Thursday, July 21, 2022

Our Solar System: Mercury Part II

 


Spin-orbit resonance


For many years it was thought that Mercury was synchronously tidally locked with the Sun, rotating once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces Earth. Radar observations in 1965 proved that the planet has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun. The eccentricity of Mercury's orbit makes this resonance stable—at perihelion, when the solar tide is strongest, the Sun is nearly still in Mercury's sky.


The rare 3:2 resonant tidal locking is stabilized by the variance of the tidal force along Mercury's eccentric orbit, acting on a permanent dipole component of Mercury's mass distribution. In a circular orbit there is no such variance, so the only resonance stabilized in such an orbit is at 1:1 (e.g., Earth–Moon), when the tidal force, stretching a body along the "center-body" line, exerts a torque that aligns the body's axis of least inertia (the "longest" axis, and the axis of the aforementioned dipole) to point always at the center. However, with noticeable eccentricity, like that of Mercury's orbit, the tidal force has a maximum at perihelion and therefore stabilizes resonances, like 3:2, ensuring that the planet points its axis of least inertia roughly at the Sun when passing through perihelion.


The original reason astronomers thought it was synchronously locked was that, whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury's rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury's 3:2 spin-orbit resonance, a solar day lasts about 176 Earth days. A sidereal day (the period of rotation) lasts about 58.7 Earth days.


Simulations indicate that the orbital eccentricity of Mercury varies chaotically from nearly zero (circular) to more than 0.45 over millions of years due to perturbations from the other planets. This was thought to explain Mercury's 3:2 spin-orbit resonance (rather than the more usual 1:1), because this state is more likely to arise during a period of high eccentricity. However, accurate modeling based on a realistic model of tidal response has demonstrated that Mercury was captured into the 3:2 spin-orbit state at a very early stage of its history, within 20 (more likely, 10) million years after its formation.


Numerical simulations show that a future secular orbital resonant perihelion interaction with Jupiter may cause the eccentricity of Mercury's orbit to increase to the point where there is a 1% chance that the planet will collide with Venus within the next five billion years.


Advance of perihelion


In 1859, the French mathematician and astronomer Urbain Le Verrier reported that the slow precession of Mercury's orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps instead a series of smaller 'corpuscules') might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation. (Other explanations considered included a slight oblateness of the Sun.) The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place faith in this possible explanation, and the hypothetical planet was named Vulcan, but no such planet was ever found.


The perihelion precession of Mercury is 5,600 arc-seconds (1.5556°) per century relative to Earth, or 574.10±0.65 arc-seconds per century relative to the inertial ICRF. Newtonian mechanics, taking into account all the effects from the other planets, predicts a precession of 5,557 arc-seconds (1.5436°) per century. In the early 20th century, Albert Einstein's general theory of relativity provided the explanation for the observed precession, by formalizing gravitation as being mediated by the curvature of space-time. The effect is small: just 42.98 arc-seconds per century for Mercury; it therefore requires a little over twelve million orbits for a full excess turn. Similar, but much smaller, effects exist for other Solar System bodies: 8.62 arc-seconds per century for Venus, 3.84 for Earth, 1.35 for Mars, and 10.05 for 1566 Icarus.


Habitability


According to NASA, Mercury is not a suitable planet for Earth-like life. It has a surface boundary exosphere instead of a layered atmosphere, extreme temperatures and high solar radiation. It is unlikely that any living beings can withstand those conditions.


Mercury may have been habitable, and perhaps that life forms, albeit likely primitive microorganisms, may have existed on the planet.


Observation


Mercury's apparent magnitude is calculated to vary between −2.48 (brighter than Sirius) around superior conjunction and +7.25 (below the limit of naked-eye visibility) around inferior conjunction. The mean apparent magnitude is 0.23 while the standard deviation of 1.78 is the largest of any planet. The mean apparent magnitude at superior conjunction is −1.89 while that at inferior conjunction is +5.93. Observation of Mercury is complicated by its proximity to the Sun, as it is lost in the Sun's glare for much of the time. Mercury can be observed for only a brief period during either morning or evening twilight.


