# Theory/Astronomy

A view of the horizon on the Moon's solid surface shows a black sky without stars because of sunlight coming from the left. Credit: NASA.

Theoretical astronomy at its simplest is the definition of terms to be applied to astronomical effort and the phenomenological results. In essence it is the theory of the science of physical and logical laws with respect to any natural body in the sky especially at night.

As many of the first terms a student encounters regarding natural bodies in the sky are at a secondary level, this learning resource starts there, proceeds through a university undergraduate level, dwells occasionally at the graduate or postgraduate level (often called postdoctoral) and ultimately focuses on the state of the art, the state of the science, and a bit beyond. Enjoy!

Speculation, though, is seldom put into an article, but to stimulate the imagination and perhaps open a few doors that may seem closed at present, cautionary speculation based somewhat on current knowledge is included.

Part of the fun of theory is extending the known to what may be known to see if knowing and understanding is really occurring, or it is something else.

The laboratories of astronomy are limited to the observatories themselves. The phenomena observed are located in the heavens, far beyond the reach, let alone control, of the astronomical observer.[1] “So how can one be sure that what one sees out there is subject to the same rules and disciplines of science that govern the local laboratory experiments of physics and chemistry?”[1] “The most incomprehensible thing about the universe is that it is comprehensible.” - Albert Einstein.[1]

## Theory

The word theory means a contemplation or speculation, as opposed to action. It is a statement of how and why particular facts are related. Theory is especially often contrasted to "practice". While theories may address ideas and empirical phenomena which are not easily measurable, scientific theory is generally understood to refer to a proposed explanation of empirical phenomena, made in a way consistent with scientific method. Such theories are preferably described in such a way that any scientist in the field is in a position to understand and either provide empirical support ("verify") or empirically contradict ("falsify") it. A common distinction made in science is between theories and hypotheses. Hypotheses are individual empirically testable conjectures; while theories are collections of hypotheses that are logically linked together into a coherent explanation of some aspect of reality and which have individually or jointly received some empirical support.

Def.

1. a coherent statement or set of ideas that explains observed facts or phenomena, or which sets out the laws and principles of something known or observed; a hypothesis confirmed by observation, experiment etc.
2. the underlying principles or methods of a given technical skill, art etc., as opposed to its practice
3. a field of study attempting to exhaustively describe a particular class of constructs
4. a hypothesis or conjecture
5. a set of axioms together with all statements derivable from them. Equivalently, a formal language plus a set of axioms (from which can then be derived theorems) is called a theory.

## Astronomy

The nomology and any effort to acquire a system of laws or knowledge focusing on any natural body in the sky especially at night constitutes the theory of astronomy.

The overall theory of astronomy consists of three fundamental parts:

1. the derivation of logical laws,
2. the definitions of natural bodies (entities, sources, or objects), and
3. the definition of the sky (and associated realms).

## Skies

Although the image contains a layer of cumulus clouds, at the horizon, the Atlantic Ocean meets the edge of the sky. Location :Salvador, Bahia, Brazil, July 4, 2008. Credit: Tiago Fioreze.
This is a 360° view of the surrounding terrain, horizon and Martian sky, taken on November 23-28, 2005, by the Exploration Rover 'Spirit'. Credit: NASA.

Def. "the expanse of space that seems to be over the earth like a dome"[2] is called the sky, or sometimes the heavens.

This definition applies especially well to an individual on top of the Earth's solid crust looking around at what lies above and off to the horizon in all directions. Similarly, it applies to an individual's visual view while floating on a large body of water, where off on the horizon is still water.

The image at right shows the horizon marking the lower edge of the sky and the upper edge of the Atlantic Ocean, with a layer of cumulus clouds just above.

A more general definition of 'sky' allows for skies as seen on other worlds. At left is a 360° panarama of the horizon on Mars as perceived in the visual true-color range of the NASA Mars Exploration Rover 'Spirit' on November 23-8, 2005.

Def. an "expanse of space that seems to be [overhead] like a dome"[2] is called a sky.

Even in day light, the sky may seem absent of objects if a nearby source tends to overwhelm other luminous objects.

At top is a view of the horizon on the Moon's solid surface taken by an Apollo 16 astronaut. The image shows a black sky without stars because the sunlight coming from the left is overwhelming.

## Entities

Def.

1.a: an "independent, separate, or self-contained existence",
1.b: "the existence of a thing as contrasted with its attributes", or
2. "something that has separate and distinct existence and objective or conceptual reality",

is called an entity.[2]

Def.

1.a: "something that is or is capable of being seen, touched, or otherwise sensed",
1.b: "something physical or mental of which a subject is cognitively aware",
2. "something that arouses an emotion in an observer", or
3. "a thing that forms an element of or constitutes the subject matter of an investigation or science"

is called an object.[2]

Def.

1.a: "a mass of matter distinct from other masses" or
2.b: "something that embodies or gives concrete reality to a thing; [specifically] : a sensible object in physical space"

is called a body.[2]

Def.

1.a: "a separate and distinct individual quality, fact, idea, or [usually] entity",
1.b: "the concrete entity as distinguished from its appearances",
1.c: "a spatial entity", or
1.d: "an inanimate object distinguished from a living being"

is called a thing.[2]

Def.

1: "an observable fact or event",
2.a: "an object or aspect known through the senses rather than by though or intuition",
2.b: "an object of experience in space and time as distinguished from a thing-in-itself", or
2.c: "a fact or event of scientific interest susceptible of scientific description and explanation"

is called a phenomenon.[2]

Such words as "entity", "object", "thing", and perhaps "body", words "connoting universal properties, constitute the very highest genus or "summum genus"" of a classification of universals.[3] To propose a definition for say a plant whose flowers open at dawn on a warm day to be pollinated during the day time using the word "thing", "entity", "object", or "body" seems too general and is. But, astronomy deals with the universe, sometimes only the very local universe just above the Earth's atmosphere. These "universals" may be just the words to use.

