# Keynote lectures/Wanderers

(Redirected from Wanderers)
The hypothesis of Andreas Cellarius shows the planetary motions in eccentric and epicyclical orbits. Credit: Andreas Cellarius.

A wanderer may move in a leisurely, casual, or aimless way.

## Astronomy

Usually the wanderers are the seven classical planets, Saturn, Jupiter, the Moon, the Sun, Mercury, Mars, and Venus. Additional wanderers may also have existed in ancient times, such as the Earth's pole stars.

## Planets

With the exception of the Sun (Helios) and the Moon (Selene), none of the other classical planets apparently had a visible disk. Yet, whenever they were sighted, they were more than noteworthy, due to their brightness and the fact that they moved relative to the other stars. (The word "planet" comes from the Greek planetes, a wanderer.) This suggests that they were capable of generating something that in turn caused harm when it fell to Earth.

## Precessions

This is a composite image of Mercury taken by the MESSENGER probe. Credit: NASA-APL.

Precession of orbital axes in the plane of the ecliptic is a common occurrence and easily described using tidal effects of other planets of massive bodies in the ecliptic.

A vertical precession describes precession of orbital axes out of and back across the ecliptic. These are not so easily explained by the presence of other massive bodies in the plane of the ecliptic.

## Inclinations

The graphs show the initial (e) planetary orbital elements taken from the Development Ephemeris of JPL, DE245 (cf. Standish 1990) and the final integration results (m). Credit: Takashi Ito and Kiyotaka Tanikawa.
The diagram describes the parameters associated with orbital inclination (i). Credit: Lasunncty.

Def. "[t]he angle of intersection of a reference plane"[1] is called an inclination.

"The orbital inclination [(i) of Mercury] varies between 5° and 10° with a 106 yr period with smaller amplitude variations with a period of about 105 yr."[2]

"Inclination of [Mercury's] orbit to [the] ecliptic [is] 5.15° [on or about July 20, 2010.]"[3]

"Mercury Mean Orbital Elements (J2000) [...] Orbital inclination (deg) 7.00487 [...] Reference Date : 12:00 UT 1 Jan 2000 (JD 2451545.0) [...] Last Updated: 01 July 2013, DRW [David R. Williams]."[4]

"The next largest [orbital inclination as of September 13, 2006,] is Mercury which orbits 7° from Earth."[5]

"Mercury [...] Inclination [is] 7.00559432 degrees [as of March 20, 2014]."[6]

The graphs at the top show the initial planetary orbital elements for the planet Mercury taken from the Development Ephemeris of JPL, DE245 (cf. Standish 1990) in the left portion marked (e) and the final integration results on the right (m).[7]

The projected time spans from the integrations suggest that conditions within the solar system for the recorded data set are very stable.

## Orbital poles

This is a snapshot of the planetary orbital poles. Credit: Urhixidur.

An orbital pole is either end of an imaginary line running through the center of an orbit perpendicular to the orbital plane, projected onto the celestial sphere. It is similar in concept to a celestial pole but based on the planet's orbit instead of the planet's rotation.

The north orbital pole of a celestial body is defined by the right-hand rule: If you curve the fingers of your right hand along the direction of orbital motion, with your thumb extended parallel to the orbital axis, the direction your thumb points is defined to be north.

At right is a snapshot of the planetary orbital poles.[8] The field of view is about 30°. The yellow dot in the centre is the Sun's North pole. Off to the side, the orange dot is Jupiter's orbital pole. Clustered around it are the other planets: Mercury in pale blue (closer to the Sun than to Jupiter), Venus in green, the Earth in blue, Mars in red, Saturn in violet, Uranus in grey partly underneath Earth and Neptune in lavender. Dwarf planet Pluto is the dotless cross off in Cepheus.

## Orbital decay

Orbital decay is the process of prolonged reduction in the altitude of a satellite's orbit. This can be due to drag produced by an atmosphere [frequent collisions between the satellite and surrounding air molecules]. The drag experienced by the object is larger in the case of increased solar activity, because it heats and expands the upper atmosphere.

