The best empirical evidence that supermassive black holes do really exist is the orbits of these stars around the center of the Milky Way. Credit: Stefan Gillessen, Reinhard Genzel, Frank Eisenhauer, ESO.`{{free media}}`

A list or catalog of the specific principles incorporated into the development of the various radiation astronomies may be helpful to students and researchers alike.

These principles can be included in mathematical astronomy, astrophysics, astrochemistry, and theoretical radiation astronomy as summaries, or, a lecture on empirical radiation astronomy.

## Axioms

An axiom is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.

Def. "A proposition that commends itself to general acceptance; a well-established or universally conceded principle; a maxim, rule, law"[1] is called an axiom.

Axioms define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true. Therefore, its truth is taken for granted within the particular domain of analysis, and serves as a starting point for deducing and inferring other (theory and domain dependent) truths. An axiom is defined as a mathematical statement that is accepted as being true without a mathematical proof.[2]

## Postulates

The root meaning of the word 'postulate' is to 'demand'; for instance, Euclid demands of us that we agree that some things can be done, e.g. any two points can be joined by a straight line, etc.[3]

Ancient geometers maintained some distinction between axioms and postulates. While commenting on Euclid's books Proclus remarks that "Geminus held that this 4th Postulate should not be classed as a postulate but as an axiom, since it does not, like the first three Postulates, assert the possibility of some construction but expresses an essential property".[4] Boethius translated 'postulate' as petitio and called the axioms notiones communes.

At the foundation of the various sciences lay certain additional hypotheses which were accepted without proof. Such a hypothesis was termed a postulate. While the axioms were common to many sciences, the postulates of each particular science were different. Their validity had to be established by means of real-world experience.

Postulates should be regarded as purely formal statements, and not as facts based on experience.

## First principles

In philosophy, a first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption.

In mathematics, first principles are referred to as axioms or postulates. Gödel's incompleteness theorems have been taken to prove, among other things, that no system of axioms that describe the set of natural numbers can prove its own validity - nor perhaps can it prove every truth about the natural numbers.

In a formal logical system, that is, a set of propositions that are consistent with one another, it is probable that some of the statements can be deduced from one another. For example, in the syllogism, "All men are mortal; Socrates is a man; Socrates is mortal" the last claim can be deduced from the first two."

A first principle is one that cannot be deduced from any other. The classic example is that of Euclid's geometry; its hundreds of propositions can be deduced from a set of definitions, postulates, and common notions: all three of which constitute first principles.

In physics, a calculation is said to be from first principles, or ab initio, if it starts directly at the level of established laws of physics and does not make assumptions such as empirical model and fitting parameters.

For example, calculation of electronic structure using Schrödinger's equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.

## Empirical research

Empirical research is a way of gaining knowledge by means of direct and indirect observation or experience. Empirical evidence (the record of one's direct observations or experiences) can be analyzed quantitatively or qualitatively. Through quantifying the evidence or making sense of it in qualitative form, a researcher can answer empirical questions, which should be clearly defined and answerable with the evidence collected (usually called data). Research design varies by field and by the question being investigated. Many researchers combine qualitative and quantitative forms of analysis to better answer questions which cannot be studied in laboratory settings, particularly in the social sciences and in education.

In some fields, quantitative research may begin with a research question (e.g., "Does listening to vocal music during the learning of a word list have an effect on later memory for these words?") which is tested through experimentation in a lab. Usually, a researcher has a certain theory regarding the topic under investigation. Based on this theory some statements, or hypotheses, will be proposed (e.g., "Listening to vocal music has a negative effect on learning a word list."). From these hypotheses predictions about specific events are derived (e.g., "People who study a word list while listening to vocal music will remember fewer words on a later memory test than people who study a word list in silence."). These predictions can then be tested with a suitable experiment. Depending on the outcomes of the experiment, the theory on which the hypotheses and predictions were based will be supported or not.[5]

Accurate analysis of data using standardized statistical methods in scientific studies is critical to determining the validity of empirical research. Statistical formulas such as regression, uncertainty coefficient, t-test, chi square, and various types of ANOVA (analyses of variance) are fundamental to forming logical, valid conclusions. If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported. If not, the null hypothesis is supported (or, more correctly, not rejected), meaning no effect of the independent variable(s) was observed on the dependent variable(s).

It is important to understand that the outcome of empirical research using statistical hypothesis testing is never proof. It can only support a hypothesis, reject it, or do neither. These methods yield only probabilities.