## Meanings

On the basis of dictionary definitions, what is the difference between a 'body', an 'entity', an 'object', a 'thing', and a 'phenomenon'?

The categories for synonymy and most common usage place 'body' in "3. SUBSTANTIALITY"[4], 'entity' in the same, 'object' in "651. INTENTION"[4], 'thing' in "3. SUBSTANTIALITY"[4], and 'phenomenon' in "918. WONDER"[4]. The more common uses of the words 'object' and 'phenomenon' are not exactly the same as may be used in a specialized endeavor like a science such as astronomy. A slightly less common use of 'phenomenon' is in category "150. EVENTUALITY"[4]. For the word 'object' a slightly less common or popular meaning is in category "543. MEANING"[4]. The closest category of meaning or synonymy for 'object' to category 1. is category "375. MATERIALITY"[4].

Of each of these words, 'entity' uses the word 'existence', category "1. EXISTENCE"[4] in each definition. 'Entity' may be thought of as the most general of these terms because its meanings are the closest to category 1. The farthest from category 1. on the basis of conceptual meaning and synonymy is the word 'object' in category 375. A tentative order is 'entity' > 'phenomenon' > 'object' by generalness, or by preciseness (perhaps more description is needed beyond only existence) 'object' > 'phenomenon' > 'entity'.

'Thing' (category 3.) has the word 'entity' in three of four meanings and 'object' in the fourth. The second most popular meaning of 'thing' is in category 375.

'Body' (category 3.) has 'mass' and is closer to 'substantiality' in common usage than 'thing', and neither word has a synonym closer in meaning to 'existence'. The second most common meaning of 'body' is category "203. BREADTH, THICKNESS"[4].

This suggests a hierarchy such as 'entity' > 'body' > 'thing' > 'phenomenon' > 'object' by generalness, where 'existence' is the most general word; or, 'object' > 'phenomenon' > 'thing' > 'body' > 'entity' by preciseness. An 'astronomical object' may be expected to require a more detailed description in its definition to indicate meaning than an 'astronomical entity'. In astronomy, the concept of an 'astronomical body' may suggest a meaning closer to category 203. rather than a 'thing' or 'entity'.

The choice of general order is 'entity' > 'source' > 'object' > 'phenomena'. The term 'astronomical body' has much less popularity per Google scholar than 'object'. The body of astronomers in the International Astronomical Union is auspicious and here is considered an astronomical entity.

Def. the theory of the science of the biological, chemical, physical, and logical laws (or principles) with respect to any natural being, body, thing, entity, source, object, or phenomena in the sky especially at night is called theoretical astronomy.

## Astronomical entities

Def.

1.a: an "independent, separate, or self-contained [astronomical] existence",
1.b: "the [astronomical] existence of a [person, place, or] thing as contrasted with its attributes", or
2. "some [astronomical] thing that has separate and distinct existence and objective or conceptual reality",[2]

is called an astronomical entity.

By generalness, 'being' > 'entity' > 'phenomenon' > 'object'. Further, 'being' > 'body' > 'something' or 'thing' > 'entity'.[4]

What are some astronomical entities?

"[V]oids [are] now considered as regular astronomical entities in their own rights, [and] are clustered."[5]

There are "a plethora of observations from heavenly bodies which did not agree with each other despite being from the same astronomical entities."[6] The observations themselves, media of recording, and the heavenly bodies are all astronomical entities. So are the observers and astronomers who make or made the records. Constellations are astronomical entities. 'Sky' is an astronomical entity.[7]

Included as astronomical entities are 'astronomical objects' and 'astronomical sources', even those with large error regions of whole degrees. Diffuse background radiations, whether gamma ray or radio, are astronomical entities.

"Astronomical named entities":

1. "Names of telescopes and other measurement instruments,"
2. "Names of celestial objects,"
3. "Types of objects," and
4. "Features that can be pointed to on a spectrum".[8]

"Gazetteers are useful for finding commonly referenced names of people, places or organisations"[9] associated with astronomy. These are astronomical entities that can be used for information processing.

Astronomical entities include some journals (such as The Astrophysical Journal, the Monthly Notices of the Royal Astronomical Society, and Astronomy & Astrphysics), articles in journals and magazines, books on astronomy that may be references or be cited for astronomy information or facts.

Named entity recognition (NER) for astronomy literature:[10] NER "involves assigning broad semantic categories to entity references in text."[10]

Types of entities for Natural Language Processing (NLP):

1. names - person, location, organization;
2. temporal expressions - date, time;
3. numeric expressions - money, percent;
4. instrument name;
5. source name;
6. source type;
7. spectral feature; and
8. text and scientific databases.[10]

"Astronomy is a broad scientific domain combining theoretical, observational and computational research, which all differ in conventions and jargon."[10] "There is a major effort in astronomy to move towards integrated databases, software and telescopes."[10] ("The Virtual Observatory"[10]).