## Venus

Venus is the Evening Star, next to a crescent moon. Credit: Shakil Mustafa.
Planet Venus rises above the horizon at dawn. Credit: DarrenBaker.
The "Venus transit" -- the apparent crossing of our planetary neighbor in front of the Sun -- was captured from the unique perspective of NASA's Sun-observing TRACE spacecraft. Credit: NASA/LMSAL.
The image of the Venus transit was taken with a home-made solar filter from baader solar film. Credit: Brocken Inaglory.
The photograph shows a conjunction between Venus and Jupiter. Credit: Geraint Smith.
The planet Venus orbits just over 13 times for every 8 orbits of the Earth, creating a pentagrammic pattern of inferior conjunctions. Credit: Tomruen.

Some objects seem to wander around in the night sky relative to many of the visual points of light. At least one occasionally is present in the early morning [on the left] before sunrise as the Morning Star and after sunset as the Evening Star [on the right], the planet Venus. These wanderers and related objects are subjects for observational astronomy and some are meteors.

By observing many of the wandering lights in the night sky, an occasional occultation of the light of one astronomical object may occur by the intervention of another along a closer astronomical stratum.

An occultation of Venus by the Moon occurred "on the afternoon of October 14", 1874.[9] An earlier such occultation "occurred on May 23, 1587, and is thus recorded by [Tycho Brahe] in his Historia Celestis"[9]. "Thomas Street, in his Astronomia Carolina (A.D. 1661), mentions three occultations by Venus, being two occasions when the planet covered Regulus, and once when there was an occultation of Mars by Venus."[9] "[Thomas Street] describes [the occultation of Mars by Venus] as follows: "1590,. Oct. 2nd, 16h. 24s. Michael Mœstlin observed ♂ eclipsed by ♀.""[9]

"NASA joined the world today in viewing a rare celestial event, one not seen by any person now alive. The "Venus transit" -- the apparent crossing of our planetary neighbor in front of the Sun -- was captured from the unique perspective of NASA's Sun-observing TRACE spacecraft."[10]

"The last "Venus transit" occurred more than a century ago, in 1882, and was used to compute the distance from the Earth to the Sun."[10]

"If people miss the June 8 Venus transit, they will have another chance in 2012 (June 6) [imaged third down on the right]. After that, there will not be another Venus transit until 2117 (December 11)."[10]

A conjunction between Venus and Jupiter is shown in the second image down on the left.

The fourth image down on the right is a diagram of inferior conjunctions of Venus with Earth.

"The planet Venus orbits just over 13 times for every 8 orbits of the Earth, creating a pentagrammic pattern of inferior conjunctions. Each successive inferior conjunction occurs after about 1.6 Earth years and therefore shifts about 144 degrees in the direction opposite the Earth's orbital motion. During each cycle of 8 Earth years, the pentagram precesses about 1.5 degrees in the direction of Earth's orbital motion, reflecting the fact that the Earth:Venus orbital ratio is an approximate ('near') rather than a perfect orbital resonance."[11]

## D asteroids

"Two comets observed at low activity (visible nuclei) also have properties more consistent with D asteroids than any other class (very low reported geometric albedos of 0.02 and red colors)."[12]

## Q asteroids

lf "planetary encounters are important, the distribution of Q-type asteroids in the planet-crossing space should show a correlation with the perihelion distance, exactly as we have found here."[13]

## Earth crossers

The close approach of apollo asteroid 2007 VK184 was in May 2014. Credit: Osamu Ajiki (AstroArts) and Ron Baalke (JPL).

EC denotes Earth-crossing.[14]

"50 % of the MB Mars-crossers [MCs] become ECs within 59.9 Myr and [this] contribution ... dominates the production of ECs".[14]

## Mars crossers

"50 % of the MB Mars-crossers [MCs] become ECs within 59.9 Myr".[14]

## Centaurs

Def. an "icy planetoid that orbits the Sun between Jupiter and Neptune"[15] is called a Centaur.

"The recent investigation of the orbital distribution of Centaurs (Emel’yanenko et al., 2005) showed that there are two dynamically distinct classes of Centaurs, a dominant group with semimajor axes a > 60 AU and a minority group with a < 60 AU."[16] "[T]he intrinsic number of such objects is roughly an order of magnitude greater than that for a<60 AU".[16]

## Vesta

The angular resolution of the naked eye is about 1′; however, some people have sharper vision than that. There is anecdotal evidence that people had seen the Galilean moons of Jupiter before telescopes were invented.[17] Of similar magnitude, Uranus and Vesta had most probably been seen but could not be recognized as planets because they appear so faint even at maximum brightness that their motion could not be detected.

