All Galilean satellites have the same orbital period and rotation period.
Not only the Galilean moons, but also many of the satellites of the planets of the solar system continue to revolve with the same plane facing the main planet.
This is thought to be due to the fact that the interstellar medium gathers by point contact,
and its center of gravity is close to the main planet due to the gravity of the host planet.
When an early satellite is born in a sloppy state and grows in its gravitatioal environment
that is stretched in a direction toward Jupiter,
the state in which the satellite's center of mass is shifted to the main planet side.
So, the sateriiite's orbital period coincides with the satellite's rotation.
The orbital period of a satellite depends on the distance between Jupiter
and satellite. The interstellar medium in geostationary orbit received
the gravity of the central planet and ity is balanced by the centrifugal
force of its orbit, The interstellar medium slowly contacts and maintains
contact as it is, so that it does not fall down to Jupiter. Therefore,
geostationary orbit is considered to be the place where satellites are
born due to the easly to point connects among interstellar materials.
Jupiter's geostationary orbit is 160,000 km, and the Galilean satellite
has an orbital period outside its geostationary orbit. The explanation
of this phenomenon is as follows. As Jupiter's mass increases, the rotation
speed increases, the rotational motion of charged particles inside of the
Jupiter also accelerates, and the magnetic coupling acting at the speed
of light accelerates the externally moving charged particles, accelerating
the orbit of the collided satellites. If Galilean moons were born in Jupiter's
geostationary orbit and moved from Jupiter as they grow, then formational
order of Galilean moon will be Callisto, Ganymede, Europa, and Ion.
Table 3. shows data from Jupiter's four Galilean moons.
Table 3. Data from Jupiter's four Galilean moons
| Name | Distance | Period | Diameter | Mass | Density |
| Io | 4.2 x108m | 1.76 days | 3,632 km | 8.92×1022 kg | 3.528 g/cm3 |
| Europa | 6.71x108m | 3.55 days | 3,138 km | 4.8×1022 kg | 3.013 g/cm3 |
| Ganymede | 10.7x108m | 7.16 days | 5,262 km | 1.49×1023 kg | 1.936 g/cm3 |
| Callisto | 18.8x108m | 16.69 days | 4,820 km | 1.08×1023 kg | 1.851 g/cm3 |
Table 3. As shown in, Io's orbital period, Europa's orbital period, and
Ganymede's orbital period are approximately, 1:2:4 This is an orbital resonance
relationship, and satellites repeatedly approach each other. When satellites
come close, large satellites take in the material of smaller satellites,
which explains Europa's low mass..
Earth rotates one time in a day and the orbitting period is one year...However,
the Moon's revolution and rotation are the same, which is 27.4 days. The
center of gravity of the Moon is directed toward Earth, and the rotation
of the Moon is as slow as 27.4 days, so the rotation of the Moon is accelerated
by the rotation of the Earth. Since the moon slowly revolves around the
Earth rotating at a fast speed, universal gravitational force acts, so
the revolution of the Moon is accelerated by the rotation of the Earth,
and the revolution speed is accelerated and moves away from the Earth.
Currently, the distance from the Earth to the Moon is about 380,000 km,
and the Moon is about 3.8cm away in one year. Assuming the same recession
velocity in past eras Distance between Earth and Moon (3.8x108 m)
Divide by (8x10-2 m) to get 1010, It would have taken 10 billion years to become today's distance.
However, when the Moon is close to the Earth, the tidal effect of the Moon on the Earth is large. It is thought that the Moon was born and formed near the Earth's geostationary orbit.
If the orbital major radius is L, the orbital period is T, the mass of
the host star is M, the mass of the companion star is m, and the universal
gravitational constant is G, then these relationships are determined by Kepler's law i.e.L 3/T2 = G(M+m)/(4π 2). From this Kepler's law, the orbit is proportional to the cube root of
the Earth's mass, so let's estimate the mass ratio by finding the distance
ratio.
The ratio of the distance of the apogee to the geostationary orbit is
[(40.56/4.23) = 9.59] and at periapogee is [(36.33/4.23)= 8.59]. On the
other hand, when the Moon is in geostationary orbit, the rotation period
is 1 day, and the current orbital period is 27.3 days, so we you convert
that ratio to the ratio of orbital distance according to Kepler's law,
as L 27.3 days;/L1day={(27.3)2}
1/3 = 9.1. This corresponds to the value found for the elliptical orbit.
(last modified Apri/20, 2023)
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