Mercury can, like several other planets and the brightest stars, be seen during a total solar eclipse.


Like the Moon and Venus, Mercury exhibits phases as seen from Earth. It is "new" at inferior conjunction and "full" at superior conjunction. The planet is rendered invisible from Earth on both of these occasions because of its being obscured by the Sun, except its new phase during a transit.


Mercury is technically brightest as seen from Earth when it is at a full phase. Although Mercury is farthest from Earth when it is full, the greater illuminated area that is visible and the opposition brightness surge more than compensates for the distance. The opposite is true for Venus, which appears brightest when it is a crescent, because it is much closer to Earth than when gibbous.


Nonetheless, the brightest (full phase) appearance of Mercury is an essentially impossible time for practical observation, because of the extreme proximity of the Sun. Mercury is best observed at the first and last quarter, although they are phases of lesser brightness. The first and last quarter phases occur at greatest elongation east and west of the Sun, respectively. At both of these times Mercury's separation from the Sun ranges anywhere from 17.9° at perihelion to 27.8° at aphelion. At greatest western elongation, Mercury rises at its earliest before sunrise, and at greatest eastern elongation, it sets at its latest after sunset.


Mercury is more often and easily visible from the Southern Hemisphere than from the Northern. This is because Mercury's maximum western elongation occurs only during early autumn in the Southern Hemisphere, whereas its greatest eastern elongation happens only during late winter in the Southern Hemisphere. In both of these cases, the angle at which the planet's orbit intersects the horizon is maximized, allowing it to rise several hours before sunrise in the former instance and not set until several hours after sundown in the latter from southern mid-latitudes, such as Argentina and South Africa.


An alternate method for viewing Mercury involves observing the planet during daylight hours when conditions are clear, ideally when it is at its greatest elongation. This allows the planet to be found easily, even when using telescopes with 8 cm (3.1 in) apertures. However, great care must be taken to obstruct the Sun from sight because of the extreme risk for eye damage. This method bypasses the limitation of twilight observing when the ecliptic is located at a low elevation (e.g. on autumn evenings).


Ground-based telescope observations of Mercury reveal only an illuminated partial disk with limited detail. The first of two spacecraft to visit the planet was Mariner 10, which mapped about 45% of its surface from 1974 to 1975. The second is the MESSENGER spacecraft, which after three Mercury flybys between 2008 and 2009, attained orbit around Mercury on March 17, 2011, to study and map the rest of the planet.


The Hubble Space Telescope cannot observe Mercury at all, due to safety procedures that prevent its pointing too close to the Sun.


Because the shift of 0.15 revolutions in a year makes up a seven-year cycle (0.15 × 7 ≈ 1.0), in the seventh year Mercury follows almost exactly (earlier by 7 days) the sequence of phenomena it showed seven years before.


Observation history


Ancient astronomers


The earliest known recorded observations of Mercury are from the MUL.APIN tablets. These observations were most likely made by an Assyrian astronomer around the 14th century BC. The cuneiform name used to designate Mercury on the MUL.APIN tablets is transcribed as UDU.IDIM.GU\U4.UD ("the jumping planet"). Babylonian records of Mercury date back to the 1st millennium BC. The Babylonians called the planet Nabu after the messenger to the gods in their mythology.


The Greco-Egyptian astronomer Ptolemy wrote about the possibility of planetary transits across the face of the Sun in his work Planetary Hypotheses. He suggested that no transits had been observed either because planets such as Mercury were too small to see, or because the transits were too infrequent.

