Titius–Bode law - How Ceres was found

The Titius–Bode law (sometimes termed just Bode's law) is a hypothesis that the bodies in some orbital systems, including the Sun's, orbit at semi-major axes in a function of planetary sequence. The hypothesis correctly predicted the orbits of Ceres and Uranus, but failed as a predictor of Neptune's orbit.

The formula

The best way to see the law is to write down the sequence 0, 3, 6, 12 and so on, where each number is obtained by doubling its predecessor. Next, add 4 to each number, and divide the result by 10.

For example, Venus = (3+4)/10 = 0.7

Now get out any astronomy textbook and look up the distances of the planets from the Sun in astronomical units, the Earth-Sun distance being defined as 1. The distances are virtually identical to the terms in the number sequence for all but the outermost planets.

Planet   Titius–Bode law distance   Actual distance
Mercury            0.4                 0.39
Venus              0.7                 0.72
Earth              1.0                 1.0
Mars               1.6                 1.52
Ceres              2.8                 2.77
Jupiter            5.2                 5.2
Saturn            10.0                 9.74
Uranus            19.6                19.2
Neptune           38.8                30.06

When originally published, the law was approximately satisfied by all the known planets — Mercury through Saturn — with a gap between the fourth and fifth planets.

It was regarded as interesting, but of no great importance until the discovery of Uranus in 1781 which happens to fit neatly into the series.

Based on this discovery, Bode urged a search for a planet between Mars and Jupiter. Ceres, the largest object in the asteroid belt, was found at Bode's predicted position in 1801.

Bode's law was then widely accepted until Neptune was discovered in 1846 and found not to satisfy Bode's law.

Theoretical explanations

There is no solid theoretical explanation of the Titius–Bode law, but if there is one it is possibly a combination of orbital resonance and shortage of degrees of freedom: any stable planetary system has a high probability of satisfying a Titius–Bode-type relationship. Because of this, it has been called a "rule" rather than a "law".

Orbital resonance from major orbiting bodies creates regions around the Sun that are free of long-term stable orbits. Results from simulations of planetary formation support the idea that a randomly chosen stable planetary system will likely satisfy a Titius–Bode law.

Still, Titius–Bode law may be just a coincidence. And we really do not have other planetary systems to test it.

Asteroids

Asteroids are a class of small Solar System Bodies in orbit around the Sun. Asteroids are increasingly referred specifically to the small rocky–icy and metallic bodies of the inner Solar System out to the orbit of Jupiter.

There are millions of asteroids, many thought to be the often shattered remnants of planetesimals, bodies within the young Sun’s solar nebula that never grew large enough to become planets. A large majority of known asteroids orbit in the asteroid belt between the orbits of Mars and Jupiter or co-orbital with Jupiter.

Naming

A newly discovered asteroid is given a provisional designation (such as 2002 AT4) consisting of the year of discovery and an alphanumeric code indicating the half-month of discovery and the sequence within that half-month. Once an asteroid's orbit has been confirmed, it is given a number, and later may also be given a name.

Distribution within the Solar System

1. Asteroid belt

The majority of known asteroids orbit within the asteroid belt between the orbits of Mars and Jupiter, generally in relatively low-eccentricity (i.e., not very elongated) orbits. This belt is now estimated to contain between 1.1 and 1.9 million asteroids larger than 1 km in diameter, and millions of smaller ones. These asteroids may be remnants of a failed planet in the protoplanetary disk. In in this region the accretion of planetesimals into planets during the formative period of the Solar System was prevented by large gravitational perturbations by Jupiter.

2. Trojans

Trojan asteroids are a population that share an orbit with a larger planet or moon, but do not collide with it because they orbit in one of the two Lagrangian points of stability, L4 and L5, which lie 60° ahead of and behind the larger body.

The most significant population of Trojan asteroids are the Jupiter Trojans. A couple trojans have also been found orbiting with Mars.

3. Near-Earth asteroids

Near-Earth asteroids, or NEAs, are asteroids that have orbits that pass close to that of Earth. Asteroids that actually cross the Earth's orbital path are known as Earth-crossers. As of May 2010, 7,075 near-Earth asteroids are known and the number over one kilometre in diameter is estimated to be 500–1,000.

