formulasearchengine - User contributions [en]

Rocket propellant

2015-01-06T19:32:24Z

184.175.39.57: /* Disadvantages */

There are actually inconsistent viewpoints in regards to what somebody must try to eat to acquire the nutrition he must reside an entire and wholesome life. This information will help you acquire a much better comprehension of nutrition so that you can strategy your meals every day. All of us need to take enough fiber content. One way fibers can help you is actually by assisting you to truly feel complete. It will also aid in reducing blood vessels cholesterol. Dietary fiber can help for long-phrase troubles like many forms of cancer and diabetic issues at the same time. If you plenty of travelling, be sure you hold coupled a good electricity enhancer, like a health proteins pub. [http://Bondageuprising.com/groups/need-help-planning-healthy-meals-check-out-these-ideas/ Standard food] within an air-port are difficult to acquire. With additional security there is certainly typically bit of time to eat, and flights will no longer offer foods. Make sure you keep a few of these cafes useful in order to stop craving for food until you territory, at which point you are able to consume a well-balanced meal. To ensure that your body is to get its dietary needs achieved, you need to hedge your option with a good multivitamin pill. This vitamin can present you with the cornerstone for the minerals that you require throughout the morning. Very packaged cereals often swap grain since packaged whole grains are tastier. White flour is useful, according to the food that it must be employed in. However, grain typically provide heartier flavour along with more dietary fiber to aid correct food digestion. Make the most of your day-to-day caloric allowance by eating healthy food to gas your system. You may feel good and also be much healthier when you devote your everyday unhealthy calories wisely, for example on greens, whole grains, and proteins. The quality of the foodstuffs you eat calls for as much consideration since the amount. Meat is rich in body fat, so using turkey breasts that may be ground up is actually a far healthier alternative. The poultry meat has a lot less unhealthy calories and saturated fats in comparison to the meat. Make sure that you select ground turkey bust rather than dark meats, as this type of poultry is similar in nutritional content material to ground meat. Some soil poultry might have a mixture of darkish and typical meat which means you won't have each of the advantages of decreasing each of the unhealthy fats. Putting together a scrumptious shake might be pleasurable and satisfying. Think about this idea to add much more nourishment to your shake. Add a dab of flax-seed oil or cocoa natural powder in your smoothie on an anti-oxidant-rich pick-me-up. This would also enhance the flavoring of your own refreshment and increase your immunity process. One method to improve the healthy information of your eating habits are to utilize sugar substitutes instead of enhanced sweets. Eating sugar too frequently may also lead to diabetic issues and many other health issues. Rather, give Stevia or Splenda a try. The difference in [http://Dobryfachowiec.Co.uk/everyone-can-grow-familiar-muscle-building-straightforward-tips/ preference] is tough (as well as out of the question) to notice. Try out generally to motivate far more ingesting water through the day. It's ok to supply up fruit juice or dairy at food periods, but don't provide it as a a among-dinner solution. Filling up with liquid or milk products will make a person unlikely to possess space for significant foods. Permanently diet, unprocessed veggies come up with a great, wholesome treat. Natural fresh vegetables are ideal for eliminating yearnings, allowing you to really feel complete, and consist of lots of healthy vitamins and minerals. They're little more challenging to make than junk food is. These are cleanser and simpler to deal with than [http://Www.Dropnote.Co.kr/zbxe/gguide/154134 refined junk] food. Having unprocessed veggies is a good way to treat somewhere between foods. Explore the countless exciting possibilities of salads to enhance your level of nutrients. A salad is approximately a lot more than some lettuce and creamy getting dressed. You are able to place anything from cooked various meats or [http://www.tenfoldsales.com/content/krystalpraedmzi-success-story what is the best weight gainer For teenager] whole grains to unprocessed vegetables and fresh fruit right into a salad. Be creative! Salads are a good like a primary course or as a side recipe together with your principal dish. There are lots of excellent, healthy salad getting dressed dishes you can consider. Consist of distinctive salad substances that you haven't attempted before. Place in some peanuts or fruits, or mix in a little bit peanut butter! Do whichever it will require to make your greens preference delicious yet still be wholesome. Employing supplements once and for all nutrients will never help. Dietary supplements should act as harmonizes with to some strong diet program. Be sure your meal is full of nutrients and simply take 1 multivitamin each day. Prevent sodium when boiling hot water. It improves your sodium. Sodium is not necessary, so will not put it, and wait the handful of extra a few minutes it will require water to boil. Cooking food kabobs underneath the broiler is actually a warm and friendly dish year-round. When you cherished this short article in addition to you wish to get details with regards to [http://stemlessonplans.com/blog/view/55426/major-depression-and-steroids-hazards-for-body-weight-lifters Best Body Nutrition Weight Gainer] i implore you to visit our web site. Children really enjoy this since they can pick the fresh vegetables and beef with regard to their kabob. Pick bright vibrant veggies, like reddish onion and bell peppers. Should you prefer a healthier diet program, try to eat far more raw meals as opposed to processed food or deep-fried food. This is because cooking and finalizing can diminish normal nutrients and vitamins in food. This is also true for vegatables and fruits. In case your ideal is useful nutrients, then ingesting a properly properly-well-balanced [http://diendan.volamhuyetkiem.com/entry.php?b=3109 best weight gainer in the world] loss program is important. Obtaining the proper harmony of dietary staples is key in every meal you take in. Make an effort to have 30% fat, 20% proteins and 50Per cent carbohydrates in whichever you're going to take in. If you would like remain healthy you have to understand as much as you can. Trying to take in in the more healthy approach without the proper information and facts will probably be a waste of time. You need to understand at the very least the essentials in the technology of nutrients to be able to boost your diet program. Ingesting plenty of water is the most popular, and significant tip to keep in mind when you are trying to stay healthy. The body include a large percentage of normal water, you ought to ensure that it stays hydrated. Ingest no less than sixty oz water day-to-day. As we discussed, getting the correct info regarding nutrients may also be hard. Through taking what you understand nutrition, even though, and make an effort to change, you will certainly be in good condition.

