Miranda (moon)

Miranda is the smallest and innermost of Uranus's five round satellites. It was discovered by Gerard Kuiper on 16 February 1948 at McDonald Observatory in Texas, and named after Miranda from William Shakespeare's play The Tempest. Like the other large moons of Uranus, Miranda orbits close to its planet's equatorial plane. Because Uranus orbits the Sun on its side, Miranda's orbit is nearly perpendicular to the ecliptic and shares Uranus's extreme seasonal cycle.

At just in diameter, Miranda is one of the smallest closely observed objects in the Solar System that might be in hydrostatic equilibrium (spherical under its own gravity), and its total surface area is roughly equal to that of the U.S. state of Texas. The only close-up images of Miranda are from the Voyager 2 probe, which made observations of Miranda during its Uranus flyby in January 1986. During the flyby, Miranda's southern hemisphere pointed towards the Sun, so only that part was studied.

Miranda probably formed from an accretion disc that surrounded the planet shortly after its formation and, like other large moons, it is likely differentiated, with an inner core of rock surrounded by a mantle of ice. Miranda has one of the most extreme and varied topographies of any object in the Solar System, including Verona Rupes, a roughly scarp that may be the highest cliff in the Solar System, and chevron-shaped tectonic features called coronae. The origin and evolution of this varied geology, the most of any Uranian satellite, are still not fully understood, and multiple hypotheses exist regarding Miranda's evolution.

Discovery and name

left|thumb|upright|Gerard P. Kuiper, discoverer of Miranda

Miranda was discovered on 16 February 1948 by planetary astronomer Gerard Kuiper using the McDonald Observatory's Otto Struve Telescope. Its motion around Uranus was confirmed on 1 March 1948. It was the first satellite of Uranus discovered in nearly 100 years. Kuiper elected to name the object "Miranda" after the character in Shakespeare's The Tempest, because the four previously discovered moons of Uranus, Ariel, Umbriel, Titania, and Oberon, had all been named after characters of Shakespeare or Alexander Pope. However, the previous moons had been named specifically after fairies, whereas Miranda was a human. Subsequently discovered satellites of Uranus were named after characters from Shakespeare and Pope, whether fairies or not. The moon is also designated Uranus V.

Planetary moons other than Earth's were never given symbols in the astronomical literature. Denis Moskowitz, a software engineer who designed most of the dwarf planet symbols, proposed an M (the initial of Miranda) combined with the low globe of Jérôme Lalande's Uranus symbol as the symbol of Miranda (16px). This symbol is not widely used.

Orbit

Of Uranus's five round satellites, Miranda orbits closest to it, at roughly 129 000 km from the surface; about a quarter again as far as its most distant ring. It is the round moon that has the smallest orbit around a major planet. Its orbital period is 34 hours and, like that of the Moon, is synchronous with its rotation period, which means it always shows the same face to Uranus, a condition known as tidal locking. Miranda's orbital inclination (4.34°) is unusually high for a body so close to its planet – roughly ten times that of the other major Uranian satellites, and 73 times that of Oberon. The reason for this is still uncertain; there are no mean-motion resonances between the moons that could explain it, leading to the hypothesis that the moons occasionally pass through secondary resonances, which at some point in the past led to Miranda being locked for a time into a 3:1 resonance with Umbriel, before chaotic behaviour induced by the secondary resonances moved it out again. In the Uranian system, due to the planet's lesser degree of oblateness and the larger relative size of its satellites, escape from a mean-motion resonance is much easier than for satellites of Jupiter or Saturn.

Observation and exploration

thumb|Miranda, Uranus, and its other moons photographed by the [[Cerro Paranal Observatory.]]

Miranda's apparent magnitude is +16.6, making it invisible to many amateur telescopes. Virtually all known information regarding its geology and geography was obtained during the flyby of Uranus made by Voyager 2 on 24 January 1986, The closest approach of Voyager 2 to Miranda was —significantly less than the distances to all other Uranian moons. Of all the Uranian satellites, Miranda had the most visible surface. The discovery team had expected Miranda to resemble Mimas, and found themselves at a loss to explain the moon's unique geography in the 24-hour window before releasing the images to the press. In 2017, as part of its Planetary Science Decadal Survey, NASA evaluated the possibility of an orbiter to return to Uranus some time in the 2020s. Uranus was the preferred destination over Neptune due to favourable planetary alignments meaning shorter flight times.

