Fibonacci numbers and the Pascal Triangle

 

        

Titius-Bode Law: Uranus

        

Uranus
Orbital characteristics
Mean radius 2.87099×109 km
Eccentricity 0.0461
Revolution period 84y 3d 15.66h
Synodic period 369.7 days
Avg. Orbital Speed 6.83 km/s
Inclination 0.774°
Number of satellites 21
Physical characteristics
Equatorial diameter 51,118 km
Surface area 8,130,000,000 km2
Mass 8.686*1025 kg
Mean density 1.29 g/cm3
Surface gravity 7.77 m/s2
Rotation period -17h 14m
Axial tilt 82.14°
Albedo 0.51
Escape Speed 21.5 km/s
Cloudtop avg. temp. 55 K
Surface temp.
min mean max
59K 68K N/A K
Atmospheric characteristics
Atmospheric pressure Varies with depth
Hydrogen 83%
Helium 15%
Methane 1.99%
Ammonia 0.01%
Ethane 0.00025%
Acetylene 0.00001%
Carbon monoxide
Hydrogen sulfide
trace

        

Uranus was the first planet discovered that was not known in ancient times, though it had actually been seen many times before but ignored as simply another star (the earliest recorded sighting was in 1690 when John Flamsteed cataloged it as 34 Tauri). Sir William Herschel discovered the planet in 1781, and originally called it Georgium Sidus (George's Star) in honour of King George III of England. French astronomers began calling it Herschel before German Johann Bode proposed the name Uranus, after the Greek god. The name didn't come into common usage until around 1850.

The seventh most distant planet from the Sun It is bluish green because of methane in the atmosphere. In fact the C:H ratio is 30 to 40 time the solar value. Its atmosphere is composed of hydrogen and helium, its mantle is water and ammonia ice, and its core is rocky. Uranus has 9 faint rings. Ten new satellites were discovered by Voyager 2 when it flew by in 1985. The rings of Uranus are designated 1986U2R, 6, 5, 4, a,b,g,d , 1986U1R, and e. Enhanced Voyager 2 images of the l ring found it to break up into 5 major arcs of roughly equal length. Uranus has 17 known moons: Ariel, Belinda, Bianca, Cordelia, Cressida, Desdemona, Juliet, Miranda, Oberon, Ophelia, Portia, Puck, Rosalind, Titania, and Umbriel. Two distant satellites in non-equatorial

orbits were discovered by B. Gladman,P.Nicholson,J. A. Burns, and J. J. Kavelaars using the Palomar 5-meter telescope. The discovery was announced on Oct. 31, 1997.

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=8= 2870.99 * 106 km;
M is 1 (Mercury, Venus and Earth), 2 (Mars, Planet V and Jupiter) and 3 ( Saturn, Uranus and Pluto).
R(N=8)=8*bin(8) + 8+3 -(1/9)*[1+Ln(1+(1/9))] =522.8772;
N is the number of the "Titius - Bode Law " version :
we assume N=8 in version of the planet-Uranus 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 59.541 57.91
Venus 2 1 103.539 108.208
Earth 3 2 147.504 149.597
Mars 4 4 235.381 227.940
Planet V 5 8 411.102 -
Jupiter 6 16 762.523 778.33
Saturn 7 32 1465.349 1429.4
Uranus 8 64 2870.99 2870.99
Neptune 9 96 4276.623 4504.3
Pluto 9 128 5682.262 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)={8*256+ 8 + 3 -(1/9)[1+(1+Ln(1/11)]}*(2870.99/522.8772) *106 km
PLANET X
The probable distance of the average orbit: 11304.799 * 106 km.

        

See, also :

        

        

  2001-2003 Radoslav Jovanovic              translated: D.Filipovic   created:  May 2003.