Debits and credits

2014-01-09T00:42:39Z

184.175.14.30: "Distinguish" hatnote changed to "Redirect-distinguish".

[[File:Star-Spectroscope.jpg|thumb|The Star-Spectroscope of the Lick Observatory in 1898]]

'''Astronomical spectroscopy''' is the study of [[spectroscopy]] and [[spectra]] used in [[astronomy]] to aid scientists in advancing in the study of visible light waves dispersed according to their wavelengths. The object of study is the [[electromagnetic spectrum|spectrum]] of [[electromagnetic radiation]], including visible light, which [[radiant energy|radiates]] from [[star]]s and other hot celestial objects. Spectroscopy can be used to derive many properties of distant stars and galaxies, such as their chemical composition, temperature, density, mass, distance, luminosity, and relative motion using [[Doppler effect|Doppler shift]] measurements.

==Background==
[[File:Atmospheric electromagnetic opacity.svg|thumb|Electromagnetic transmittance, or opacity, of the Earth's atmosphere]]
Astronomical spectroscopy can be broken down into three major bands: optical, [[radio wave|radio]], and [[X-ray]]. While all spectroscopy looks at specific areas of the spectrum, different methods are required to acquire the signal depending on the frequency/wavelength. [[Ozone]] (O3) and molecular oxygen (O2) absorb light with wavelengths under 300 nm, meaning that X-ray and [[ultraviolet]] spectroscopy require the use of a satellite telescope and/or [[X-ray astronomy#Sounding rocket flights|rocket mounted detectors]].<ref name=Foukal />{{rp|27}}. Radio signals have much longer wavelengths than optical signals, and require the use of [[Radio telescope#Types|antennas or radio dishes]]. [[Infrared]] light is absorbed by atmospheric water and carbon dioxide, so while the equipment is similar to that used in optical spectroscopy, satellites are required to record much of the infrared spectrum.<ref>{{cite web|title=Cool Cosmos - Infrared Astronomy|url=http://coolcosmos.ipac.caltech.edu/cosmic_classroom/ir_tutorial/irwindows.html|publisher=California Institute of Technology|accessdate=23 October 2013}}</ref>