Composition and internal structure

thumb|Miranda compared to [[1 Ceres and the Moon]]

At 1.15 g/cm3, Miranda is the least dense of Uranus's round satellites. That density suggests a composition of more than 60% water ice. Miranda's surface may be mostly water ice, though it is far rockier than its corresponding satellites in the Saturn system, indicating that heat from radioactive decay may have led to internal differentiation, allowing silicate rock and organic compounds to settle in its interior. Miranda is too small for any internal heat to have been retained over the age of the Solar System.

Precisely how a body as small as Miranda could have enough internal energy to produce the myriad of geological features seen on its surface has not been established with certainty, though the currently favoured hypothesis is that it was driven by tidal heating during a past time when it was in 3:1 orbital resonance with Umbriel. The resonance would have increased Miranda's orbital eccentricity to 0.1, and generated tidal friction due to the varying tidal forces from Uranus. As Miranda approached Uranus, tidal force increased; as it retreated, tidal force decreased, causing flexing that would have warmed Miranda's interior by 20 K, enough to trigger melting. The period of tidal flexing could have lasted for up to 100 million years. Also, if clathrate existed within Miranda, as has been hypothesised for the satellites of Uranus, it may have acted as an insulator, since it has a lower conductivity than water, increasing Miranda's temperature still further. Miranda may have also once been in a 5:3 orbital resonance with Ariel, which would have also contributed to its internal heating. However, the maximum heating attributable to the resonance with Umbriel was likely about three times greater.

Geography

Miranda has a unique surface. Among the geological structures that cover it are fractures, faults, valleys, craters, ridges, gorges, depressions, cliffs, and terraces. This moon is a mosaic of highly varied zones. Some areas are older and darker. As such, they bear numerous impact craters, as is expected of a small inert body. (all named in reference to works by William Shakespeare)

! Name !! Type !! Length (diameter) (km) !! Latitude (°) !! Longitude (°) !! Origin of the name

| Mantua Regio

| rowspan="4"|Regiones|| 399 || −39.6 || 180.2 ||Italian region of part of the plot of The Two Gentlemen of Verona

| Ephesus Regio || 225 || −15 || 250 ||The twins' house in Turkey in The Comedy of Errors

| Sicilia Regio || 174 || −30 || 317.2 ||Italian region of the plot of The Winter's Tale

| Dunsinane Regio || 244 || −31.5 || 11.9 || Hill in Scotland at which Macbeth is defeated

| Arden Corona

| rowspan="3" | Coronae|| 318 || −29.1 || 73.7 || Forest in England where the plot of As You Like It takes place

| Elsinore Corona || 323 || −24.8 || 257.1 || Castle in Denmark that is the setting for Hamlet

| Inverness Corona || 234 || −66.9 || 325.7 || Macbeth's castle in Scotland

| Argier Rupes

| rowspan="2"|Rupes|| 141 || −43.2 || 322.8 || Region of France where the beginning of the plot of The Tempest takes place

| Verona Rupes || 116 || −18.3 || 347.8 || Italian city where the plot of Romeo and Juliet takes place

| Alonso

| rowspan="7" | Impact crater || 25 || −44 || 352.6 || King of Naples in The Tempest

| Ferdinand || 17 || −34.8 || 202.1 || Son of the King of Naples in The Tempest

| Francisco || 14 || −73.2 || 236 || A lord of Naples in The Tempest

| Gonzalo || 11 || −11.4 || 77 || An honest old councilor from Naples in The Tempest

| Prospero || 21 || −32.9 || 329.9 || Legitimate Duke of Milan in The Tempest

| Stephano || 16 || −41.1 || 234.1 || A drunken butler in The Tempest

| Trinculo || 11 || −63.7 || 163.4 || A jester in The Tempest

Regiones

The regiones identified on the images taken by the Voyager 2 probe are named "Mantua Regio", "Ephesus Regio", "Sicilia Regio", and "Dunsinane Regio". a surface with a relatively high albedo, and a series of gorges which extend northwards from a point near the pole. At a latitude of around −55°, north-south oriented gorges tend to intersect with others, which follow an east-west direction. The low number of impact craters indicates that Inverness is the youngest among the three coronae observed on the surface of Miranda.

