3.4 Formation of planet and the geostationary orbit
The following are data on four moons with orbits close to the Jupiter,
and the two moons on Mars. These satellites are orbited near the geostationary
orbit of the center planets. [CG is provided by Pixta}
[Metis] L Metis = 120,960km, T Metis = 6.97 hours, dmaxs=60km,
[Adrastea] L Adrastea = 128,980km, T Adrastea = 7.15hours, dmaxs=20km,
LGeostationary orbit of Jupiter = 160,180km, T Geostationary orbit of Jupiter = 9.94 hours
[Amalthea] L Amalthea = 181,300km, T Amalthea = 11.77hours, dmaxs=270km,
[Thebe] L Thebe = 221,900km, T Thebe = 16.08hours dmaxs=110km.
[Phobos] L Phobos = .9,370 km, T Phobos = 7.65 hours, dmaxs=26.8km,
LGeostationary orbit of Mars =20,400 km TGeostationary orbit of Mars = 24.62 hours.
[Deimos] L Deimos = 23,500 km. T Deimos = 30.3 hours, dmaxs=15km.
Radius of the geostationary orbit is determined by the condition where
gravity of material (Fg) is equal centrifugal force (Fc). That is Fg=Fc;
GMm/(R2)=mRω2, i.e. GM= R3(2π/T)2. The geostationary radius is given by Eq.(6).
Lgeostationary radius ={GMT2/(4π2 )}1/3 (6)
Table 1. Planetary orbital orbit, rotation cycle, gravitational zone and
synchronous orbit
| Mercury | Venus | Earth | Mars | Jupiter | Saturn | Uranus | Neptune | [Unit] | |
| Ldistance from the Sum | 0.579 | 1.082 | 1.496 | 2.279 | 7.783 | 14.294 | 28.75 | 45.44 | [1011m] |
| Tperiod of rotation | 58.65 | 243.0 | 0.997 | 1.026 | 0.414 | 0.444 | 0.718 | 0.671 | [day] |
| Lgeosynchronous orbit | 24.3 | 153.7 | 4.23 | 2.04 | 16.01 | 11.22 | 8.27 | 8.35 | [107m] |
| Lgravitational zone | 2.4 | 16.9 | 25.9 | 12.9 | 2402 | 2416 | 1899 | 3231 | [107m] |
Table 1 shows the data including the geostationary radius (Lgeostationary orbit) on the planets in the solar system.
The geostationary orbit of the Sun on the current rotation period of the
Sun is determined by using Eq. (7).
Lgeosynchronous orbit of the Sun) = 2.53 X1010m. (7)
This distance is half the value of orbital radius of Mercury. The orbit of planets in the solar system is very farther than the current geostationary orbit of the Sun.
This indicates that the planets were born at the time when the Rotation period of the Sun had been longer than that of current.
The value of Lgravitational zone are shown in table (1) obtained by using Eq.(8) as the distance from the
planet where the gravitational force of the Sun and the gravitational force
of the planet are equal.
MSun/(L*boundary from the Sun)2 =Mplanet/(L*boundary from planet)2 (8)
The solar wind is reached to the edge of the outer solar system. If
the temperature of interstellar material is 10 K at the end of the solar
system,the distance to the edge of the solar system (Lsolar system) is determined as the corresponding value of the gravitational potential of the Sun for a hydrogen ions.
The distance to the end of the solar system can be estimated from the Virial theorem of Eq. (9).
2・Etemperature = mp・MSun・G/( Lsolar system) (9)
By using, the energy of temperature is 10K=1.38 x10-22 J, M Sun=1.988 x1030 kg, the distance to the end of the solar system (L edge of solar system ) is given by Eq.(10).
Ledge of solar system= 8.0 x 1014 m. (10)
The value is about half of the distance to the Oort cloud( (10,000 au =1.5x1015m).
* The numerical values were used from the Science chronology
Index -3.4-