Entity categories include 'galaxy', 'nebula', 'star', 'star cluster', 'supernova', 'planet', 'frequency', 'duration', 'luminosity', 'position', 'telescope', 'ion', 'survey', and 'date'.[10]

### Dominant groups

The term "dominant group" is used in astronomy to identify other astronomical entities of importance. The genera differentia for possible definitions of "dominant group" fall into the following set of orderable pairs:

Genera differentia for "dominant group"[4]
Synonym for "dominant" Category Number Category Title Synonym for "group" Category Number Catgeory Title
“superior” 36 SUPERIORITY "arrangement" 60 ARRANGEMENT
“influential” 171 INFLUENCE "class" 61 CLASSIFICATION
“musical note” 462 HARMONICS "assembly" 74 ASSEMBLAGE
“most important” 670 IMPORTANCE "size" 194 SIZE
“governing” 739 GOVERNMENT "painting", "grouping" 572 ART
"master" 747 MASTER "association", "set" 786 ASSOCIATION
----- --- ------- "sect" 1018 RELIGIONS, CULTS, SECTS

'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term for "dominant group"; for example, "superior class", "influential sect", "master assembly", "most important group", and "dominant painting". "Dominant" falls into category 171. "Group" is in category 61. Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739, or "dominant party", where "party" is in category 74.

dominant group

"A particular subject of interest is the cluster ion series (NH3)nNH4+, since it is the dominant group of ions over the whole investigated temperature range."[11] For astrochemisty, "[t]hese studies are expected to throw light on the sputtering from planetary and interstellar ices and the possible formation of new organic molecules in CO--NH3–H2O ice by megaelectronvolt ion bombardment."[11]

All alternate terms for dominant group [relative synonyms] used in astronomy are astronomical entities. Here are some examples from the literature:

master class

1. "Once created, device class objects are registered with an instance of the master class."[12]
2. "For ATIC, a possible set of defined classes would be a master class event, and sub-classes header, silicon, scintillator, bgo and track."[13]

superior size

1. "The superior size and albedo of Venus completely turn the scale, with the result that Venus at her brightest is about 12 times brighter than Mercury at his brightest."[14]
2. "There is no reason to question but that they are simply ordinary meteors, which from their superior size and unusually slow speed have survived to reach the earth's surface."[15]

influential set

1. "Together with Leonard Searle, he wrote an influential set of papers which established that stellar disks are truncated at about four exponential scale-lengths, and that the vertical scale-height of disks is constant with radius."[16]
2. "Until now Themo has been best known for an influential set of questions on Aristotle's Meteorologica, which is closely related to similar sets by Nicole Oresme and, putatively, Simon Tunsted."[17]

## Sources

The image is some of the astronomical sources within the error circle around Serpens XR-1, (X-ray, XR), an early X-ray source. Legend: red * - star, X - X-ray source, LMXB - low-mass X-ray binary (Serpens X-1), Mira - Mira variables, gammaBurst - gamma-ray burst source, DkNeb - dark nebula, RRLyr - RR Lyrae variable star, Cepheid - Cepheid variable star. Credit: Aladin at SIMBAD.

Def. a natural source usually of radiation in the sky especially at night is called an astronomical source.

An astronomical source may have generated or be capable of generating electromagnetic radiation, a star, or a galaxy, for example. A source reflects, generates, transmits, or fluoresces that which may be detectable.

A celestial source is any astronomical source except the Earth.

An astronomical source usually has intensity often as a spatial, temporal, or spectral profile. Such a profile may be continuous, intermittent, transient, fluctuating, aperiodic, or unpredictable.

Some astronomical objects are not detectable directly as a source but instead may be absorbers of a portion of a signal from a source further away.

The image at right is a celestial map of the astronomical sources within the original detected error circle around the first apparent astronomical X-ray source discovered in the constellation Serpens Cauda (Serpens XR-1, or Serpens X-1). The other sources within this error circle are stars, other X-ray sources, a gamma-ray burst source, and a dark nebula.

In the theory of source astronomy comes at least an attempt to answer "Where did it come from?" Is there a causality? Is it modal? Or, is it of uncountable origin?

## Objects

This view of the rising Earth greeted the Apollo 8 astronauts as they came from behind the Moon after the lunar orbit insertion burn. Credit: NASA.
This true-color image shows North and South America as they would appear from space 35,000 km (22,000 miles) above the Earth. Credit: Reto Stöckli, Nazmi El Saleous, and Marit Jentoft-Nilsen, NASA GSFC.

The science of astronomy consists of three fundamental parts:

1. physical and logical laws,
2. any natural entity, source, or object, and
3. the sky.

The SIMBAD reference database "contains identifications, 'basic data', bibliography, and selected observational measurements for several million astronomical objects."[18] "The specificity of the SIMBAD database is to organize the information per astronomical object".[18] "Building a reference database for ... all astronomical objects outside the Solar System – has been the first goal of the CDS".[18] "The only astronomical objects specifically excluded from SIMBAD are the Sun and Solar System bodies."[18]

Def. a natural object in the sky especially at night is called an astronomical object.

As indicated above about the astronomical objects in the SIMBAD database and in the learning reference astronomy, there are many objects between the observer on the ground atop some portion of the Earth's crust and astronomical objects other than the Sun and Solar System bodies. Further, for those observers looking toward the Earth from another location such as near the Moon in the photograph at above right, it seems that the Earth is a natural object. On the Earth 384,000 km away, the sunset terminator bisects Africa.

A closer view of Earth shows some of the astronomical objects near the Earth and apparently just above the surface, where an observer may be. Some of these objects such as clouds probably by convention are more likely to be studied by planetary observers, or weather observers, rather than astronomical observers.

With perspectives other than upwards from the Earth's crustal surface, the word "sky" may seem insufficient or inappropriate, although studying the Earth as part of planetary science may leave interesting astronomical objects near the Earth that are occasionally "in the sky". The idea being that the Earth cannot be in its own sky, or can it? Perhaps, it is more a matter of whether other observers agree that what an observer is observing is astronomy or planetary science, or both.

### Star by dictionary

For the object, "star", a dictionary definition is

1.a: "any natural luminous body visible in the sky [especially] at night",
1.b: "a self-luminous gaseous celestial body of great mass whose shape is [usually] spheroidal and whose size may be as small as the earth or larger than the earth's orbit".[2]

This definition seems okay for a dictionary, but is it adequate for a science, and especially, astronomy?

## Astrochemistry

Def. the study of the chemical composition of stars and outer space is called astrochemistry.