===Optical spectroscopy===
[[Image:Blazedgrating.jpg|thumb|Incident light reflects at the same angle (black lines), but a small portion of the light is refracted as coloured light (red and blue lines).]]
Physicists have been looking at the solar spectrum since [[Isaac Newton]] first used a simple prism to observe the refractive properties of coloured light.<ref name=Opticks /> In the early 1800s [[Joseph von Fraunhofer]] used his skills as a glass maker to create very pure prisms, which allowed him to observe 574 dark lines in a seemingly continuous spectrum.<ref name=Fraunhofer /> Soon after he combined telescope and prism to observe the spectrum of [[Venus]], the [[Moon]], [[Mars]], and various stars such as [[Betelgeuse]]; his company continued to manufacture and sell high-quality refracting telescopes based on his original designs until its closure in 1884.<ref name=Hearnshaw />{{rp|28–29}}

The resolution of a prism is limited by its size; a larger prism will provide a more detailed spectrum, but the increase in mass makes it unsuitable for highly detailed work.<ref name=Kitchin /> This issue was resolved in the early 1900s with the development of high-quality reflection gratings by [[John Stanley Plaskett|J.S. Plaskett]] at the [[Dominion Observatory]] in Ottawa, Canada.<ref name=Hearnshaw />{{rp|11}} Light striking a mirror will reflect at the same angle, however a small portion of the light will be refracted at a different angle; this is dependent upon the indices of refraction of the materials and the wavelength of the light.<ref name=Ball /> By creating a [[blazed grating|"blazed" grating]] which utilizes a large number of parallel mirrors, the small portion of light can be focused and visualized. These new spectroscopes were more detailed than a prism, required less light, and could be focused on a specific region of the spectrum by tilting the grating.<ref name=Kitchin />

The limitation to a blazed grating is the width of the mirrors, which can only be ground a finite amount before focus is lost; the maximum is around 1000 lines/mm. In order to overcome this limitation holographic gratings were developed. Holographic gratings use a thin film of dichromated gelatin on a glass surface, which is subsequently exposed to a [[Interference (wave propagation)|wave pattern]] created by an [[interferometer]]. This wave pattern sets up a reflection pattern similar to the blazed gratings but utilizing [[Bragg's law|Bragg diffraction]], a process where the angle of reflection is dependent on the arrangement of the atoms in the gelatin. Holographic gratings can have up to 6000 lines/mm and can be up to twice as efficient in collecting light as blazed gratings. Because they are sealed between two sheets of glass, holographic gratings are very versatile, potentially lasting decades before needing replacement.<ref>{{cite journal|last=Barden|first=S.C.|coauthors=J.A. Arns and W.S. Colburn|title=Volume-phase holographic gratings and their potential for astronomical applications|journal=Proc. SPIE|date=July 1998|volume=3355|pages=866–876|doi=10.1117/12.316806|series=Optical Astronomical Instrumentation|editor1-last=d'Odorico|editor1-first=Sandro}}</ref>

===Radio spectroscopy===
{{main|Radio astronomy}}
Radio astronomy first started with [[Karl Guthe Jansky|Karl Jansky]] in the early 1930s. Working for [[Bell Labs]], he built a radio antenna to look at potential sources of interference for transatlantic radio transmissions. One of the sources of static discovered came not from Earth, but from the center of the [[Milky Way]], in the constellation [[Sagittarius A|Sagittarius]].<ref>{{cite web|last=Ghigo|first=F|title=Karl Jansky|url=http://www.nrao.edu/whatisra/hist_jansky.shtml|work=National Radio Astronomy Observatory|publisher=Associated Universities, Inc.|accessdate=24 October 2013}}</ref> In 1942, [[James Stanley Hey|JS Hey]] captured the sun's radio frequency using military radar receivers.<ref name=Foukal />{{rp|26}}