Quasi-satellites

Some asteroids have unusual horseshoe orbits that are co-orbital with the Earth or some other planet.

Sometimes these horseshoe objects temporarily become quasi-satellites for a few decades or a few hundred years, before returning to their earlier status. Both Earth and Venus are known to have quasi-satellites.

Largest Moon of Uranus - Titania (17th Moon outwards from Uranus)

Uranus has 27 known moons, all of which are named after characters from the works of William Shakespeare and Alexander Pope.

Titania is the largest of the moons of Uranus and the eighth largest moon in the Solar System

Discovery

Titania was spotted by Sir William Herschel on January 11, 1787, six years after he had discovered the planet itself.



Naming

The responsibility for naming was taken by John Herschel, son of the discoverer of Uranus. Herschel, instead of assigning names from Greek mythology, named the moons after magical spirits in English literature. Titania is named after the queen of the fairies in Shakespeare's A Midsummer Night's Dream.

Stats

Diameter: 1,577 km

Semi-major axis: 435,910 km

Orbital Period: 8.71 days

Orbit

Titania orbits Uranus at the distance of about 436,000 km, being the second farthest from the planet among its five major moons. Its orbital period is around 8.7 days, coincident with its rotational period. In other words, Titania is a synchronous or tidally locked satellite, with one face always pointing toward the planet.

Formation

Titania probably formed from an accretion disk that surrounded the planet just after its formation.

Titania consists of approximately equal amounts of ice and rock, and is likely differentiated into a rocky core and an icy mantle. A layer of liquid water may be present at the core–mantle boundary. The surface of Titania, which is relatively dark and slightly red in color, appears to have been shaped by both impacts and endogenic processes.

Atmosphere

The presence of carbon dioxide on the surface suggests that Titania may have a tenuous seasonal atmosphere of CO2. Other gases like nitrogen or methane are unlikely to be present, because the moon's weak gravity could not prevent them escaping into the space.

Exploration Status

So far the only close-up images of Titania have been from the Voyager 2 probe, which photographed the moon during its flyby of Uranus in January 1986.

No other spacecraft has ever visited the Uranian system or Titania, and no mission is planned in the foreseeable future.

Largest Moon of Neptune - Triton (7th Moon outwards from Neptune)

Discovery

Neptune has thirteen known moons. The largest of which is Triton, discovered by William Lassell on October 10, 1846, just 17 days after the discovery of Neptune itself.

Naming
Triton is named after the Greek sea god Triton, the son of Poseidon (the Greek god comparable to the Roman Neptune). The name was first proposed by Camille Flammarion in his 1880 book Astronomie Populaire, but it did not come into common use until at least the 1930s.


Voyager 2 photomosaic of Triton's sub-Neptunian hemisphere.



Triton is the only large moon in the Solar System with a retrograde orbit, which is an orbit in the opposite direction to its planet's rotation.

Stats

Diameter: 2,705 km

Semi-major axis: 354,759 km

Orbital Period: 5.88 days

Triton is the seventh largest moon in the Solar System, and is larger than the dwarf planets Pluto and Eris. Because of its retrograde orbit and composition similar to Pluto's, it is thought to have been captured from the Kuiper belt.

Capture from Kuiper belt

The proposed capture of Triton may explain several features of the Neptunian system, including the extremely eccentric orbit of Neptune's moon Nereid and the scarcity of moons as compared to the other gas giants.

Triton's initially eccentric orbit would have intersected orbits of irregular moons and disrupted those of smaller regular moons, dispersing them through gravitational interactions.

Two types of mechanisms have been proposed for Triton's capture.

In order to be gravitationally captured by a planet, a passing body must lose sufficient energy to be slowed down to a speed less than that required to escape. An early theory of how Triton may have been slowed was by collision with another object, either one that happened to be passing by Neptune (which is unlikely), or a moon or proto-moon in orbit around Neptune (which is more likely).

A more recent and now favored hypothesis suggests that, before its capture, Triton had a massive companion similar to Pluto's moon Charon with which it formed a binary. When the binary encountered Neptune, it interacted in such a way that orbital energy was transferred from Triton to its companion; the latter was expelled, while Triton became bound to Neptune.