## Empirical evidence

Empirical evidence (as distinct from empirical research) refers to objective evidence that appears the same regardless of the observer. For example, a thermometer will not display different temperatures for each individual who observes it. Temperature, as measured by an accurate, well calibrated thermometer, is empirical evidence. By contrast, non-empirical evidence is subjective, depending on the observer. Following the previous example, observer A might truthfully report that a room is warm, while observer B might truthfully report that the same room is cool, though both observe the same reading on the thermometer. The use of empirical evidence negates this effect of personal (i.e., subjective) experience.

## Meteors

This ultraviolet-wavelength image mosaic, taken by NASA's Galaxy Evolution Explorer (GALEX), shows a comet-like "tail" stretching 13 light years across space. Credit: NASA.`{{free media}}`

Each of the many senses possessed by intelligent life forms on Earth adds information about the objects or entities sensed and concluded about, that transit, continue occupation of a position for longer periods, or apparently change course or position in the sky.

## First principles of radiation astronomy

1. Arguably, the first principle of radiation astronomy is that there is a sky and it is not impervious.
2. It may be an axiom that "there is a sky". But, it is probably a postulate that the sky "is not impervious."
3. Another early principle may be that outer space exists and it is not a perfect vacuum. Here again that "outer space exists" may be an axiom and that "it is not a perfect vacuum" may be another postulate.

A further principle is a vacuum in which there are no matter particles and no photons. A similar concept is the quantum electrodynamics vacuum (QED vacuum). QED vacuum is a state with no matter particles (hence the name), and also no photons, no gravitons, etc. This state QED vacuum is impossible to achieve experimentally. (Even if every matter particle could somehow be removed from a volume, it would be impossible to eliminate all the blackbody photons.)

Conversely, it could be stated that space is only a manifestation of the ubiquity of electromagnetic radiation. Space may be the result of that manifestation rather than a container in which electromagnetic radiation radiates.

## Objects

Volcanic bombs are thrown into the sky and travel some distance before returning to the ground. This bomb is in the Craters of the Moon National Monument and Preserve, Idaho, USA. Credit: National Park Service.`{{free media}}`

## Strong forces

Mount Redoubt in Alaska erupted on April 21, 1990. The mushroom-shaped plume rose from avalanches of hot debris that cascaded down the north flank. Credit: R. Clucas, USGS.`{{free media}}`

The radiation of the plume from Mount Redoubt or Mira producing a 13-lyr long tail required a strong force.

## Electromagnetics

This is a panorama photograph taken during a lightning storm over Bucharest, Romania. Credit: Catalin.Fatu.`{{free media}}`

The radiation of electrons away from the Earth, or positive charges toward the Earth, is electromagnetic and packs a punch.

## Craters

This is an aerial view of the Barringer Meteor Crater about 69 km east of Flagstaff, Arizona. Credit:D. Roddy, U.S. Geological Survey.`{{free media}}`

The meteor radiated toward the Earth created the Barringer Meteor Crater.

## Liquid objects

This image shows a late-summer rainstorm in Denmark. The nearly black color of the cloud's base indicates the foreground cloud is probably cumulonimbus. Credit: Malene Thyssen.`{{free media}}`

## Rocky objects

These images show the libration of the Moon over a single lunar month. Credit: Tomruen.`{{free media}}`

## Atmospheres

This is a graph of the global mean atmospheric water vapor superimposed on an outline of the Earth. Credit: NASA.`{{free media}}`

## Meteorites

The Williamette Meteorite is on display at the American Museum of Natural History in New York City. Credit: Dante Alighieri.`{{free media}}`
This image is a cross-section of the Laguna Manantiales meteorite showing Widmanstätten patterns. Credit: Aram Dulyan.`{{free media}}`

"A meteorite is a natural object originating in outer space that survives impact with the Earth's surface. ... Most meteorites derive from small astronomical objects called meteoroids. When a meteoroid enters the atmosphere, frictional, pressure, and chemical interactions with the atmospheric gasses cause the body to heat up and emit light, thus forming a fireball, also known as a meteor or shooting/falling star.

Widmanstätten patterns, also called Thomson structures, are unique figures of long nickel-iron crystals, found in the octahedrite iron meteorites and some pallasites. They consist of a fine interleaving of kamacite and taenite bands or ribbons called lamellæ. Commonly, in gaps between the lamellæ, a fine-grained mixture of kamacite and taenite called plessite can be found.

## Observatories

This is the dome of the Zeiss telescope at Merate Astronomical Observatory, Merate (LC), Italy. Credit: CAV.`{{free media}}`

The domes of observatories, such as in the image at right, and the objects inside used to observe and control these observatories are made of chemicals.