Radio [[astronomical interferometer|interferometry]] was pioneered in 1946, when [[Joseph Lade Pawsey]], [[Ruby Payne-Scott]] and [[Lindsay McCready]] used a [[sea interferometry|single antenna atop a sea cliff]] to observe 200 MHz solar radiation. Two incident beams, one directly from the sun and the other reflected from the sea surface, generated the necessary interference.<ref>{{cite journal|last=Pawsey|first=Joseph|last2=Payne-Scott|first2=Ruby|last3=McCready|first3=Lindsay|year=1946|journal=[[Nature (journal)|Nature]]|title=Radio-Frequency Energy from the Sun|volume=157|page=158|doi=10.1038/157158a0|issue=3980}}</ref> The first multi-receiver interferometer was built in the same year by [[Martin Ryle]] and Vonberg.<ref>{{cite journal|author=Ryle & Vonberg|year=1946|title=Solar Radiation on 175 Mc./s|journal=Nature|doi=10.1038/158339b0|volume=158|page=339|first2=D. D.|issue=4010}}</ref><ref name="Robertson">{{Cite book
| last = Robertson
| first = Peter
| title = Beyond southern skies: radio astronomy and the Parkes telescope
| publisher = University of Cambridge
| year = 1992
| pages = 42, 43
| url = http://books.google.com.au/books?id=QgQ-SFKIMdoC&pg=PA42&dq=sea+interferometry&cd=1#v=onepage&q=sea%20interferometry&f=false
| isbn = 0-521-41408-3}}</ref> In 1960, Ryle and [[Antony Hewish]] published the technique of [[aperture synthesis]] to analyze interferometer data.<ref>{{cite web|url=http://www.nrao.edu/library/Memos/Misc/Howard_Chronological_History_0674.pdf|title=A Chronological History of Radio Astronomy|accessdate=2 December 2013|author=W. E. Howard}}</ref> The aperture synthesis process, which involves [[autocorrelation|autocorrelating]] and [[discrete Fourier transform]]ing the incoming signal, recovers both the spatial and frequency variation in flux.<ref>{{cite web|url=http://www.nrao.edu/index.php/learn/radioastronomy/radiotelescopes|title=How Radio Telescopes Work|accessdate=2 December 2013}}</ref> The result is a [[data cube|3D image]] whose third axis is frequency. For this work, Ryle and Hewish were jointly awarded the 1974 [[Nobel Prize in Physics]].<ref>{{cite web|url=http://www.nobelprize.org/nobel_prizes/physics/laureates/1974/press.html|title=Press Release: The 1974 Nobel Prize in Physics|accessdate=2 December 2013}}</ref>

===X-ray spectroscopy===
{{main|X-ray astronomy}}

==Stars and their properties==

===Chemical properties===
[[Image:Spectral lines continous.png|thumb|[[Spectrum|Continuous spectrum]]]]
[[Image:Spectral lines emission.png|thumb|[[Emission spectrum|Emission lines]]]]
[[Image:Spectral lines absorption.png|thumb|[[Absorption spectroscopy|Absorption lines]]]]
Newton used a prism to split white light into a spectrum of color, and Fraunhofer's high-quality prisms allowed scientists to see dark lines of an unknown origin. It was not until the 1850s that [[Gustav Kirchhoff]] and [[Robert Bunsen]] would describe the phenomena behind these dark lines; hot solid objects produce light with a continuous [[spectrum]], hot gasses emit light at specific wavelengths, and hot solid objects surrounded by cooler gasses will show a near-continuous spectrum with dark lines corresponding to the emission lines of the gasses.<ref name=Hearnshaw />{{rp|42–44}}<ref name=Jenkins /> By comparing the [[absorption spectroscopy|absorption lines]] of the sun with [[Emission spectrum|emission spectra]] of known gasses, the chemical composition of stars can be determined.