"An important goal for theoretical astrochemistry is to elucidate which organics are of true interstellar origin, and to identify possible interstellar precursors and reaction pathways for those molecules which are the result of aqueous alterations."[19]

### Atmospheres

Def. a layer of gases that may surround a material body of sufficient mass,[3] and that is held in place by the gravity of the body is called an atmosphere.

Def. the gases surrounding the Earth or any astronomical body is called an atmosphere.

### Interplanetary medium

Def. that part of outer space between the planets of a solar system and its star is called interplanetary space.

Def. the material which fills the solar system and through which all the larger solar system bodies such as planets, asteroids and comets move is called an interplanetary medium.

### Interstellar medium

Def. the matter that exists in the space between the star systems in a galaxy is called an interstellar medium.

### Intergalactic medium

Def. a rarefied plasma[20] that is organized in a cosmic filamentary structure[21] is called the intergalactic medium (IGM).

### Ions

Def. an atom or group of atoms bearing an electrical charge such as the sodium and chlorine atoms in a salt solution is called an ion.

### Materials

Def. matter which may be shaped or manipulated, particularly in making something is called a material.

Def. any instrument used in astronomy for observing distant objects is called a telescope.

Def. an object, usually made of glass, that focuses or defocuses the light or an electron beam that passes through it is called a lens.

### Meteorites

This image shows a cast of the Middlesbrough meteorite, a textbook example of an oriented meteorite that fell on March 14, 1881, in Middlesbrough, North Yorkshire, England, UK. Credit: Meteorite Recon (Dr. Svend Buhl).

Def. a metallic or stony object that is the remains of a meteor is called a meteorite.

### Shelters

Def. a refuge, haven or other cover or protection from something is called a shelter.

Def. anything shaped like a common structural element of architecture that resembles the hollow upper half of a sphere, a cupola], often used as a cover is called a dome.

## Astrognosy

The diagram shows the Earth's radial density distribution according to the Preliminary Reference Earth Model (PREM). Credit: AllenMcC.

Astrognosy deals with the materials of celestial objects and their general exterior and interior constitution.

The theoretical constitution of the Earth is illustrated using the one-dimensional Preliminary Reference Earth Model[22] (PREM) at right. The density in kg-m-3 of radial layers is plotted against radius in km.

## Astrography

This is the Lick Observatory north tower, looking northeast, in the summer of 1980. Credit: Jane Lidz.

The geography applicable to astronomy may be designated 'astrogeography'. But, this term is often more restricted. "[T]he relationship between outer-space geography and geographic position (astrogeography), and the evolution of current and future military space strategy"[23] has been identified and evaluated.[23]

Def. the art of describing or delineating the stars; a description or mapping of the heavens is called astrography.

Def. a place where stars, planets and other celestial bodies are observed is called an observatory.

From the Ebers Papyrus, a year has 360 days of twelve months of thirty days each.[24]

"A period of 360 days, comprising 12 months of 30 days each, was assigned by the Mesopotamians to the year in days and months at least by the third millennium BC."[25]

In ancient Iran (Persia), the year was 360 days with 12 months of 30 days each.[26][27]

"All Veda [India] texts speak uniformly and exclusively of a year of 360 days [12 months of 30 days each]. Passages in which this length of the year is directly stated are found in all the Brahmanas."[28] This period dates to approximately the third millennium (~5,000 b2k).[29]

An ancient Chinese calendar had a 360 day year of twelve months of thirty days each.[30]

The Mayans had an old tradition that the year had twelve months of thirty days each, 360 days in a year.[31]

"The Peruvian year was divided into twelve Quilla, or moons, of thirty days."[32]

Apparently, with each of these locations around the globe and several others near to the Mediterranean Sea, the year had exactly 360 days of 12 months of 30 days each, then at some point near 2700 b2k the year became lengthened to today's year.

## Astrohistory

Def. (from 1945) "those parts of human interest in celestial phenomena which are amenable to mathematical treatment" are called astronomy.[33] This is Neugebauer's definition of astronomy.[34]

Def. "the search for astronomical strata whose contents could be classified" is called astronomy.[35] This is Herschel's definition of astronomy.[36]

"Mere "star ordering" is not "astronomy", so far as the modern usage of the term implies, regardless of the word's etymology".[25]

Def. (from 2000) "the accurate mapping of the heavens in order to make possible the accurate prediction of phenomena" is called astronomy.[25]

Def. "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties" is called astronomy.[37]

### Electrical Sun

"[T]he solar corona is eminently variable, and therefore like our aurora borealis, which is known to be electric."[38] "This vast electric mass must have a great electric repulsion through vacant space, and it lends probability to my position that it drives away from the sun the tails of comets and our zodiacal light and aurora borealis."[38] "Electricity alone can repel electricity."[38] "[T]he direction of the comets' tails is but the interaction between the sun and the comets, the same as the action between a charged prime conductor and a charged pith ball of an electric machine."[38]

"[A] variety of geophysical and astrophysical phenomena can be explained by a net charge on the Sun of -1.5 x 1028 e.s.u."[39] This figure was later reduced by a factor of five.[40]

"There appears to be considerable misunderstanding on the part of physicists of the nature and degree of the observational support of gravitational theory. For example, it appears to be commonly believed that the observations of planetary motion agree with computed orbits to the accuracy of the observations. On the other hand, it has long been known by the astronomers that there are sizable systematical discrepancies between computed and observed orbits".[41]

### Milky Way

Democritus "lived at Abdère 300 years before the Christian era [2300 b2k]. In a short fragment quoted by Plutarch, he declares that the Milky Way is an agglomeration of small stars too far away to be perceived singly."[42]

### Coronal clouds

The solar corona is photographed between 1901-2. Credit: Popular Science Monthly Volume 60.