This hypothesis is supported by several lines of evidence, including binaries being very common among the large Kuiper belt objects. The event was brief but gentle, saving Triton from collisional disruption. Events like this may have been common during the formation of Neptune, or later when it migrated outward.

Orbit

Triton takes as long to rotate on its axis as it does to make one orbit of Neptune; and therefore always keeps the same hemisphere pointed to Neptune.

Atmosphere

Triton has a surface of mostly frozen nitrogen, a mostly water ice crust, an icy mantle and a substantial core of rock and metal.

Triton is one of the few moons in the Solar System known to be geologically active. As a consequence, its surface is relatively young and has relatively few impact craters, with a complex geological history revealed in intricate and mysterious cryovolcanic and tectonic terrains. Part of its crust is dotted with geysers believed to erupt nitrogen.

Triton has a tenuous nitrogen atmosphere, with trace amounts of carbon monoxide and small amounts of methane near the surface. Like Pluto's atmosphere, the atmosphere of Triton is believed to have resulted from evaporation of nitrogen from the moon's surface.

The surface temperature is at least −237.6 °C because Triton's nitrogen ice is in the warmer, hexagonal crystalline state, and the phase transition between hexagonal and cubic nitrogen ice occurs at that temperature.

Largest Moon of Saturn - Titan (21st Moon outwards from Saturn)

Discovery

Titan was discovered in 1655 by Christiaan Huygens using a 57-millimeter objective lens on a refracting telescope of his own design.

Naming

The name Titan, and the names of all seven satellites of Saturn then known, come from John Herschel (son of William Herschel, discoverer of Mimas and Enceladus) in his 1847 publication Results of Astronomical Observations Made at the Cape of Good Hope. He suggested the names of the mythological Titans, sisters and brothers of Kronos, the Greek Saturn.

Stats

Titan is frequently described as a planet-like moon. Titan has a diameter roughly 50% larger than Earth's moon and is 80% more massive. It is the second-largest moon in the Solar System, after Jupiter's moon Ganymede, and it is larger by volume than the smallest planet, Mercury.

Diameter: 5,151 km

Semi-major axis: 1,221,930 km

Orbital Period: 15.95 days

Orbit

Titan takes as long to rotate on its axis as it does to make one orbit of Saturn; and therefore always keeps the same hemisphere pointed to Saturn.

Composition

Titan is primarily composed of water ice and rocky material. Much as with Venus prior to the Space Age, the dense, opaque atmosphere prevented understanding of Titan's surface until new information accumulated with the arrival of the Cassini–Huygens mission in 2004.

This includes the discovery of liquid hydrocarbon lakes in the satellite's polar regions. These are the only large, stable bodies of surface liquid known to exist anywhere other than Earth. The surface is geologically young; although mountains and several possible cryovolcanoes have been discovered, it is smooth and few impact craters have been discovered.

Atmosphere

The atmosphere of Titan is largely composed of nitrogen; minor components lead to the formation of methane and ethane clouds and nitrogen-rich organic smog. The climate — including wind and rain — creates surface features similar to those of Earth, such as sand dunes, rivers, lakes and seas (probably of liquid methane or ethane) and shorelines, and, like on Earth, is dominated by seasonal weather patterns.

Life?

With its liquids (both surface and subsurface) and robust nitrogen atmosphere, Titan is viewed as analogous to the early Earth, although at a much lower temperature.

The satellite has thus been cited as a possible host for microbial extraterrestrial life or, at least, as a prebiotic environment rich in complex organic chemistry. Researchers have suggested a possible underground liquid ocean might serve as a biotic environment.

It has also been suggested that a form of life may exist on the surface, using liquid methane as a medium instead of water; and anomalies in atmospheric composition have been reported which are consistent with the presence of such a life-form, but which could also be due to an exotic non-living chemistry.

Largest Moon in the Solar System - Ganymede (7th Moon outwards from Jupiter)

Discovery

Ganymede's discovery is credited to Galileo Galilei, who was the first to observe it on January 7, 1610. The satellite's name was soon suggested by astronomer Simon Marius, for the mythological Ganymede, cupbearer of the Greek gods and Zeus's lover.