## Solar systems

For the first time, astronomers have been able to directly follow the motion of an exoplanet as it moves to the other side of its host star. Credit: ESO/A.-M. Lagrange.

"For the first time [as shown in the image at the right], astronomers have been able to directly follow the motion of an exoplanet as it moves to the other side of its host star. The planet has the smallest orbit so far of all directly imaged exoplanets, lying as close to its host star as Saturn is to the Sun."[18]

"The team of astronomers used the NAOS-CONICA instrument (or NACO), mounted on one of the 8.2-metre Unit Telescopes of ESO's Very Large Telescope (VLT), to study the immediate surroundings of Beta Pictoris in 2003, 2008 and 2009. In 2003 a faint source inside the disc was seen, but it was not possible to exclude the remote possibility that it was a background star. In new images taken in 2008 and spring 2009 the source had disappeared! The most recent observations, taken during autumn 2009, revealed the object on the other side of the disc after having been hidden either behind or in front of the star. This confirmed that the source indeed was an exoplanet and that it was orbiting its host star. It also provided insights into the size of its orbit around the star."[18]

"The above composite shows the reflected light on the dust disc in the outer part, as observed in 1996 with the ADONIS instrument on ESO's 3.6-metre telescope. In the central part, the observations of the planet obtained in 2003 and autumn 2009 with NACO are shown. The possible orbit of the planet is also indicated, albeit with the inclination angle exaggerated."[18]

## Exocomets

An exocomet, or extrasolar comet, is a comet outside the Solar System, which includes interstellar comets and those that orbit stars other than the Sun. The first exocomets were detected in 1987[19][20] around Beta Pictoris, a very young A-type main-sequence star. There are now a total of 11 stars around which exocomets have been observed or suspected.[21][22][23][24]

All discovered exocometary systems (Beta Pictoris, HR 10,[21] HR 2174 = HD 42111,[22] 49 Ceti, 5 Vulpeculae, 2 Andromedae, HD 21620, HD 110411 = rho Virginis,[23][25] and more recently HD 172555[24]) are around very young A-type stars. And, HD 145964 is spectral type B9V according to SIMBAD.

## Interstellar comets

"If other planetary systems exist and have generated Oort clouds in a similar fashion, then there should be a substantial population of comets in interstellar space, and our solar system should occasionally encounter these interstellar wanderers."[26]

## Rogue planets

A rogue planet — also known as an interstellar planet, nomad planet, free-floating planet or orphan planet — is a planetary-mass object which has either been ejected from its system or was never gravitationally bound to any star, brown dwarf or other such object, and that therefore orbits the galaxy directly.[27][28][29] Astronomers agree that either way, the definition of planet should depend on its current observable state and not its origin.

Larger planetary-mass objects which were not ejected, but have always been free-floating, are thought to have formed in a similar way to stars, and the IAU has proposed that those objects be called sub-brown dwarfs[30] (an example of this is Cha 110913-773444, which may be an ejected rogue planet or may have formed on its own and be a sub-brown dwarf).[31] The closest rogue planet to Earth yet discovered, CFBDSIR 2149-0403, is around 100 light years away.[32]

When a planetary-sized object passes in front of a background star, its gravitational field causes a momentary increase in the visible brightness of the background star. This is known as microlensing. Astrophysicist Takahiro Sumi of Osaka University in Japan and colleagues, who form the Microlensing Observations in Astrophysics (MOA) and the Optical Gravitational Lensing Experiment (OGLE) collaborations, carried out a study of microlensing which they published in 2011. They observed 50 million stars in our galaxy using the 1.8 meter MOA-II telescope at New Zealand's Mount John Observatory and the 1.3 meter University of Warsaw telescope at Chile's Las Campanas Observatory. They found 474 incidents of microlensing, ten of which were brief enough to be planets of around Jupiter's size with no associated star in the immediate vicinity. The researchers estimated from their observations that there are nearly two free-floaters for every star in our galaxy.[33][34][35] Other estimations suggest a much larger number, up to 100,000 times more free-floating planets than stars in our Milky Way.[36]

## Contact binaries

A contact binary is a binary star system whose component stars are so close that they touch each other or have merged to share their gaseous envelopes. Almost all known contact binary systems are eclipsing binaries;[37] eclipsing contact binaries are known as W Ursae Majoris variables, after their type star, W Ursae Majoris.[38]