Arden Corona

Arden Corona, present in the front hemisphere of Miranda, extends over approximately from east to west. The other dimension, however, remains unknown because the terrain extended beyond the terminator (on the hemisphere plunged into night) when Voyager 2 photographed it. The outer margin of this corona forms parallel and dark bands which surround in gentle curves a more clearly rectangular core at least wide. The overall effect has been described as an ovoid of lines. The interior and belt of Arden show very different morphologies. The interior topography appears regular and soft. It is also characterized by a mottled pattern resulting from large patches of relatively bright material scattered over a generally dark surface. The stratigraphic relationship between the light and dark marks could not be determined from the images provided by Voyager 2. The area at the margin of Arden is characterized by concentric albedo bands which extend from the western end of the crown where they intersect crateriform terrain (near 40° longitude) and on the side east, where they extend beyond the, in the northern hemisphere (near 110° longitude). The contrasting albedo bands are composed of outer fault scarp faces. The age of a crater does not give an indication of the date of formation of the terrain it marked. On the other hand, this date depends on the number of craters present on a site, regardless of their age. The more impact craters a terrain has, the older it is. Scientists use these as "planetary chronometers"; they count observed craters to date the formation of the terrain of inert natural satellites devoid of atmospheres, such as Callisto.

No multiple ring crater, nor any complex crater with a central peak, has been observed on Miranda.

The density of impact craters could be established for different areas of Inverness, and made it possible to establish the age of each. Considering these measurements, the entire geological formation was formed in a relative unit of time. However, other observations make it possible to establish that the youngest zone, within this crown, is the one which separates the "chevron", from Argier Rupes. The two zones of the crown seem to have formed during the same geological period, but other geological elements suggest that the perimeter of Elsinore is younger than its core. However, it is the anti-Uranian hemisphere which is densest in craters. This situation could be explained by a past event having caused a reorientation of Miranda's axis of rotation by 90° compared to that which is currently known. This sub-nebula either existed around Uranus for some period of time after its formation, or was created following a cosmic impact which would have given its great obliquity to the axis of rotation of Uranus. It seems that the most recent geological formations only date back a few hundred million years. Some scientists even speak of several cycles of collision and re-accretion of the moon. This geological hypothesis was depreciated in 2011 in favor of hypotheses involving Uranian tidal forces. These would have pulled and turned the materials present under Inverness and Arden to create fault scarps. The stretching and distortion caused by Uranus's gravity, which alone could have provided the heat source necessary to power these uprisings.

The oldest known regions on the surface of Miranda are cratered plains such as Sicilia Regio and Ephesus Regio. The formation of these terrains follows the accretion of the moon then its cooling. Unlike those observed on Jupiter's moon Io, these orbital resonance phenomena between Miranda and Ariel could not lead to a stable capture of the small moon. By successively escaping several orbital resonances, Miranda alternated phases of heating and cooling. Another explanation proposed for the formation of these two coronae would be the product of a diapir which would have formed in the heart of the moon. On this occasion Miranda would have at least partially differentiated. Considering the size and position of these coronae, it is possible that their formation contributed to changing the moment of inertia of the moon. It is probable that these different geological episodes followed one another without interruption.

The phenomena of orbital resonances, and mainly that associated with Umbriel, but also, to a lesser extent, that of Ariel, would have had a significant impact on the orbital eccentricity of Miranda, and would also have contributed to the internal heating and geological activity of the moon. The whole would have induced convection movements in its substrate and allowed the start of planetary differentiation. At the same time, these phenomena would have only slightly disturbed the orbits of the other moons involved, which are more massive than Miranda. However, Miranda's surface may appear too tortured to be the sole product of orbital resonance phenomena.

After Miranda escaped from this resonance with Umbriel, through a mechanism that likely moved the moon into its current, abnormally high orbital tilt, the eccentricity would have been reduced. The tidal forces would then have erased the eccentricity and the temperature at the heart of the moon. This would have allowed it to regain a spherical shape, without allowing it to erase the impressive geological artifacts such as Verona Rupes.