The major [[Fraunhofer lines]], and the elements they are associated with, are shown in the following table:

{| 
| valign="top" |
{| class="wikitable"
!Designation
!Element
!Wavelength ([[nanometer|nm]])
|-
|y
|[[Oxygen|O2]]
|898.765
|-
|Z
|O2
|822.696
|-
|A
|O2
|759.370
|-
|B
|O2
|686.719
|-
|C
|[[Hydrogen|H]]α
|656.281
|-
|a
|O2
|627.661
|-
|D1
|[[Sodium|Na]]
|589.592
|-
|D2
|Na
|588.995
|-
|D3 or d
|[[Helium|He]]
|587.5618
|-
|e
|[[Mercury (element)|Hg]]
|546.073
|-
|E2
|[[Iron|Fe]]
|527.039
|-
|b1
|[[Magnesium|Mg]]
|518.362
|-
|b2
|Mg
|517.270
|-
|b3
|Fe
|516.891
|-
|b4
|Mg
|516.733
|}
| valign="top" | 
{| class="wikitable"
!Designation
!Element
!Wavelength ([[nanometer|nm]])
|-
|c
|Fe
|495.761
|-
|F
|Hβ
|486.134
|-
|d
|Fe
|466.814
|-
|e
|Fe
|438.355
|-
|G'
|Hγ
|434.047
|-
|G
|Fe
|430.790
|-
|G
|[[Calcium|Ca]]
|430.774
|-
|h
|Hδ
|410.175
|-
|H
|Ca+
|396.847
|-
|K
|Ca+
|393.368
|-
|L
|Fe
|382.044
|-
|N
|Fe
|358.121
|-
|P
|[[Titanium|Ti]]+
|336.112
|-
|T
|Fe
|302.108
|-
|t
|[[Nickel|Ni]]
|299.444
|}
|} 

Not all of the elements in the sun were immediately identified. Two examples are listed below.
*In 1868 [[Norman Lockyer]] and [[Pierre Janssen]] independently observed a line next to the sodium doublet (D1 and D2) which Lockyer determined to be a new element. He named it [[Helium]], but it wasn't until 1895 the element was found on Earth.<ref name=Hearnshaw />{{rp|84–85}}
*In 1869 the astronomers [[Charles Augustus Young]] and [[William Harkness]] independently observed a novel green emission line in the Sun's [[corona]] during an eclipse. This "new" element was incorrectly named [[coronium]], as it was only found in the corona. It was not until the 1930s that [[Walter Grotrian]] and [[Bengt Edlén]] discovered that the spectral line at 530.3 nm was due to [[highly charged ion|highly ionized]] iron (Fe13+).<ref name=Morison /> Other unusual lines in the coronal spectrum are also caused by highly charged ions, such as [[nickel]] and [[calcium]], the high ionization being due to the extreme temperature of the [[corona|solar corona]].<ref name=Foukal />{{rp|87,297}}
To date more than 20 000 absorption lines have been listed for the [[Sun]] between 293.5 and 877.0 nm, yet only approximately 75% of these lines have been linked to elemental absorption.<ref name=Foukal />{{rp|69}}

By analyzing the width of each spectral line in an emission spectrum, both the elements present in a star and their relative abundances can be determined.<ref name=Ball /> Using this information stars can be categorized into [[Metallicity#Stellar populations|stellar populations]]; Population I stars are the youngest stars and have the highest metal content (our Sun is a Pop I star), while Population III stars are the oldest stars with a very low metal content.<ref name=Gregory>{{cite book|last=Gregory|first=Stephen A.; Michael Zeilik|title=Introductory astronomy & astrophysics|year=1998|publisher=Saunders College Publ.|location=Fort Worth [u.a.]|isbn=0-03-006228-4|page=322|edition=4.}}</ref><ref name=PopIII>{{cite journal|last=Pan|first=Liubin|coauthors=Scannapieco, Evan; Scalo, Jon|title=MODELING THE POLLUTION OF PRISTINE GAS IN THE EARLY UNIVERSE|journal=The Astrophysical Journal|date=1 October 2013|volume=775|issue=2|page=111|doi=10.1088/0004-637X/775/2/111}}</ref>