## Zero-age contacts

“Zero-age contact must be a consequence of star fission under critical angular momentum.”[39] When the angular momentum is too large, the star breaks into a detached binary.[39] When the angular momentum is too small, the star remains as a single star.[39] BH Centauri and V1010 Ophiuchi have zero-age radii and are zero-age contact systems.[39] BH Centauri is an overcontact system.[39]

## Common envelope binaries

"This diagram suggests a reverse common envelope process for binary star formation. At some point in star formation, two cores, one for a main-sequence star (yellow) and the other for a red giant (gray) form within a common envelope. As mass transfer continues or decelerates, the red giant transfers to at or below its Roche lobe (dashed green line) and a partially stable binary is formed." Credit: Marshallsumter and Cryptic C62 *derivative work: Trex2001.

A common envelope (CE) refers to a short-lived (months to years) phase in the evolution of a binary star in which the largest of the two stars (the donor star) has initiated unstable mass transfer to its companion star. Breach of the common envelope crosses the Lagrange Point L1 with the donor-star mass beyond the Roche Lobe acting as the third dynamic point in a formerly binary system. Mass transfer is unstable when the radius of the donor star expands more rapidly or shrinks less rapidly than does the binary orbit. Hence, the donor will start mass transfer when it overfills its Roche lobe and as a consequence the orbit may shrink while the star expands, causing it to overflow the Roche lobe even more, which accerelates the mass transfer, causing the orbit to shrink faster and the donor to expand faster, etcetera. This leads to the run-away process of dynamically unstable mass transfer. The result will be the fast expansion of the donor's stellar envelope, which will then engulf the companion star. Hence the name common envelope.

## Overcontact systems

This is a computer generated picture of V701 Scorpii. Credit: K.-C. Leung and Robert E. Wilson.

When stars share an envelope the pair may be called an overcontact binary.[40][41][42]

BH Centauri is a zero-age overcontact binary system with primary and secondary masses equal to (9.4±5.4) and (7.9±5.4) Mʘ.[43] With later analysis including more recent data, "the mass ratio went from 0.97 to 0.84, and the degree of overcontact went from 21% to 48%."[43]

V1010 Ophiuchi and V701 Scorpii are both overcontact systems.[44] For V1010 Ophiuchi "the masses are 2 and 1 M while the radii are 2.1 and 1.5 R. The location in the HR diagram suggests that they are zero-age stars, as do the radii".[44]

At the right is a computer generated picture of the overcontact system V701 Scorpii. The overcontact in V701 Scorpii appears to be almost twice as much as in V1010 Ophiuchi.

"Most people would agree that fission is the most probable way to form binary systems, especially the close systems. The angular momentum must be the deciding factor as to whether a gas cloud becomes a single star or a binary system."[44]

## Bifurcations

Def. a "division into two"[45] is called bifurcation.

Bifurcation means the splitting of a main body into two parts. Bifurcation theory is the study of bifurcation in dynamical systems. The forking of a river into its tributaries is referred to as river bifurcation. A bifurcation can be a false dilemma in which two alternative statements are held to be the only possible options when there are more options. In cybernetics, a bifurcation is when a system switches from one stable state to another, where minor fluctuations may play a crucial role in deciding the outcome.

“About a century ago, Liapounov and Poincaré found that the sequence of Jacobi’s ellipsoids branches towards pear-shaped configurations for sufficiently high rotation.”[46]

Equatorial break-up and instability occur at the point of bifurcation.[47]

“Bifurcation of protostars can occur because of excessive angular momentum either during hydrodynamic collapse (‘fragmentation’), or else after the star has arrived on the HR diagram as a visible, slowly contracting star (‘fission’).”[48]

Spectral types B2-B5 and F3-G2 binaries with orbital periods shorter than 10 or 100 yr may result from the bifurcation of rapidly rotating protostars.[49]

Binary formation by ... bifurcation is difficult to achieve theoretically for compressible viscous gases and may not occur frequently or ever.[50]

Systems of spectroscopic binaries of periods less than 3.6 days "involve separations that are less than 2.5 times the sum of the radii of the components."[50]

These systems "probably have already exchanged mass and no longer have their original mass ratios."[50]

For these systems, we are unable to give their mecahnisms of origin.[50]

Provisionally, "most or all binaries [are] formed in capture processes (including initial star formation in bound systems) and that bifurcation or fission need not have occurred frequently."[50]

For the inclusion of compressibility and viscosity in theoretical calculations, "it is very difficult to produce binaries by fission and only under special circumstances."[50]

“In view of the high frequency of spectroscopic binaries, the formation mechanism must be a frequent one, not a rare occurrence."[50]

For most binaries to result from fission of a star into at least two stars, the expanding separation between the binaries must result in capture rather than expulsion from the system.