## Spectroscopy

The relative absorption of an infrared laser. In the red line's profile you can see the hyperfine-structure of the first excited level of rubidium. Credit: Clemens Adolphs.`{{free media}}`

"Spectroscopy is the study of the interaction between matter and radiated energy.[6][7] The concept comprises any interaction with radiative energy as a function of its wavelength or frequency. Spectroscopic data is often represented by a spectrum, a plot of the response of interest as a function of wavelength or frequency. Spectrometry and spectrography are terms used to refer to the measurement of radiation intensity as a function of wavelength and are often used to describe experimental spectroscopic methods. Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers.

## Interplanetary medium

The Zodiacal Light is over the Faulkes Telescope, Haleakala, Maui. Credit: 808caver.`{{free media}}`

## Locations on Earth

This image shows the pyramids of Giza. Credit: [Liberato].`{{free media}}`
National Observatory of Athens, Greece, is on top of the Nymphs' Hill.`{{free media}}`

To locate themselves on the surface of the Earth, various grid systems are devised using special points of reference. Each local center of civilization that realized the need for locating itself produced a system. One such system, the geographic coordinate system has based its locational grid on "[a] line passing near the Royal Observatory, Greenwich (near London in the United Kingdom UK). Another on French Institut Géographique National (IGN) maps still uses a longitude meridian passing through Paris, along with longitude from Greenwich.

## Extreme locations

The large white arrow indicates Luna 21. The smaller white arrows indicate the rovers tracks. The black arrow indicates the crater where it picked up its fatal load of lunar dust. The grey dot lower left of the crater is thought to be the rover itself. Credit: NASA.`{{free media}}`

## History/Ancient|Ancient history

This image is a photo of the Nimrud lens in the British museum.`{{free media}}`

The ancient history period dates from around 8,000 to 3,000 b2k.

Efforts to magnify objects in the sky probably began with the use of crystal lenses. "Lens-shaped crystals have long been known from Bronze Age contexts"[8]. These are "usually recognized as short-focus magnifying lenses."[8]

The slightly oval lens [40 x 35 mm] has been roughly ground and has a focal point about 110 millimetres (4.5 in) from the flat side.[9][10]

## Recent history

This photograph is of an astrolabe quadrant from England of 1388. Credit: PHGCOM.
This is an image of a biconvex lens. Credit: Tamasflex.`{{free media}}`

## Physics

This beautiful galaxy is tilted at an oblique angle on to our line of sight, giving a "birds-eye view" of the spiral structure. Credit: Hubble data: NASA, ESA, and A. Zezas (Harvard-Smithsonian Center for Astrophysics); GALEX data: NASA, JPL-Caltech, GALEX Team, J. Huchra et al. (Harvard-Smithsonian Center for Astrophysics); Spitzer data: NASA/JPL/Caltech/S. Willner (Harvard-Smithsonian Center for Astrophysics.`{{free media}}`

Def. a “straight line along which an observer has a clear view”[11] is called line of sight.

## Technology

The International Space Station is featured in this image photographed by an STS-134 crew member on the space shuttle Endeavour after the station and shuttle began their post-undocking relative separation. Credit: NASA.`{{free media}}`

## Hypotheses

1. An empiricism in astronomy may say more about reality than the best physics theory.

## References

1. axiom, n., definition 1a. Oxford English Dictionary Online, accessed 2012-04-28. Cf. Aristotle, Posterior Analytics I.2.72a18-b4.
2. Ted Sundstorm, "Mathematical reasoning: writing and proof," Prentice Hall, 2003, p 71.
3. Wolff, P. Breakthroughs in Mathematics, 1963, New York: New American Library, pp 47–8
4. T. L. Heath 1956. The Thirteen Books of Euclid's Elements. New York: Dover. p200
5. Goodwin, C. J. (2005). Research in Psychology: Methods and Design. USA: John Wiley & Sons, Inc.
6. Crouch, Stanley; Skoog, Douglas A. (2007). Principles of instrumental analysis. Australia: Thomson Brooks/Cole. ISBN 0-495-01201-7.
7. . doi:10.1351/pac198658121737.
8. Dimitris Plantzos (July 1997). "Crystals and Lenses in the Graeco-Roman World". American Journal of Archaeology 101 (3): 451-64. Retrieved 2011-10-17.
9. Austen Henry Layard (1853). Discoveries in the ruins of Nineveh and Babylon: with travels in Armenia. G.P. Putnam and Co. pp. 197–8,674.
10. D. Brewster (1852). "On an account of a rock-crystal lens and decomposed glass found in Niniveh". Die Fortschritte der Physik (Deutsche Physikalische Gesellschaft).
11. line of sight. San Francisco, California: Wikimedia Foundation, Inc. May 3, 2012. Retrieved 2012-06-16.