Fibonacci numbers and the Pascal Triangle

 

        

Titius-Bode Law: Earth

        

Earth
Orbital characteristics
Mean radius 149,597,870 km
Perihelion 0.983 AU
Aphelion 1.017 AU
Eccentricity 0.0167
Orbital period 365.25636 days
Avg. Orbital Speed 29.79 km/s
Inclination
Satellites 1 (the Moon)
Satellite of Sun
Physical characteristics
Equatorial 12,756.3 km
Surface area 5.10072×108 km2
Mass 5.974×1024 kg
Mean density 5.515 g/cm3
Surface gravity 9.78 m/s2
Escape velocity 11.2 km/s
Rotation period 23.9345 hours
Axial tilt 23.45°
Albedo 37-39%
Surface temperature
min mean max
182 K 282 K 333 K
Atmospheric characteristics
Pressure 101.325 Pa
nitrogen 78%
oxygen 21%
argon 1%
carbon dioxide
vapor
trace

        

The third planet from the Sun. From the astronomical perspective, Earth belongs to the group of terrestrial planets, which also includes Mercury, Venus and Mars. It is with this group, and also the Moon, that its origin, structure and evolution are often compared. Earth has an atmosphere intermediate in density between those of Venus and Mars. It is unique in possessing vast oceans of liquid water. The complex interaction between ocean, atmosphere and planetary surface determines the energy balance and the temperature regime. Cloud cover is typically 50 per cent, and heat trapped within the atmosphere (the greenhouse effect ) raises the average temperature by more than 30 degrees. The present composition of the atmosphere is 77 per cent molecular nitrogen, 21 per cent molecular oxygen, 1 per cent water vapour and 0.9 per cent argon. Carbon dioxide is the most important trace constituent. The high concentration of oxygen, which dates from 2,000 million years ago, is a direct result of the existence of plants. The presence of oxygen allowed the formation of the high-level ozone layer, which shields the surface from solar ultraviolet radiation damaging to life. Earth is the only major planet known for certain to be geologically active. Its large-scale features have    all been determined

by the creation, destruction, relative movement and interaction of a dozen or so crustal plates - comprising the lithosphere - which slide over the less rigid asthenosphere below. Collisions between plates produce folded mountains and zones of seismic activity are concentrated along the plate boundaries. Seismic waves generated during earthquakes reveal the internal structure of the Earth by the way they propagate. At the centre, there is a molten metallic core of iron and nickel, possibly with a solid core at the very centre. The central temperature is around 4,000°C. A silicate mantle overlies the core. The outermost crust is about 10 kilometres (6 miles) thick under the oceans and 30 kilometres (20 miles) thick where there are continents. In planetary terms, the surface of the Earth is very young. The basaltic rocks forming the ocean floors are among the youngest. The Precambrian shields - which occupy about 10 per cent of the surface - are the oldest, and the nearest approximation to the cratered terrain that forms a large part of other planetary surfaces. Weathering has removed all but a few traces of whatever impact craters there were. The molten metallic core gives rise to the Earth's magnetic field and magnetosphere. A layer of electrically charged particles between heights of about 50 and 600 kilometres (30 and 400 miles) form the ionosphere. The funnelling of charged particles by the magnetic field to regions between latitudes of 60° and 75° creates the phenomenon of the aurorae. Satellite measurements have shown that the Earth is also an intense source of radio waves at kilometre wavelengths, though these are generated high up and are not detectable at ground level.

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=3= 149.597 * 106 km;
M is 1 (Mercury, Venus and Earth), 2 (Mars, Planet V and Jupiter) and 3 ( Saturn, Uranus and Pluto).
R(N=3)=3*bin(3) + 3+1 -(1/4)*[1+Ln(1+(1/4))] = 9.694;
N is the number of the "Titius - Bode Law " version :
we assume N=3 in version of the planet-Earth 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 56.304 57.91
Venus 2 1 103.053 108.208
Earth 3 2 149.597 149.597
Mars 4 4 242.344 227.940
Planet V 5 8 427.631 -
Jupiter 6 16 798.069 778.33
Saturn 7 32 1538.845 1429.4
Uranus 8 64 3020.324 2870.99
Neptune 9 96 4501.794 4504.3
Pluto 9 128 5983.226 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)={3*256+ 4 -(1/4)[1+(1+Ln(1/11)]}*(149.597/9.694) *106 km
PLANET X
The probable distance of the average orbit: 11909.246 * 106 km.

        

See, also :

        

  2001-2003 Radoslav Jovanovic                 created:  August 2003.