"Beginning with the daguerreotype of the corona of 1851, the Reverend Lecturer had thrown on the screen pictures illustrating the form of the corona in different years. The drawings of those of 1867, 1878, and 1900 all showed long equatorial extensions with openings at the solar poles filled with beautiful rays."[43] "The intermediate years, as, for example, 1883, 1886, and 1896 showed the four groups of synclinals which mainly constitute the corona gradually descending towards the equator of the sun, with a corresponding opening of the polar regions."[43]

"Some of the theories of the solar corona were then illustrated and discussed."[43]

1. "The corona is not of the nature of an atmosphere round the sun, for the pressure at the sun's limb would be enormous, while the thinness of the chromospheric lines show that it is not."[43]
2. "comets, such as that of 1843, have approached the sun with enormous velocities within the region of the prominences without suffering disruption or retardation."[43]
3. "If not an atmosphere of particles of gas, still less is it an atmosphere of solid stones or meteorites."[43]
4. "Meteor streams do circle round the sun, but there is no reason why the positions of the orbits, or the intrinsic brightness of such streams should vary with the sun-spot period."[43]
5. "the appearance of the corona does not seem to be such as the projection of meteor streams upon the celestial vault would give."[43]
6. "Prof. Schaeberle has proposed a mechanical origin of the solar corona, due to the forces of ejection of particles from the solar limb, as evidenced by the prominences, and the force of gravity under the particular conditions of the solar rotation and the inclination of its axis to the earth's orbit."[43]
7. "The electrical theory of the corona does not negative the mechanical theory, but supplements it. In addition to the forces of gravity and ejection, it takes account of the repulsive force which the sun exerts on matter which has the same electrical sign as itself, and which has been ejected from it."[43]
8. "it would seem that the solar corona is of the nature of an electrical aurora round the sun."[43]
9. "the coronoidal discharges in poor vacua obtained by Prof. Pupin about an insulated metal ball are exceedingly like the rays and streamers of the solar corona."[43]

### Zodiacal lights

The Zodiacal Light is over the Faulkes Telescope, Haleakala, Maui. Credit: 808caver.

"According to Gruson and Brugsch the Egyptians were acquainted with, and even worshipped, the zodiacal light from the very earliest times, as a phenomenon visible throughout the East before sunrise and after sunset. It was described as a glowing sheaf or luminous pyramid perpendicular to the horizon in summer, and inclined more or less during the winter. Indeed the Egyptians represented the zodiacal light under the form of a triangle which sometimes stood upright and at other times was inclined."[44]

## Astromathematics

A hyperbolic pass is indicated by the blue line with an eccentricity of 1.3. A parabolic pass is the green line. The elliptical orbit in red has an eccentricity (e) of 0.7. Credit: Stamcose.

The simplest description of the paths astronomical objects may take when passing each other includes a hyperbolic and parabolic pass. When capture occurs it usually produces an elliptical orbit.

Def. mathematics used in the study of astronomy, astrophysics and cosmology is called astromathematics.

The planet Mercury is especially susceptible to Jupiter's influence because of a small celestial coincidence: Mercury's perihelion, the point where it gets closest to the Sun, precesses at a rate of about 1.5 degrees every 1000 years, and Jupiter's perihelion precesses only a little slower. One day, the two may fall into sync, at which time Jupiter's constant gravitational tugs could accumulate and pull Mercury off course. This could eject it from the Solar System altogether[45] or send it on a collision course with Venus or Earth.[46]

### Orbital theory

The animated elliptical orbit has an eccentricity of 0.6. Credit: Willow.
The ellipse and some of its mathematical properties is described. Credit: .

Orbits come in many shapes and motions. The simplest forms are a circle or an ellipse.

The foci of an ellipse are two special points F1 and F2 on the ellipse's major axis and are equidistant from the center point. The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major axis ( PF1 + PF2 = 2a ). Each of these two points is called a focus of the ellipse.

In the gravitational two-body problem, if the two bodies are bound to each other (i.e., the total energy is negative), their orbits are similar ellipses with the common barycenter being one of the foci of each ellipse. The other focus of either ellipse has no known physical significance. Interestingly, the orbit of either body in the reference frame of the other is also an ellipse, with the other body at one focus.

Ideally, the motion of two oppositely charged particles in empty space would also be an ellipse.

A real orbit (and its elements) changes over time due to gravitational perturbations by other objects and the effects of relativity. A Keplerian orbit is merely an idealized, mathematical approximation at a particular time.

### Eccentricities

"Mercury's orbit eccentricity [e] varies between about 0.11 and 0.24 with the shortest time lapse between the extremes being about 4 x 105 yr".[47] "Smaller amplitude variations occur with about a 105 yr period."[47]

### Inclinations

The diagram describes the parameters associated with orbital inclination (i). Credit: Lasunncty.

"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."[47]

### Obliquities

In axial tilt, axial tilt (also called obliquity) is the angle between an object's rotational axis, and a line perpendicular to its orbital plane. The planet Venus has an axial tilt of 177.3° because it is rotating in retrograde direction, opposite to other planets like Earth. The planet Uranus is rotating on its side in such a way that its rotational axis, and hence its north pole, is pointed almost in the direction of its orbit around the Sun. Hence the axial tilt of Uranus is 97°.[48]

The obliquity of the Earth's axis has a period of about 41,000 years.[49]

### Precessions

The equinoxes of Earth precess with a period of about 21,000 years.[49]

### Orbital poles

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.

### Resonances

The animation shows Io's Laplace resonance with Europa and Ganymede. Credit: User:Matma Rex.

An orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. The physics principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, and the other body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i.e., their ability to alter or constrain each other's orbits. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

### Orbital decays

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.

