Fibonacci numbers and the Pascal Triangle

 

        

Titius-Bode Law: Venus

        

Venus
Orbital characteristics
Mean radius 108,208,930 km
Eccentricity 0.0068
Revolution period 224.701 days
Synodic period 583.92 days
Avg. Orbital Speed 35.1 km/s
Inclination 3.394°
Number of satellites 0
Physical characteristics
Equatorial diameter 12,103.6 km
Surface area 4.60×108km2
Mass 4.869×1024 kg
Mean density 5.24 g/cm3
Surface gravity 8.87 m/s2
Rotation period -243.02 days
Axial tilt 2.64°
Albedo 0.65
Escape Speed 10.4 km/s
Surface* temp.
min* mean max
228K 737K 773K
(*min temperature refers to cloud tops only)
Atmospheric characteristics
Atmospheric pressure 9321.9 kPa
Carbon dioxide 96%
Nitrogen 3%
Sulfur dioxide
Water vapor
arbon monoxide
Argon
Helium
Neon
Carbonyl sulfide
Hydrogen chloride
Hydrogen fluoride
trace

        

The second major planet of the solar system, in order from the Sun. It is one of the "terrestrial" planets, similar in nature to Earth and only slightly smaller. Like the Earth, it is surrounded by a substantial atmosphere. Venus can come closer to the Earth than any other planet and can be the brightest object in the sky (apart from the Sun and Moon). Because its orbit lies inside the Earth's, its position in the sky can never be further than 47° away from the Sun. As a result, Venus can be viewed either in the western sky in the evening, or in the eastern sky in the morning. It is sometimes called the "morning star" or the "evening star". As a further consequence of its location within the Earth's orbit, Venus appears to go through a cycle of phases similar to the Moon's. At its brightest and nearest, even a small telescope will show that Venus is actually a crescent. The surface is perpetually covered by dense, highly reflecting clouds which show few features in visible light, though ultraviolet photographs reveal a banded structure, including a characteristic Y-shaped feature. These clouds consist of droplets of dilute sulphuric acid, created by the action of sunlight on the carbon dioxide, sulphur compounds and water vapour present in the atmosphere. The atmosphere is almost entirely of carbon dioxide, and the surface pressure is more than 90 times that at the surface of the Earth. The exceptionally high surface temperature of 730 K (450°C) is a result of the

greenhouse effect. Venus was the target of a large number of Soviet and American probes in the 1970s and 1980s, notably the Soviet Venera and Vega series and the American Pioneer Venus. The extremely high temperature and pressure present considerable difficulties and many of the probes were destroyed either before returning data or after a relatively short period of operation. Nevertheless, it proved possible to analyse the chemical composition of some surface rocks and to return limited panoramic views of the surface terrain, showing rocky desert landscapes. The first radar maps produced by spacecraft orbiting the planet showed that most of the surface consists of vast plains, above which several large plateaux rise to heights of several kilometres. The two main highland areas are Ishtar Terra in the northern hemisphere and Aphrodite Terra in the equatorial region. The Maxwell Montes are the highest feature, rising to 11 kilometres above the mean level of the planetary surface. In 1990, the US Magellan probe arrived in orbit around Venus and commenced a programme of mapping the surface in much greater detail than had been achieved previously, by means of sophisticated radar techniques. Ample evidence has been found of both impact features and volcanic activity in the relatively recent past. By solar system standards, the surface of Venus is young: the oldest craters appear to date from 800 million years ago. However, no evidence has yet been found of current volcanism. The thick atmosphere and high surface temperature mean that impact craters take forms rather different from those on other planets and satellites. Smaller meteorites burn up readily on passing through the atmosphere so there is an absence of smaller craters. The material thrown out in the powerful impacts of larger meteorites did not travel far and tended to spread round the craters in molten form. Large numbers of volcanic features have been identified: lava flows, small domes 2-3 kilometres across, larger volcanic cones hundreds of kilometres across, "coronae" and so-called "arachnoids". The coronae of Venus are circular or oval volcanic structures surrounded by ridges, grooves and radial lines. They appear to be collapsed volcanic domes and are different from any features seen on other planets or satellites. The "arachnoids", which get their informal name from their spider-like appearance, are similar in form to coronae, but generally smaller. According to one theory, arachnoids may be precursors to coronae. The bright lines extending outwards for many kilometres indicate formations that may have been created when magma upwelled from the planet's interior, causing the surface to crack.

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=2=108.208 * 106 km;
M is 1 (Mercury, Venus and Earth), 2 (Mars, Planet V and Jupiter) and 3 ( Saturn, Uranus and Pluto).
R(N=2)=2*bin(2) + 2+1 -(1/3)*[1+Ln(1+(1/3))] =4.5708;
N is the number of the "Titius - Bode Law " version :
we assume N=2 in version of the planet-Venus 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 59.931 57.91
Venus 2 1 108.208 108.208
Earth 3 2 156.065 149.597
Mars 4 4 251.083 227.940
Planet V 5 8 440.696 -
Jupiter 6 16 819.641 778.33
Saturn 7 32 1577.330 1429.4
Uranus 8 64 3092.558 2870.99
Neptune 9 96 4607.766 4504.3
Pluto 9 128 6122.896 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)={2*256+ 2+1 -(1/3)[1+(1+Ln(1/3)]}*(108.208/4.5708) *106 km
PLANET X
The probable distance of the average orbit: 12183.479 * 106 km.

        

See, also :

        

        

  2001-2003 Radoslav Jovanovic                  created:  August 2003.