Together with Io, Europa and Callisto, they are collectively known as Galilean satellites after the discover.





Stats

Ganymede is the largest moon in the Solar System and it is even 8% larger than that the planet Mercury. It also has the highest mass of all planetary satellites, with 2.02 times the mass of the Earth's moon.

Diameter: 5,262 km

Semi-major axis: 1,070,412 km

Orbital Period: 7.15 days

Ganymede completes an orbit in roughly seven days and participates in a 1:2:4 orbital resonance with the moons Europa and Io, respectively.

Ganymede takes as long to rotate on its axis as it does to make one orbit of Jupiter; and therefore always keeps the same hemisphere pointed to Jupiter.

Composition

Ganymede is composed of approximately equal amounts of silicate rock and water ice. It is a fully differentiated body with an iron-rich, liquid core. A saltwater ocean is believed to exist nearly 200 km below Ganymede's surface, sandwiched between layers of ice.

Its surface is composed of two main types of terrain. Dark regions, saturated with impact craters and dated to four billion years ago, cover about a third of the satellite. Lighter regions, crosscut by extensive grooves and ridges and only slightly less ancient, cover the remainder. The cause of the light terrain's disrupted geology is not fully known, but was likely the result of tectonic activity brought about by tidal heating.

Ganymede is the only satellite in the Solar System known to possess a magnetosphere, likely created through convection within the liquid iron core. The meager magnetosphere is buried within Jupiter's much larger magnetic field and connected to it through open field lines.

Atmosphere

Ganymede also has a thin oxygen atmosphere that includes O, O2, and possibly O3 (ozone). Atomic hydrogen is a minor atmospheric constituent. Whether the satellite has an ionosphere associated with its atmosphere is unresolved.

Life?

There is a distinct possibility that Ganymede's saltwater ocean could harbour life. If there are thermal vents on the floor of this saltwater ocean as there are on Earth, it is remotely possible that similar organisms to those which live around the vents on Earth could also survive there.

But because of the depth of the saltwater ocean (possibly 200 km) from the surface of Ganymede, we may never know whether life exist there.

Moons of Mars - Phobos and Deimos

Mars has two small moons, Phobos and Deimos, which are thought to be captured asteroids. Both satellites were discovered in 1877 by Asaph Hall, and are named after the characters Phobos (panic/fear) and Deimos (terror/dread) who, in Greek mythology, accompanied their father Ares, god of war, into battle. Ares was known as Mars to the Romans.

Color image of Phobos obtained by Mars Reconnaissance Orbiter on March 23, 2008.

Diameter: 22.2 km (27×21.6×18.8)

Semi-major axis: 9377 km

Orbital period: 7.66 h

Color image of Deimos taken by the Mars Reconnaissance Orbiter on February 21, 2009.

Diameter: 12.6 km (10×12×16)

Semi-major axis: 23 460 km

Orbital period: 30.35 h



Origin

The origin of the Martian moons is still controversial. Phobos and Deimos both have much in common with carbonaceous C-type asteroids, with spectra, albedo, and density very similar to those of C- or D-type asteroids. Based on their similarity, one hypothesis is that both moons may be captured main-belt asteroids.

Both moons have very circular orbits which lie almost exactly in Mars's equatorial plane, and hence a capture origin requires a mechanism for circularizing the initially highly eccentric orbit, and adjusting its inclination into the equatorial plane, most probably by a combination of atmospheric drag and tidal forces, although it is not clear that sufficient time is available for this to occur for Deimos.

Capture also requires dissipation of energy. The current Mars atmosphere is too thin to capture a Phobos-sized object by atmospheric braking. Geoffrey Landis has pointed out that the capture could have occurred if the original body was a binary asteroid that separated under tidal forces.

Phobos could be a second-generation Solar System object that coalesced in orbit after Mars formed, rather than forming concurrently out of the same birth cloud as Mars.

Another hypothesis is that Phobos and Deimos were formed by ejected materials, after a collision between Mars with a large planetesimal, similar to the prevailing theory for the origin of Earth's moon.

Observations of Phobos in the thermal infrared suggest a composition containing mainly phyllosilicates, which are well known from the surface of Mars.