## Fissions

In the first frame, a neutron is about to be captured by the nucleus of a U-235 atom. In the second frame, the neutron has been absorbed and briefly turned the nucleus into a highly excited U-236 atom. In the third frame, the U-236 atom has fissioned, resulting in two fission fragments (Ba-141 and Kr-92) and three neutrons, all with large amounts of kinetic energy. Credit: Fastfission.

Def. the "process of splitting [...] into smaller particles"[51] is called fission.

"Binary formation by fission or bifurcation of a contracting rotating protostar" is difficult to achieve theoretically for compressible viscous gases and may not occur frequently or ever.[50]

Generally, fission is the splitting of something into two parts. In anthropology, fission is the process whereby a nation-state divides and becomes multiple states. In biology, fission is the subdivision of a cell or a multi-cellular body into two or more parts and the regeneration of each of the parts into a complete individual. In physics, nuclear fission is a nuclear reaction in which an atomic nucleus splits into smaller parts (lighter nuclei), often producing free neutrons and photons (in the form of gamma rays), and releasing a tremendous amount of energy. A large atomic nucleus such as uranium (236U) is split into two smaller particles (141Ba and 92Kr). Most nuclear fissions are binary fissions, but occasionally (2 to 4 times per 1000 events), three positively-charged fragments are produced in a ternary fission.

"Most people would agree that fission is the most probable way to form binary systems, especially the close systems."[44]

"[F]ission is now commonly considered to be the most likely explanation for the existence of close binaries".[52] But, "the hypothesis cannot be regarded as proved until the evolution of a rotating protostar has been followed from an initial state as a single star to a final state as a detached binary system."[52] "[T]he high frequency of close binaries over a wide mass range surely implies that no special characteristics of the properties of stellar matter are essential to binary formation".[52] "[T]he initial departure from axial symmetry is due to the onset of dynamical overstability for a mode of low order".[52] "[G]ravitational torques between the debris and the main component (i.e., before fission) significantly influence the latter’s evolution."[52] "[G]eneral trends emerge ... :

1. [f]ollowing the appearance of departures from axial symmetry, a substantial fraction of mass is nearly always lost as debris,
2. [e]volution into a bar-shaped structure is common ... ,
3. [when] fission [occurs], it leads to a binary of small mass ratio, typically towards the lower end of the range 0.1-0.5."[52]

With "significant mass exchange ... during [the] contact phase ... , the mass ratio immediately following fission may have little relevance to observed mass ratios."[52]

"[F]ission [can] occur only in stars whose interior state at least approximates to incompressibility. With even the lowest degree of central condensation which [may] occur in a purely gaseous star, fission [is] an impossibility, [as] any excess of angular momentum [relieves] itself by equatorial ejection of matter" as debris.[53] "About one-third of the stars observed ... are binaries which have almost certainly been formed by fission, so that these, at least, must have been in something approximating to the liquid [or fluid] state when fission took place."[53] "At different temperatures the atoms [are] of different sizes through being ionized down to different levels."[53]

"The idea of fission in rapidly rotating stars [is] not a return to the classical fission theory of Darwin and Jeans."[54] “If fission occurs at all, it is probably catastrophic in character and has little resemblance to rotational breakup.”[54] "[M]any close binaries are now in effect single objects possessing two massive nuclei, and a single envelope surrounding them."[54] When such as object "tends to shed its envelope, exposing the separate nuclei as a normal double star, we [shall] call this process fission."[54] When "the trend is in the opposite direction, we should probably speak of fusion."[54]

## Fragmentations

Def.

1. a "part broken off"[55]
2. "a small, detached portion"[55]
3. "an imperfect part"[55]

is called a fragment.

Def. the act or process of producing a fragment is called fragmentation.