===Temperature and size===
[[File:Black body.svg|thumb|Black body curves for various temperatures.]]
In 1860 [[Gustav Kirchhoff]] proposed the idea of a [[black body]], a material that emits electromagnetic radiation at all wavelengths.<ref name=Kirchhoff /><ref name=Pradhan /> In 1894 [[Wilhelm Wien]] derived an expression relating the temperature (T) of a black body to its peak emission wavelength (λmax).<ref name=Massoud />
:<math>\lambda_\text{max} T = b</math>
''b'' is a [[proportionality constant|constant of proportionality]] called ''Wien's displacement constant'', equal to {{physconst|bwien|round=auto|after=.}} This equation is called [[Wien's displacement law|Wien's Law]]. By measuring the peak wavelength of a star, the surface temperature can be determined.<ref name=Jenkins /> For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 [[Kelvin]].

The [[luminosity]] of a star is a measure of the [[radiant energy|electromagnetic energy]] output in a given amount of time.<ref name=Australia /> Luminosity (L) can be related to the temperature (T) of a star by
:<math>L= 4 \pi R^2 \sigma T^4</math> ,

where R is the radius of the star and σ is the [[Stefan–Boltzmann]] constant, with a value of {{physconst|sigma|round=auto|after=.}} Thus, when both luminosity and temperature are known (via direct measurement and calculation) the radius of a star can be determined.

{{See also|Luminosity|Magnitude (astronomy)}}

==Galaxies==
The spectra of [[galaxy|galaxies]] look similar to stellar spectra, as they consist of the combined light of millions of stars.

Doppler shift studies of [[galaxy cluster]]s by [[Fritz Zwicky]] in 1937 found that most galaxies were moving much faster than seemed to be possible from what was known about the mass of the cluster. Zwicky hypothesized that there must be a great deal of non-luminous matter in the galaxy clusters, which became known as [[dark matter]].<ref name=Zwicky /> Since his discovery, astronomers have determined that a large portion of galaxies (and most of the universe) is made up of dark matter. In 2003, however, four galaxies (NGC 821, [[Messier 105|NGC 3379]], NGC 4494, and [[NGC 4697]]) were found to have little to no dark matter influencing the motion of the stars contained within them; the reason behind the lack of dark matter is unknown.<ref name=Romanowsky />

In the 1950s, strong radio sources were found to be associated with very dim, very red objects. When the first spectrum of one of these objects was taken there were absorption lines at wavelengths where none were expected. It was soon realised that what was observed was a normal galactic spectrum, but highly red shifted.<ref name=Matthews /><ref name=Wallace /> These were named ''quasi-stellar radio sources'', or [[quasars]], by [[Hong-Yee Chiu]] in 1964.<ref name=Chiu /> Quasars are now thought to be galaxies formed in the early years of our universe, with their extreme energy output powered by super-massive [[black hole]]s.<ref name= Wallace />

The properties of a galaxy can also be determined by analyzing the stars found within them. [[NGC 4550]], a galaxy in the Virgo Cluster, has a large portion of its stars rotating in the opposite direction as the other portion. It is believed that the galaxy is the combination of two smaller galaxies that were rotating in opposite directions to each other.<ref name=Rubin /> Bright stars in galaxies can also help determine the distance to a galaxy, which may be a more accurate method than [[parallax]] or [[Cosmic distance ladder#Standard candles|standard candles]].<ref name=Kudritzki />

==Interstellar medium==
The [[interstellar medium]] is matter that occupies the space between [[star systems]] in a galaxy. 99% of this matter is gaseous - [[hydrogen]], [[helium]], and smaller quantities of other ionized elements such as [[oxygen]]. The other 1% is dust particles, thought to be mainly [[graphite]], [[silicate]]s, and ices.<ref name=KitchinGas /> Clouds of the dust and gas are referred to as [[nebula]]e.

