Fibonacci numbers and the Pascal Triangle

 

        

Titius-Bode Law: Jupiter

        

JUPITER
Orbital characteristics
Mean radius 7.7833*108km
Eccentricity 0.0483
Revolution period 11y 315d 1.1h
Synodic period 398.9 days
Avg. Orbital Speed 13.1 km/s
Inclination 1.308°
Number of satellites 61
Physical characteristics
Equatorial diameter 142,984 km
Surface area 6.41×1010 km2
Mass 1.899×1027 kg
Mean density 1.33 g/cm3
Surface gravity 22.88 m/s2
Rotation period 9h 55.5m
Axial tilt 3.12°
Albedo 0.52
Escape Speed 60.2 km/s
Surface temp.
min mean max
110K  152K  N/A K
Atmospheric characteristics
Atmospheric pressure 70 kPa
Hydrogen 81%
Helium 17%
Methane 0.1%
Water vapor 0.1%
Ammonia 0.02%
Ethane 0.0002%
Phosphine 0.0001%
Hydrogen sulfide 0.0001%

        

The largest planet in the solar system and the fifth in order from the Sun. After Venus, it is the second-brightest planet as seen from Earth. Jupiter is a giant ball of gas, ten times the size of the Earth and one-tenth of the Sun's diameter. Its mass is 0.1 per cent that of the Sun and its composition (by number of molecules) is very similar to the Sun's: 90 per cent hydrogen (in its molecular form in Jupiter) and 10 per cent helium. Of trace gases, the most significant are water vapour, methane and ammonia. There is no solid surface beneath the cloud layer. Instead, a gradual transition from gas to liquid takes place as the pressure increases with depth below the outermost layers, followed by an abrupt change to a metallic liquid, in which the atoms are stripped of their electrons. At the very centre there may be a small core of rock and perhaps ice. A source of internal energy, heat generated when Jupiter formed by gravitational collapse, causes the planet to radiate between 1.5 times and twice as much heat as it absorbs from the Sun. Observed visually, the disc of Jupiter is seen to be crossed by alternating light zones and dark belts. Results from four space probes that passed by Jupiter between 1973 and 1981 (Pioneers 10 and 11, Voyagers 1 and 2), and from the Galileo mission have revealed the full complexity of the flow patterns within these bands. There are five or six in each hemisphere, correlating with wind currents. White or coloured ovals appear as relatively long-lived features. The best-known and most conspicuous is the Great Red Spot, which has been observed for around 300 years. The origin of this feature, which is as wide as the Earth, is uncertain; one popular theory is that it is essentially a huge anticyclone. The coloured clouds are in the highest layers of Jupiter in a region with a depth of only 0.1-0.3 per cent of the total radius. The origin of their coloration remains a mystery, though it seems certain that it must have to do with trace constituents of the atmosphere, and is evidence of complex chemistry. Cloud colour correlates with altitude: blue features are the deepest, followed by brown, then white, with red being the highest. A probe released by the Galileo spacecraft in 1995 parachuted through Jupiter's upper atmosphere and returned data on the composition and physical conditions. Ground-based observations of the entry site indicated that it may have been a relatively cloud-free spot, explaining why hardly any evidence was found for the expected three layers of cloud consisting of ammonia crystals at the highest level, ammonium hydrosulphide in the middle, with water and ice crystals below. Winds up to 530 km/hour (330 mph) were even faster than anticipated. The abundance of helium was only about half that expected. A likely explanation is the concentration of helium towards the centre of the planet. The probe also discovered an intense radiation belt. The existence of a faint ring around Jupiter was first suggested by results from Pioneer 11 in 1974 and confirmed by direct Voyager images. The main part lies between 1.72 and 1.81 Jupiter radii from the centre of the planet. The nature of the ring is such that many of the particles must have dimensions measured in micrometres. A constant source of replenishment is required, which may be a population of orbiting boulder-sized objects, constantly bombarded by high-velocity particles. There are sixteen known natural satellites orbiting Jupiter. They fall into four distinct groups. The four small inner satellites (Metis, Adrastea, Amalthea and Thebe) and the four large Galilean satellites (Io, Europa, Ganymede and Callisto) are in circular orbits in the equatorial plane. The third group (Leda, Himalia, Lysithea and Elara) are small satellites in circular orbits, inclined at angles between 25° and 29° to the equatorial plane and at distances between 11 and 12 million kilometres from Jupiter. The outermost group (Ananke, Carme, Pasiphae and Sinope) are small satellites in retrograde orbits that are relatively eccentric ellipses, inclined substantially to the equatorial plane. These orbits all lie between 21 and 24 million kilometres from Jupiter. The four Galilean satellites and their movements in orbit are easily visible with a small telescope or binoculars. Radio emission from Jupiter was discovered in 1955. It was the first indication of the presence of the strong magnetic field, which is 4,000 times stronger than the Earth's. The magnetosphere is consequently 100 times larger. The radio emission is caused by the spiralling of electrons around the field lines. Trapped electrons near the planet give rise to synchrotron radiation at decimetre wavelengths. Decametric radiation, observed only from certain regions of the planet, is associated with the interaction between Jupiter's ionosphere and Io, whose orbit lies within a huge plasma torus: this interaction also creates aurorae. Radiation at kilometre wavelengths was discovered by the Voyager probes, originating at high latitudes near the planet and in the plasma torus.

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=6= 778.33 * 106 km;
M is 1 (Mercury, Venus and Earth), 2 (Mars, Planet V and Jupiter) and 3 ( Saturn, Uranus and Pluto).
R(N=6)=6*bin(6) + 6+2 -(1/6)*[1+Ln(1+(1/6))] = 103.8381;
N is the number of the "Titius - Bode Law " version :
we assume N=6 in version of the planet-Jupiter 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 58.4599 57.91
Venus 2 1 103.5597 108.208
Earth 3 2 148.6025 149.597
Mars 4 4 238.5935 227.940
Planet V 5 8 418.5185 -
Jupiter 6 16 778.33 778.33
Saturn 7 32 1497.9257 1429.4
Uranus 8 64 2937.0968 2870.99
Neptune 9 96 4376.2653 4504.3
Pluto 9 128 5815.4231 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)={6*256+ 6+2 -(1/6)[1+(1+Ln(1/11)]}*(778.33/103.8381) *106 km
PLANET X
The probable distance of the average orbit: 11572.063 * 106 km.

        

See, also :

        

        

  2001-2003 Radoslav Jovanovic                 created:  August 2003.