Fibonacci numbers and the Pascal Triangle

 

        

Titius-Bode Law: Planet V

        

        

Asteroid-Belt :The region between the orbits of Mars and Jupiter (centered around 2.8 AU) in which most asteroids are found. The largest, Ceres, is nearly 1,000 kilometres (600 miles) across and they range in size down to dust particles. Many thousands have been individually identified and it is believed that there could be half a million with diameters larger than 1.6 kilometres (1 mile). However, the total mass of all asteroids is less than one-thousandth the mass of the Earth. Most asteroid orbits are concentrated in the asteroid belt between Mars and Jupiter at distances ranging from 2.0 to 3.3 AU from the Sun. There are however asteroids in orbits nearer the Sun, such as the Amor group, the Apollo group and the Aten group, and some more distant from the Sun, such as the Centaurs. The Trojan asteroids share Jupiter's orbit. Asteroids can be classified according to their spectra of reflected sunlight: 75 per cent are very dark, carbonaceous C-types, 15 per cent are greyish, silicaceous (stony) S-types and the remaining 10 per cent consist of the M-types (metallic) and a number of rare varieties. The classes are linked to the known types of meteorite. The evidence suggests that many asteroids and meteorites have similar compositions, so asteroids may be the parent bodies of meteorites. The darkest asteroids reflect only 3-4 per cent of the sunlight falling on them, while the brightest reflect up to 40 per cent. Many vary regularly in brightness as they rotate. In general, asteroids are irregularly shaped; the smallest asteroids rotate the most rapidly and are the most irregular in shape. The Galileo spacecraft, on its way to Jupiter, flew by two asteroids, Gaspra (on 29 October 1991) and Ida (on 28 August 1993). Detailed images showed their rocky surfaces to be pitted with numerous craters, and that Ida has a small satellite. From the ground, it is possible to obtain information about the three-dimensional structure of asteroids through radar studies using the large radio dish of the Arecibo Observatory. Asteroids are believed to be the remnants of the material from which the solar system formed. This view is supported by the way the predominating asteroid type changes with increasing distance from the Sun within the asteroid belt. High-speed collisions between asteroids are now gradually resulting in their break-up.

Space scientists John Chambers and Jack Lissauer of NASA's Ames Research Center hypothesize that along with Mercury, Venus, Earth, and Mars -- the terrestrial, rocky planets -- there was a fifth terrestrial world, likely just outside of Mars's orbit and before the inner asteroid belt. Moreover, Planet V was a troublemaker.
"The extra planet formed on a low-eccentricity orbit that was long-lived, but unstable," Chambers reported. About 3.9 billion years ago, Planet V was perturbed by gravitational interactions with the other inner planets. It was tossed onto a highly eccentric orbit that crossed the inner asteroid belt, a reservoir of material much larger than it is today. Planet V's close encounters with the inner belt of asteroids stirred up a large fraction of those bodies, scattering them about. The perturbed asteroids evolved into Mars crossing orbits, and temporarily enhanced the population of bodies on Earth-crossing orbits, and also increased the lunar impact rate. After doing its destabilizing deeds, Planet V was lost too, most likely spinning into the Sun, the NASA team reported.

         

Neptune
Orbital characteristics
Mean radius 4.5043*109km
Eccentricity 0.0097
Revolution period 164y 288d 13h
Synodic period 367.5 days
Avg. Orbital Speed 5.5 km/s
Inclination 1.774°
Number of satellites 11
Physical characteristics
Equatorial diameter 49572 km
Surface area 7.65*109km2
Mass 1.024*1026 kg
Mean density 1.64 g/cm3
Surface gravity 11.0 m/s2
Rotation period 16h 6.5m
Axial tilt 28.31°
Albedo 0.41
Escape Speed 23.5 km/s
Surface temp.
min mean max
50K 53K N/AK
Atmospheric characteristics
Atmospheric pressure kPa
Hydrogen >84%
Helium >12%
Methane 2%
Ammonia 0.01%
Ethane 0.00025%
Acetylene 0.00001%

We propose that the Solar System contained a fifth planet with an orbit between Mars and Jupiter.

Planet V was Neptune!

The Neptune formed 3.9 billion years ago, 420 million km from the Sol.We propose that Planet V--Neptune destabilized the orbit of comet-like bodies and was ejected on the orbit between Uranus and Pluto.


Neptune:The planet having the second greatest average distance from the Sun. It was discovered by Adams and Le Verrier in 1846. It is bluish green and has an atmosphere of hydrogen and helium, an icy mantle, and a rocky core. Neptune emits more energy than it receives from the Sun. It was be visited by Voyager 2 in Aug. 1989, which discovered six new satellites and a set of ring arcs. Neptune is the windiest planet in the solar system, with wind speeds of 600 m s-1 ( Mach 1 at 59 K). The rings of Neptune are designated 1989N3R, 1989N2R, 1989N4R, and 1989N1R.

        

The original Rasko Jovanovic`s formulation of the " Titius-Bode Law " is now available. This formulation is that the mean distance R(k) of the planet from the Sun is :

where k = 1-Mercury, 2- Venus, 3- Earth, 4- Mars, 5- Planet V, 6- Jupiter, 7- Saturn, 8- Uranus, and 9 - Pluto;
AUN=5= 417.8796 * 106 km;
R(N=5)=5*bin(5) + 5+2 -(1/6)*[1+Ln(1+(1/6))] = 46.8076;
N is the number of the "Titius - Bode Law " verzion :
we assume N=5 in version of the planet-V and the mean distance R(k) of the planet(k) from the Sun is:

Here are the distances of planets calculated from this rule and compared with real ones:

Planet k bin(k) T-B rule distance*106 km Real distance*106 km
Mercury 1 0 60.402 57.91
Venus 2 1 105.215 108.208
Earth 3 2 149.949 149.597
Mars 4 4 239.286 227.940
Planet V 5 8 417.8796 -
Jupiter 6 16 775.014 778.33
Saturn 7 32 1489.245 1429.4
Uranus 8 64 2917.678 2870.99
Neptune 9 96 4346.108 4504.3
Pluto 9 128 5774.523 5913.52

THE PROBABLE LOCATION OF THE PLANET X
The orbit of Pluto have some unregularities, what induces some astronomers to belive in the existence of a 10th planet of the Solar System. In accordance to the Bode's Law, was working out a calculation for location the probable position of the supposed 10th planet.
R(10)={5*256+ 5+2 -(1/6)[1+(1+Ln(1/11)]}*(417.8796/46.8076) *106 km
PLANET X
The probable distance of the average orbit: 11488.1955 * 106 km.

        

See, also :

        

  2001-2003 Radoslav Jovanovic                 created:  August 2003.