In ancient China, Mercury was known as "the Hour Star" (Chen-xing 辰星). It was associated with the direction north and the phase of water in the Five Phases system of metaphysics. Modern Chinese, Korean, Japanese and Vietnamese cultures refer to the planet literally as the "water star" (水星), based on the Five elements. Hindu mythology used the name Budha for Mercury, and this god was thought to preside over Wednesday. The god Odin (or Woden) of Germanic paganism was associated with the planet Mercury and Wednesday. The Maya may have represented Mercury as an owl (or possibly four owls; two for the morning aspect and two for the evening) that served as a messenger to the underworld.


In medieval Islamic astronomy, the Andalusian astronomer Abū Ishāq Ibrāhīm al-Zarqālī in the 11th century described the deferent of Mercury's geocentric orbit as being oval, like an egg or a pignon, although this insight did not influence his astronomical theory or his astronomical calculations. In the 12th century, Ibn Bajjah observed "two planets as black spots on the face of the Sun", which was later suggested as the transit of Mercury and/or Venus by the Maragha astronomer Qotb al-Din Shirazi in the 13th century. (Note that most such medieval reports of transits were later taken as observations of sunspots.)


In India, the Kerala school astronomer Nilakantha Somayaji in the 15th century developed a partially heliocentric planetary model in which Mercury orbits the Sun, which in turn orbits Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century.


Ground-based telescopic research


The first telescopic observations of Mercury were made by Galileo in the early 17th century. Although he observed phases when he looked at Venus, his telescope was not powerful enough to see the phases of Mercury. In 1631, Pierre Gassendi made the first telescopic observations of the transit of a planet across the Sun when he saw a transit of Mercury predicted by Johannes Kepler. In 1639, Giovanni Zupi used a telescope to discover that the planet had orbital phases similar to Venus and the Moon. The observation demonstrated conclusively that Mercury orbited around the Sun.


A rare event in astronomy is the passage of one planet in front of another (occultation), as seen from Earth. Mercury and Venus occult each other every few centuries, and the event of May 28, 1737 is the only one historically observed, having been seen by John Bevis at the Royal Greenwich Observatory. The next occultation of Mercury by Venus will be on December 3, 2133.


The difficulties inherent in observing Mercury mean that it has been far less studied than the other planets. In 1800, Johann Schröter made observations of surface features, claiming to have observed 20-kilometer-high (12 mi) mountains. Friedrich Bessel used Schröter's drawings to erroneously estimate the rotation period as 24 hours and an axial tilt of 70°. In the 1880s, Giovanni Schiaparelli mapped the planet more accurately, and suggested that Mercury's rotational period was 88 days, the same as its orbital period due to tidal locking. This phenomenon is known as synchronous rotation. The effort to map the surface of Mercury was continued by Eugenios Antoniadi, who published a book in 1934 that included both maps and his own observations. Many of the planet's surface features, particularly the albedo features, take their names from Antoniadi's map.


In June 1962, Soviet scientists at the Institute of Radio-engineering and Electronics of the USSR Academy of Sciences, led by Vladimir Kotelnikov, became the first to bounce a radar signal off Mercury and receive it, starting radar observations of the planet. Three years later, radar observations by Americans Gordon H. Pettengill and Rolf B. Dyce, using the 300-meter Arecibo radio telescope in Puerto Rico, showed conclusively that the planet's rotational period was about 59 days. The theory that Mercury's rotation was synchronous had become widely held, and it was a surprise to astronomers when these radio observations were announced. If Mercury were tidally locked, its dark face would be extremely cold, but measurements of radio emission revealed that it was much hotter than expected. Astronomers were reluctant to drop the synchronous rotation theory and proposed alternative mechanisms such as powerful heat-distributing winds to explain the observations.


Italian astronomer Giuseppe Colombo noted that the rotation value was about two-thirds of Mercury's orbital period, and proposed that the planet's orbital and rotational periods were locked into a 3:2 rather than a 1:1 resonance. Data from Mariner 10 subsequently confirmed this view. This means that Schiaparelli's and Antoniadi's maps were not "wrong". Instead, the astronomers saw the same features during every second orbit and recorded them, but disregarded those seen in the meantime, when Mercury's other face was toward the Sun, because the orbital geometry meant that these observations were made under poor viewing conditions.