## Astrophysics

“Contrary to the belief generally held by laboratory physicists, astronomy has contributed to the growth of our understanding of physics.”[1]

Def. the physical properties of celestial bodies and with the interaction between matter and radiation in celestial bodies and in the space between them is called astrophysics.

Theoretical astronomy seeks to understand what is behind cosmic events by taking the physics from the laboratory and testing it in models against the data obtained from observations. This is usually referred to as Draft:astrophysics. But, often the observations seem more than just what the physics can describe. Adding in extra tidbits may help to describe and help to produce better agreement. If these extra tidbits are physical in nature, they are part of theoretical astrophysics, if astronomical in nature, then theoretical astronomy.

### Astronomical units

Def. "1 day (d)" is called the astronomical unit of time.[50]

Def. "365.25 days" is called a Julian year.[50]

Def. "36,525 days" is called a Julian century.[50]

Def. "the distance from the centre of the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days" is called the Astronomical Unit (AU).[50]

Def. "149,597,870,700 meters" is called the Astronomical Unit.[51]

Def. "the mass of the Sun" is called the astronomical unit of mass.[50]

Def. the rate at which a star radiates energy in all directions is called luminosity.

Def. "the distance at which one Astronomical Unit subtends an angle of one arcsecond" is called the parsec (pc).[50]

Def. "the distance traveled by light in one Julian year in a vacuum" is called the light-year (ly).[50]

### Auroras

Laboratory experiment produces aurora at the poles of a sphere. Credit: David Monniaux.

Computer simulations are usually used to represent auroras. The image at right shows a terrella in a laboratory experiment to produce auroras.

### Fluctuating visible source

At the bottom of this visible emission model is a visual intensity curve. Credit: Stanlekub.

Consider only that portion of the emission of the visible source at right that is a level maximum. If this is the first observation received, a reasonable theoretical explanation from physics is a constant black body visible source, like a light bulb. In a physics laboratory, a steady voltage/current power supply produces a steady intensity.

Now consider the full length observation indicated by the moving green circle. From a physics perspective, it appears the power supply is not steady. Using alternating current (AC) to power the light bulb at 60 cycles per second may trigger the detector to yield an oscillatory intensity curve if its response time is short enough to resolve the use of AC. This is a possible theoretical physics; hence, theoretical astrophysics additional explanation of what may be happening.

A theoretical astronomy explanation is indicated in the colorful figure above as two visible sources, unresolved by the detector (seen only as a point source), but possibly responsible for the changes in the visible light received at the detector. Which do you think is more likely: a fluctuating power supply or an eclipsing binary?

Physics deals with forces, fields, energy, kinetics, and radiation. Astronomy has its own laws with respect to entities or bodies in motion. Application of a field to an astronomical phenomenon may clarify what is happening. That's the focus of astrophysics. Theory is needed to bring the physics in line with the magnitude of the situation and its complexity.

### Luminosity

The luminosity of stars is measured in two forms: apparent (visible light only) and bolometric (total radiant energy). (A bolometer is an instrument that measures radiant energy over a wide band by absorption and measurement of heating.) When not qualified, "luminosity" means bolometric luminosity, which is measured either in the SI units, watts; or in terms of solar luminosities, ${\displaystyle L_{\odot }}$, that is, how many times as much energy the object radiates as the Sun.

Luminosity is an intrinsic measurable property independent of distance, and is appraised as absolute magnitude, corresponding to the apparent luminosity in visible light of a star as seen at the interstellar distance of 10 parsecs, or bolometric magnitude corresponding to bolometric luminosity. In contrast, apparent brightness is related to the distance by an inverse square law. In addition to this brightness decrease from increased distance there is an extra linear decrease of brightness for interstellar "extinction" from intervening interstellar dust. Visible brightness is usually measured by apparent magnitude. Both absolute and apparent magnitudes are on an inverse logarithmic scale, where 5 magnitudes increase counterparts a 100th part decrease in nonlogarithmic luminosity.

By measuring the width of certain absorption lines in the stellar spectrum, it is often possible to assign a certain luminosity class to a star without knowing its distance. Thus a fair measure of its absolute magnitude can be determined without knowing its distance nor the interstellar extinction, and instead the distance and extinction can be determined without measuring it directly through the yearly parallax. Since the stellar parallax is usually too small to be measured for many far away stars, this is a common method of determining distances.

"The luminosity of a star ${\displaystyle L}$ (assuming the star is a black body, which is a good approximation) is also related to temperature ${\displaystyle T}$ and radius ${\displaystyle R}$ of the star by the equation:

${\displaystyle L=4\pi R^{2}\sigma T^{4}\,}$

where

σ is the Stefan-Boltzmann constant 5.67x10-8 W·m-2·K-4

Given a visible luminosity (not total luminosity), one can calculate the apparent magnitude of a star from a given distance:

${\displaystyle m_{\rm {star}}=m_{\rm {sun}}-2.5\log _{10}\left({L_{\rm {star}} \over L_{\odot }}\cdot \left({\frac {d_{\rm {sun}}}{d_{\rm {star}}}}\right)^{2}\right)}$

where

mstar is the apparent magnitude of the star (a pure number)
msun is the apparent magnitude of the Sun (also a pure number)
Lstar is the visible luminosity of the star
${\displaystyle L_{\odot }}$ is the solar visible luminosity
dstar is the distance to the star
dsun is the distance to the Sun

### Nucleosynthesis

"Our calculations show that production of [lithium] in low-energy flares [by nucleosynthesis], taking place in the surfaces of T Tauri-like stars, is energetically possible and can give the observed excesses over the interstellar abundance."[52]