There are three main types of nebula: [[dark nebula|absorption]], [[reflection nebula|reflection]], and [[emission nebula|emission]] nebulae. Absorption (or dark) nebulae are made of dust and gas in such quantities that they obscure the starlight behind them, making [[Photometry (astronomy)|photometry]] difficult. Reflection nebulae, as their name suggest, reflect the light of nearby stars. Their spectra are the same as the stars surrounding them, though the light is bluer; shorter wavelengths scatter better than longer wavelengths. Emission nebulae emit light at specific wavelengths depending on their chemical composition.<ref name=KitchinGas />

===Gaseous emission nebulae===
In the early years of astronomical spectroscopy, scientists were puzzled by the spectrum of gaseous nebulae. In 1864 [[William Huggins]] noticed that many nebulae showed only emission lines rather than a full spectrum like stars. From the work of Kirchhoff, he concluded that nebulae must contain "enormous masses of luminous gas or vapour."<ref name=Huggins /> However, there were several emission lines that could not be linked to any terrestrial element, brightest among them lines at 495.9 nm and 500.7 nm.<ref name=Tennyson /> These lines were attributed to a new element, [[nebulium]], until [[Ira Sprague Bowen|Ira Bowen]] determined in 1927 that the emission lines were from highly ionised oxygen (O+2).<ref name=Hirsh /><ref name=Bowen /> These emission lines could not be replicated in a laboratory because they are [[forbidden mechanism|forbidden lines]]; the low density of a nebula (one atom per cubic centimetre)<ref name=KitchinGas /> allows for [[Metastability|metastable]] ions to decay via forbidden line emission rather than collisions with other atoms.<ref name=Tennyson />

Not all emission nebulae are found around or near stars where solar heating causes ionisation. The majority of gaseous emission nebulae are formed of neutral hydrogen. In the [[ground state]] neutral hydrogen has two possible [[spin (physics)|spin states]]: the [[electron]] has either the same spin or the opposite spin of the [[proton]]. When the atom transitions between these two states, it releases an emission or absorption line of 21 cm.<ref name=KitchinGas /> This line is within the radio range and allows for very precise measurements:<ref name=Tennyson />
*Velocity of the cloud can be measured via [[Astronomical spectroscopy#Doppler Shift|Doppler shift]]
*The intensity of the 21 cm line gives the density and number of atoms in the cloud
*The temperature of the cloud can be calculated
Using this information the shape of the Milky Way has been determined to be a [[spiral galaxy]], though the exact number and position of the spiral arms is the subject of ongoing research.<ref name=Efremov />

===Complex molecules===
{{main|List of interstellar and circumstellar molecules}}
Dust and molecules in the interstellar medium not only obscures photometry, but also causes absorption lines in spectroscopy. Their spectral features are generated by transitions of component electrons between different energy levels, or by rotational or vibrational spectra. Detection usually occurs in radio, microwave, or infrared portions of the spectrum.<ref name=Shu /> The chemical reactions that form these molecules can happen in cold, diffuse clouds<ref name=GoddardISM /> or in the hot ejecta around a [[white dwarf]] star from a [[nova]] or [[supernova]].<ref name=Buckyball /> [[Polycyclic aromatic hydrocarbon]]s such as [[acetylene]] (C2H2) generally group together to form graphites or other sooty material,<ref name=DustChemistry /> but other [[organic compound|organic molecules]] such as [[acetone]] ((CH3)2CO)<ref name=Acetone /> and [[buckminsterfullerene]]s (C60 and C70) have been discovered.<ref name=Buckyball />

==Motion in the universe==
[[File:Redshift blueshift.svg|thumb|Redshift and blueshift]]
Stars and interstellar gas are bound by gravity to form galaxies, and groups of galaxies can be bound by gravity in [[galaxy clusters]].<ref name=Hubble /> With the exception of stars in the [[Milky Way]] and the galaxies in the [[Local Group]], almost all galaxies are moving away from us due to the [[Metric expansion of space|expansion of the universe]].<ref name=Morison />

