Chap.3 How Planets Were Formed
3.1 Process of accumulation of planets in each orbit
In the current solar system, the mass of the sun is 99.86%, and the total
mass of planets is about 0.14% of the solar system. Most of the material
in the solar system was gathered on the Sun by the gravity of the heliocentric,
but the remaining 0.14 % of matter orbits in the heliocentric gravitation.
In the strong heliocentric gravitational field, the orbiting materials
exists only in the orbit determined by Kepler's third law ; (r3/T2)=G(m+M)/(4π2). Here M is the mass of the Sun, and m is the mass of matter orbiting.
Since M is very large compared with m, matter in the orbit in the gravitational
field at the center of the Sun has extremely little influence on the magnitude
of the mass (m) and orbits at about the same speed. Materials of various
sizes continue to orbit the same orbit.
There, solid substances orbiting at the same speed come into silent contact.
At the contact point between solids in slow contact, they adhere to the
Coulomb force and become lumps. The enlarged mass also orbits in the same
orbit. Therefore, about 0.14% of the cosmic dust in the proto-solar system became
a lump in each orbit, the lumps beccame a planetesimal and plnetesimals
became asteroid, and planet.
So, the planets currently orbiting have the characteristics of the distribution of the interstellar medium in the solar system.
3.2 Distribution of interstellar medium in gas giants planets
The relationship between the distribution of the density of the primordial
interstellar medium with respect to its distance from the Sun is estimated
from the mass (mplanet) and position (Lsun-planet) of the exoplanets of the solar system.
Set the value of the infinity point to 0, and when the planet moves from the Sun to its current position,
the change in the potential due to the gravity of the Sun is the gravitational potential energy of the planet.
According to Newton's mechanics, the gravitational potential energy of a planet is inversely proportional to its distance from the center of mass (LSun-planet). The gravitational potential of each point (Φ point) is proportional
to the m planet of the planet
and it is implosion of the distance is inversely proportion to LSun-planet as described in Eq. (4),
Φplanet=-mplanet・(G・MSun)/
)=-G・MSun・(mplanet/LSun-planet) (4)
Figure 7 shows the common logarithm of the value (m planet/LSun-planet) for each planet in the solar system,
with the distance from the Sun on the horizontal axis.
Fig .7 shows the gravitational potential energy that is collected by
the planets. For the exoplanets Jupiter, Saturn, and Uranus, the value
of (m planet/L Sun-planet) is decreasing exponentially with respect to its distance from the Sun.
This indicates that gas giant planets grew in a state where the density distribution of the
proto-stellar medium is distributed exponentially with respect to the distance
from the Sun.
Fig.7 .Planetary gravitational potential of the Sun.
Note that the (m/L) value of Neptune, which is more than 4 billion km away from the Sun,
does not hold the exponential rule. On the other hand, since terrestrial rocky planets approach the Sun, the exponential rule does not hold for rocky planets.
(last modified Feb/28, 2023)
index -3.1-