"[T]here is evidence of lithium production in some stars due to some undefined mechanism. The observations show that the Li abundance on some red giants ... and young stars exceeds the average abundance in the universe by 2 orders of magnitude".[53] It is "suggested that Li produced in the helium envelopes of red giants comes to the surface of the stars as the result of a strong convection."[53] For young stars, "the production of the light elements in nonthermal nuclear reactions seems the most appropriate mechanism that can be responsible for enrichment of stellar photospheres by Li."[53] "At least 0.3 metric tons of excited Li and Be nuclei were produced during the solar flare of 1991 November 15. One can estimate the equilibrium concentration of 7Li nuclei in the solar atmosphere by assuming that they are produced only in solar flares and that a leakage of Li nuclei occurs with the solar wind."[53]

Although 7Be is usually assumed to have been produced by the Big Bang nuclear fusion, excesses (100x) of the isotope on the leading edge[54] of the Long Duration Exposure Facility (LDEF) relative to the trailing edge suggest that "most of the sun's fusion must occur near the surface rather than the core."[55] The particular reaction

3He(α,γ)7Be

3He + 4He → 7Be + γ (429 keV)

and the associated reaction chains

7Be(e-e)7Li(p,α)α

and

7Be(p,γ)8B → 2α + e+ + νe

generate 14% and 0.1% of the α-particles, respectively, and 10.7% of the present-epoch luminosity of the Sun.[56] Usually, the 7Be produced is assumed to be deep within the core of the Sun; however, such 7Be would not escape to reach the leading edge of the LDEF.

### Stars

Def. "any object forming on a dynamical timescale, by gravitational instability", is called a star.[57]

### Starspots

Several periodic cycles are evident in the continuous recording of sunspots, most notably the 11 year (131 ± 14 month) cycle. The green line represents continuous monthly averages reported by the Solar Influences Data Center since 1749. Credit: Slashme.

"[T]here have been three possible periods of marked solar anomaly during the last 1000 years: the Maunder Minimum, another minimum [the Spörer Minimum] in the early 16th century, and a period of anomalously high activity in the 12th and early 13th centuries."[58]

The basic causes of the solar variability and solar cycles are still under debate, with some researchers suggesting a link with the tidal forces due to the gas giants Jupiter and Saturn,[59][60] or due to the solar inertial motion.[61][62]

### Weak equivalence principle

All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration, independent of their properties, including their rest mass.[63]

"The observation of a neutrino burst within 3 h of the associated optical burst from supernova 1987A in the Large Magellanic Cloud provides a new test of the weak equivalence principle, by demonstrating that neutrinos and photons follow the same trajectories in the gravitational field of the galaxy."[64]

## Astrotechnology

This image is of the large astrolabe made by Gualterus Arsenius in 1569. Credit: David Monniaux.
The Hipparcos satellite is being tested in the Large Solar Simulator at ESTEC. Credit: Michael Perryman.

The astrolabe was effectively an analog calculator capable of working out several different kinds of problems in spherical astronomy.

Some form of an "astrolabe" may have been in use by the third millennium BC.[25]

Hipparcos is the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects.

These measurements allow "the accurate determination of proper motions and parallaxes of stars, their distance and tangential velocity.

## Planetary sciences

Planetary science (rarely planetology) is the scientific study of planets (including Earth), moons, and planetary systems, in particular those of the solar system and the processes that form them. It studies objects ranging in size from micrometeoroids to gas giants, aiming to determine their composition, dynamics, formation, interrelations and history. It is a strongly interdisciplinary field, originally growing from astronomy and earth science,[65] but which now incorporates many disciplines, including planetary astronomy, planetary geology (together with geochemistry and geophysics), atmospheric science, oceanography, hydrology, theoretical planetary science, glaciology, and the study of extrasolar planets.[65] Allied disciplines include space physics, when concerned with the effects of the Sun on the bodies of the Solar System, and astrobiology.

### Planets

Def. "a celestial body that

(a) is in orbit around the Sun,

(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and

(c) has cleared the neighbourhood around its orbit" is called a planet.[66]

The proposed more general definition for a planet in orbit around another star substitutes "a star" for "the Sun" in part (a), keeps part (b), does not contain part (c), and adds "is neither a star nor a satellite of a planet."[67]

Def. "a celestial body that

(a) is in orbit around the Sun,

(b) has sufficient mass for its self-gravity to overcome rigid forces so that it assumes a hydrostatic equilibrium (nearly round) shape,

(c) has not cleared the neighbourhood around its orbit, and

(d) is not a satellite" is called a dwarf planet.[66]

Def. "[a]ll other objects [not a planet or dwarf planet], except satellites, orbiting the Sun" are called collectively Small Solar-System Bodies.[66]

Def. a wanderer that is a moving light in the sky is called a planet.[66] This is the original description meant by the word "planet".[66]

From a theoretical planetary physics perspective: "The shape of objects with mass above 5 x 1020 kg and diameter greater than 800 km would normally be determined by self-gravity, but all borderline cases would have to be established by observation."[67]

Def. a celestial body "formed by accumulation of a rocky core, on a much longer timescale, ≳ 107 yr, with subsequent acquisition of a gaseous envelope if the circumstances allow this, and with an initially fractionated elemental composition" is called a planet.[57]

## Meta-astronomy

Meta-astronomy, or metaastronomy, is the collection of approaches to theoretical astronomy that may be considered when seeking to understand an astronomical phenomenon.

## Heliognosy

This image is a theory for the interior of the Sun. Credit: NASA.
This diagram contains the neutrino flux predictions for the 2005 Bahcall and Serenelli Standard Solar Model. Credit: John N. Bahcall, Aldo M.Serenelli, and Sarbani Basu.

In the model shown at right the Sun and regions around it are labeled. "The core of the Sun is considered to extend from the center to about 0.2 to 0.25 solar radius.[68] It is the hottest part of the Sun and of the Solar System. It has a density of up to 150 g/cm³ (150 times the density of liquid water) and a temperature of close to 15,000,000 kelvin [15 MK] The core is made of hot, dense gas in the plasmic state. The core, inside 0.24 solar radius, generates 99% of the fusion power of the Sun. It is in the core region that solar neutrinos may be produced.