Ground-based optical observations did not shed much further light on Mercury, but radio astronomers using interferometry at microwave wavelengths, a technique that enables removal of the solar radiation, were able to discern physical and chemical characteristics of the subsurface layers to a depth of several meters. Not until the first space probe flew past Mercury did many of its most fundamental morphological properties become known. Moreover, recent technological advances have led to improved ground-based observations. In 2000, high-resolution lucky imaging observations were conducted by the Mount Wilson Observatory 1.5 meter Hale telescope. They provided the first views that resolved surface features on the parts of Mercury that were not imaged in the Mariner 10 mission. Most of the planet has been mapped by the Arecibo radar telescope, with 5 km (3.1 mi) resolution, including polar deposits in shadowed craters of what may be water ice.


Research with space probes


Reaching Mercury from Earth poses significant technical challenges, because it orbits so much closer to the Sun than Earth. A Mercury-bound spacecraft launched from Earth must travel over 91 million kilometers (57 million miles) into the Sun's gravitational potential well. Mercury has an orbital speed of 47.4 km/s (29.5 mi/s), whereas Earth's orbital speed is 29.8 km/s (18.5 mi/s). Therefore, the spacecraft must make a large change in velocity (delta-v) to get to Mercury and then enter orbit, as compared to the delta-v required for, say, Mars planetary missions.


The potential energy liberated by moving down the Sun's potential well becomes kinetic energy, requiring a delta-v change to do anything other than pass by Mercury. Some portion of this delta-v budget can be provided from a gravity assist during one or more fly-bys of Venus. To land safely or enter a stable orbit the spacecraft would rely entirely on rocket motors. Aerobraking is ruled out because Mercury has a negligible atmosphere. A trip to Mercury requires more rocket fuel than that required to escape the Solar System completely. As a result, only three space probes have visited it so far. A proposed alternative approach would use a solar sail to attain a Mercury-synchronous orbit around the Sun.


Mariner 10


The first spacecraft to visit Mercury was NASA's Mariner 10 (1974–1975). The spacecraft used the gravity of Venus to adjust its orbital velocity so that it could approach Mercury, making it both the first spacecraft to use this gravitational "slingshot" effect and the first NASA mission to visit multiple planets. Mariner 10 provided the first close-up images of Mercury's surface, which immediately showed its heavily cratered nature, and revealed many other types of geological features, such as the giant scarps that were later ascribed to the effect of the planet shrinking slightly as its iron core cools. Unfortunately, the same face of the planet was lit at each of Mariner 10's close approaches. This made close observation of both sides of the planet impossible, and resulted in the mapping of less than 45% of the planet's surface.


The spacecraft made three close approaches to Mercury, the closest of which took it to within 327 km (203 mi) of the surface. At the first close approach, instruments detected a magnetic field, to the great surprise of planetary geologists—Mercury's rotation was expected to be much too slow to generate a significant dynamo effect. The second close approach was primarily used for imaging, but at the third approach, extensive magnetic data were obtained. The data revealed that the planet's magnetic field is much like Earth's, which deflects the solar wind around the planet. For many years after the Mariner 10 encounters, the origin of Mercury's magnetic field remained the subject of several competing theories.


On March 24, 1975, just eight days after its final close approach, Mariner 10 ran out of fuel. Because its orbit could no longer be accurately controlled, mission controllers instructed the probe to shut down. Mariner 10 is thought to be still orbiting the Sun, passing close to Mercury every few months.


