introduction
Cosmogonists believe that planet's rotation is determined by a combination of
processes that occur during and after its accretion from a protoplanetary disk. A
considerable progress toward understanding the origin of terrestrial planet rotations
has been made over the last two decades (Lissauer et al.
2000
; Hughes
2003
).
Most conventional models of planet formation begin with a protoplanetary disk
gas and dust orbiting a central protostar and proceed to collisional coagulation
of dust particles into 10
12
-10
18
g (kilometer-sized) planetesimals. A swarm of
10
10
-10
16
planetesimals accumulate gravitationally into 10
26
-10
27
g (Mars-sized)
planetary embryos. Near 1 AU, in a narrow accumulation zone of semimajor axis
width
a
0.05 AU, formation of a planetary embryo is characterized by runaway
growth of the largest body in the zone on a timescale of the order 10
5
years.
Several independent research groups have corroborated this finding by using distinct
numerical methods: gas dynamic statistical simulations or direct N-body orbital
integrations. The final stage is described by giant impacts between embryos that
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