The radiation zone or radiative zone is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion, rather than by convection.[69] Energy travels through the radiation zone in the form of electromagnetic radiation as photons. Within the Sun, the radiation zone is located in the intermediate zone between the solar core at .2 of the Sun's radius and the outer convection zone at .71 of the Sun's radius.[69]

The convection zone of a star is the range of radii in which energy is transported primarily by convection. Stellar convection consists of mass movement of plasma within the star which usually forms a circular convection current with the heated plasma ascending and the cooled plasma descending. This is the granular zone in the outer layer of a star.

The standard solar model (SSM) is a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma). This model, technically the spherically symmetric quasi-static model of a star, has stellar structure described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined.

## Heliography

As the Sun consists of a plasma and is not solid, it rotates faster at its equator than at its poles. This behavior is known as differential rotation, and is caused by convection in the Sun and the movement of mass, due to steep temperature gradients from the core outwards. This mass carries a portion of the Sun’s counter-clockwise angular momentum, as viewed from the ecliptic north pole, thus redistributing the angular velocity.

"Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator (latitude φ=0 deg), and to decrease as latitude increases. The differential rotation rate is usually described by the equation:

${\displaystyle \omega =A+B\,\sin ^{2}(\varphi )+C\,\sin ^{4}(\varphi )}$

where ω is the angular velocity in degrees per day, φ is the solar latitude and A, B, and C are constants. The values of A, B, and C differ depending on the techniques used to make the measurement, as well as the time period studied.[70] A current set of accepted average values[71] is:

A= 14.713 deg/day (± 0.0491)
B= –2.396 deg/day (± 0.188)
C= –1.787 deg/day (± 0.253)

## Heliometry

The butterfly diagam shows paired sunspot pattern. The graph is of sunspot Wolf number versus time. Credit: .

"[B]y assuming a harmonic variation having a period of 11.13 years ... the phases of such a variation [in polar diameter minus equatorial diameter of the Sun] coincide to within one-fifth of a year with the phases of the sun-spot fluctuations; that, at times corresponding to minimum of sun-spottedness, the polar diameter is relatively larger; that, at times of maximum sun-spottedness, the equatorial diameter is relatively larger. The amplitude of the variation is extremely small, but its reality would seem to be established. [This] at least renders the existence of such periodic fluctuations in the shape of the sun more probable than their non-existence."[72]

"Solar oblateness, the difference between the equatorial and polar diameters, reflects certain fundamental properties of the Sun. ... the oblateness reflects properties of the Sun's interior, ... [There is] a time varying, excess equatorial brightness [producing] a difference between the equatorial and polar limb darkening functions ... at times when the excess brightness is reduced, the intrinsic visual oblateness can be obtained from the observations without detailed knowledge of the excess brightness. A period of reduced excess brightness occurred in 1973 September."[73] The period of reduced excess equatorial brightness occurred between solar cycle maximum around 1970 and minimum around 1975. Considering excess equatorial brightness and seeking to perform measurements at opportunities of reduced excess equatorial brightness has the effect of reducing solar oblateness from some 86.6 ± 6.6 milli-arcsec to 18.4 ± 12.5 milli-arcsec.[73]

The Babcock Model describes a mechanism which can explain magnetic and sunspot patterns observed on the Sun.

1. The start of the 22-year cycle begins with a well-established dipole field component aligned along the solar rotational axis. The field lines tend to be held by the highly conductive solar plasma of the solar surface.
2. The solar surface plasma rotation rate is different at different latitudes, and the rotation rate is 20 percent faster at the equator than at the poles (one rotation every 27 days). Consequently, the magnetic field lines are wrapped by 20 percent every 27 days.
3. After many rotations, the field lines become highly twisted and bundled, increasing their intensity, and the resulting buoyancy lifts the bundle to the solar surface, forming a bipolar field that appears as two spots, being kinks in the field lines.
4. The sunspots result from the strong local magnetic fields in the solar surface that exclude the light-emitting solar plasma and appear as darkened spots on the solar surface.
5. The leading spot of the bipolar field has the same polarity as the solar hemisphere, and the trailing spot is of opposite polarity. The leading spot of the bipolar field tends to migrate towards the equator, while the trailing spot of opposite polarity migrates towards the solar pole of the respective hemisphere with a resultant reduction of the solar dipole moment. This process of sunspot formation and migration continues until the solar dipole field reverses (after about 11 years).
6. The solar dipole field, through similar processes, reverses again at the end of the 22-year cycle.
7. The magnetic field of the spot at the equator sometimes weakens, allowing an influx of coronal plasma that increases the internal pressure and forms a magnetic bubble which may burst and produce an ejection of coronal mass, leaving a coronal hole with open field lines. Such a coronal mass ejections are a source of the high-speed solar wind.
8. The fluctuations in the bundled fields convert magnetic field energy into plasma heating, producing emission of electromagnetic radiation as intense ultraviolet (UV) and X-rays.

## Stellar evolution

Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main sequence star.

Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, while more massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole.

## Galaxy formation and evolution

The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have generated the variety of structures observed in nearby galaxies. It is one of the most active research areas in astrophysics.

Galaxy formation is hypothesized to occur, from structure formation theories, as a result of tiny quantum fluctuations in the aftermath of the Big Bang. The simplest model for this that is in general agreement with observed phenomena is the ${\displaystyle \Lambda }$ Cold Dark Matter cosmology; that is to say that clustering and merging is how galaxies gain in mass, and can also determine their shape and structure.

## Hypotheses

1. The capability of theorizing in hominins goes back perhaps four million years.

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