MESSENGER


A second NASA mission to Mercury, named MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging), was launched on August 3, 2004. It made a fly-by of Earth in August 2005, and of Venus in October 2006 and June 2007 to place it onto the correct trajectory to reach an orbit around Mercury. A first fly-by of Mercury occurred on January 14, 2008, a second on October 6, 2008, and a third on September 29, 2009. Most of the hemisphere not imaged by Mariner 10 was mapped during these fly-bys. The probe successfully entered an elliptical orbit around the planet on March 18, 2011. The first orbital image of Mercury was obtained on March 29, 2011. The probe finished a one-year mapping mission, and then entered a one-year extended mission into 2013. In addition to continued observations and mapping of Mercury, MESSENGER observed the 2012 solar maximum.


The mission was designed to clear up six key issues: Mercury's high density, its geological history, the nature of its magnetic field, the structure of its core, whether it has ice at its poles, and where its tenuous atmosphere comes from. To this end, the probe carried imaging devices that gathered much-higher-resolution images of much more of Mercury than Mariner 10, assorted spectrometers to determine abundances of elements in the crust, and magnetometers and devices to measure velocities of charged particles. Measurements of changes in the probe's orbital velocity were expected to be used to infer details of the planet's interior structure. MESSENGER's final maneuver was on April 24, 2015, and it crashed into Mercury's surface on April 30, 2015. The spacecraft's impact with Mercury occurred near 3:26 pm EDT on April 30, 2015, leaving a crater estimated to be 16 m (52 ft) in diameter.


BepiColombo


The European Space Agency and the Japanese Space Agency developed and launched a joint mission called BepiColombo, which will orbit Mercury with two probes: one to map the planet and the other to study its magnetosphere. Launched on October 20, 2018, BepiColombo is expected to reach Mercury in 2025. It will release a magnetometer probe into an elliptical orbit, then chemical rockets will fire to deposit the mapper probe into a circular orbit. Both probes will operate for one terrestrial year. The mapper probe carries an array of spectrometers similar to those on MESSENGER, and will study the planet at many different wavelengths including infrared, ultraviolet, X-ray and gamma ray. BepiColombo conducted the first of its six planned Mercury flybys on October 1, 2021.


Notes


In astronomy, the words "rotation" and "revolution" have different meanings. "Rotation" is the turning of a body about an axis that passes through the body, as in "Earth rotates once a day." "Revolution" is motion around a centre that is external to the body, usually in orbit, as in "Earth takes a year for each revolution around the Sun." The verbs "rotate" and "revolve" mean doing rotation and revolution, respectively.


Pluto was considered a planet from its discovery in 1930 to 2006, but after that it has been reclassified as a dwarf planet. Pluto's orbital eccentricity is greater than Mercury's. Pluto is also smaller than Mercury, but was thought to be larger until 1976.


The Sun's total angular displacement during its apparent retrograde motion as seen from the surface of Mercury is ~1.23°, while the Sun's angular diameter when the apparent retrograde motion begins and ends is ~1.71°, increasing to ~1.73° at perihelion (midway through the retrograde motion).


It is important to be clear about the meaning of 'closeness'. In the astronomical literature, the term 'closest planets' often means 'the two planets that approach each other most closely'. In other words, the orbits of the two planets approach each other most closely. However, this does not mean that the two planets are closest over time. For example, essentially because Mercury is closer to the Sun than Venus, Mercury spends more time in proximity to Earth; it could, therefore, be said that Mercury is the planet that is 'closest to Earth when averaged over time'. However, using this time-average definition of 'closeness'—as noted above—it turns out that Mercury is the closest planet to all other planets in the solar system. For that reason, arguably, the proximity-definition is not particularly helpful. An episode of the BBC Radio 4 programme 'More or Less' explains the different notions of proximity well.


Some sources precede the cuneiform transcription with "MUL". "MUL" is a cuneiform sign that was used in the Sumerian language to designate a star or planet, but it is not considered part of the actual name. The "4" is a reference number in the Sumero–Akkadian transliteration system to designate which of several syllables a certain cuneiform sign is most likely designating.

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