Fragmentation of the molecular cloud during the formation of protostars is an acceptable explanation for the formation of a binary or multiple star system.[56][57]

With respect to low-mass star formation, "fragmentation to form a binary star [may be] most simply achieved if collapse is initiated by an external impulse."[58] "On its own, [the] process under which a dense molecular cloud core can collapse to form a binary, or multiple, star system would produce wide binaries".[58] "[C]lose binaries [may be] formed because of mutual interactions between the protostellar discs surrounding the various fragments."[58] "[T]he most likely collision which has an effect on the core is the one for which [the velocity change imparted by the impulse,] Δv ~ cs [(the internal sound speed),] induced by a clump of mass ~0.1Mʘ."[58] "[T]he impulsive collapse of the cloud cores [requires] that they are not primarily magnetically supported in their central regions."[58]

"The sources are separated by 17", or 4200 AU. Binary separations of this order are consistent with early fragmentation in a relatively dense cloud ("prompt initial fragmentation," e.g., Pringle 1989; Looney et al. 2000), in which case the individual sources would have distinct protostellar envelopes."[59]

"In a binary formed via gravitational fragmentation, we would expect the separation to correspond to the local Jeans length (Jeans 1928):"[59]

${\displaystyle \lambda _{J}=({\pi c_{s}^{2} \over G\mu _{p}m_{H}n})^{1/2},}$

"where cs is the local sound speed, and μp = 2.33 and n are the mean molecular weight and mean particle density, respectively. A Jeans length of 4200 AU would require a relatively high density (n ~ 6 x 105 cm−3, assuming cs = 0.2 km s−1). The mean density of the Per-Bolo 102 core, measured within an aperture of 104 AU, is 4 x 105 cm−3, close to the required value."[59]

## Fissions by fusions

A binary star system that includes a nearby white dwarf can produce certain types of spectacular stellar explosions, including the nova and a Type 1a supernova.[60] The explosion is created when the white dwarf accretes hydrogen from the companion star, building up mass until the hydrogen undergoes fusion.[61]

## V1010 Ophiuchi

These are light curves for the V1010 Ophiuchi system. Credit: Kam-Ching Leung and Robert E. Wilson.
This diagram shows the contact configuration of V1010 Ophiuchi. Credit: Kam-Ching Leung and Robert E. Wilson.

Def. binaries "in which the stellar components are close enough that proximity effects are important but far enough apart that a large temperature differential may be maintained between the two stars" are called near-contact binaries.[62]

"V1010 Oph ... is one of the brightest and best studied of the near-contact (P=0.66d) binaries."[62] "The period of the binary is known to be decreasing ..., which can be understood in terms of conservative mass transfer (Shaw 1990)."[62] "If this star is truly an evolved system, it may have been in contact previously. ... [I]t is not now in contact"[62].

The temperatures of the two stars have been estimated spectrally as 8200 K and 5671 ± 30 K.[63]

The first image at the right contains two light curves for V1010 Ophiuchi: the top is in yellow at 550.0 nm and the bottom is in blue at 435.0 nm.[63]

The "eclipses are complete and the primary minimum is a transit [...] The system is in contact [shown in the second diagram at the right], with a surface potential near that of the inner contact surface [...] The temperature difference (2529 K) between the primary and secondary is quite large. This suggests that the temperature gradient at the interface must be very steep."[63]

"The appreciable departure between the theoretical light curves and the observations [in the first figure at the right] at the ascending branch of the secondary minimum is due to [a large asymmetry from absorbing gaseous matter]."[63]

"There are two likely ways to form contact systems:

1. through star fission with critical angular momentum, i.e. the angular momentum is just right for the star to divide, but not large enough for it to be detached (zero-age contact);
2. through mass exchange in which one or both components expand to fill the common envelope during the course of stellar evolution."[63]

"V1010 Oph has essentially a ZAMS radius. Thus this system is likely to be essentially a zero-age contact system [formed through star fission]."[63]

## BH Centauri

"The eclipsing binary system BH Cen is a close (contact) binary in the extremely young galactic cluster Córdoba XXVI (NGC 2944)."[64]

In 1928-30, "from ten light minima ... a (half) period P = 0.395790 7 [days is derived]."[65][66] This half period estimate becomes the period P = 0.791 581 4 d,[39] for the observations in 1928-30.

From more recent observations around 1977, P = 0.791 616 d.[43] And, from 1979, P = 0.791 592 10 ± 0.000 14.[64]

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