===Doppler effect and redshift===
The motion of stellar objects can be determined by looking at their spectrum. Because of the [[Doppler effect]], objects moving towards us are [[blueshift]]ed, and objects moving away are [[redshift]]ed. The wavelength of redshifted light is longer, appearing redder than the source. Conversely, the wavelength of blueshifted light is shorter, appearing bluer than the source light:
:<math>\frac{\lambda-\lambda_0}{\lambda_0}=\frac{v_0}{c}</math>
where <math>\lambda_0</math> is the emitted wavelength, <math>v_0</math> is the velocity of the object, and <math>\lambda</math> is the observed wavelength. Note that v<0 corresponds to λ<λ0, a blueshifted wavelength. A redshifted absorption or emission line will appear more towards the red end of the spectrum than a stationary line. In 1913 [[Vesto Slipher]] determined the [[Andromeda Galaxy]] was blueshifted, meaning it was moving towards the Milky Way. He recorded the spectra of 20 other galaxies — all but 4 of which were redshifted — and was able to calculate their velocities relative to the Earth. [[Edwin Hubble]] would later use this information, as well as his own observations, to define [[Hubble's law]]: The further a galaxy is from the Earth, the faster it is moving away from us.<ref name=Morison /><ref name=HubbleLaw /> Hubble's law can be generalised to
:<math>v = H_0 d</math>
where <math>v</math> is the velocity (or Hubble Flow), <math>H_0</math> is the [[hubble's law#Observed values|Hubble Constant]], and <math>d</math> is the distance from Earth.

Redshift (z) can be expressed by the following equations:<ref name=redshift />
{| class="wikitable" style="margin:auto;"
|+ '''Calculation of redshift, <math>z</math>'''
! '''Based on wavelength''' !! '''Based on frequency'''
|- align=center
| <math>z = \frac{\lambda_{\mathrm{obsv}} - \lambda_{\mathrm{emit}}}{\lambda_{\mathrm{emit}}}</math>
| <math>z = \frac{f_{\mathrm{emit}} - f_{\mathrm{obsv}}}{f_{\mathrm{obsv}}}</math>
|- align=center
| <math>1+z = \frac{\lambda_{\mathrm{obsv}}}{\lambda_{\mathrm{emit}}}</math>
| <math>1+z = \frac{f_{\mathrm{emit}}}{f_{\mathrm{obsv}}}</math>
|}

In these equations, frequency is denoted by <math>f</math> and wavelength by <math>\lambda</math>. The larger the value of z, the more redshifted the light and the farther away the object is from the Earth. As of January 2013, the largest galaxy redshift of z~12 was found using the [[Hubble Ultra-Deep Field]], corresponding to an age of over 13 billion years (the universe is approximately 13.82 billion years old).<ref name=Ellis /><ref name=EllisRef /><ref name=PlanckHubble />

The Doppler effect and Hubble's law can be combined to form the equation
<math>z = \frac{v_{Hubble}}{c}</math>,
where c is the speed of light.

===Peculiar motion===
Objects that are gravitationally bound will rotate around a common center of mass. For stellar bodies, this motion is known as [[peculiar velocity]], and can alter the Hubble Flow. Thus, an extra term for the peculiar motion needs to be added to Hubble's law:<ref name=PeculiarMotion />
:<math>v_{total} = H_0 d + v_{pec}</math>
This motion can cause confusion when looking at a solar or galactic spectrum, because the expected redshift based on the simple Hubble law will be obscured by the peculiar motion. For example, the shape and size of the [[Virgo Cluster]] has been a matter of great scientific scrutiny due to the very large peculiar velocities of the galaxies in the cluster.<ref name=VirgoCluster />

===Binary stars===
[[File:Wiki Spect Binaries v2.gif|thumb|right|Two stars of different size orbiting the center of mass. The spectrum can be seen to split depending on the position and velocity of the stars.]]
Just as planets can be gravitationally bound to stars, pairs of stars can orbit each other. Some [[binary star]]s are visual binaries, meaning they can be observed orbiting each other through a telescope. Some binary stars, however, are too close together to be [[angular resolution|resolved]].<ref name=BinaryStars /> These two stars, when viewed through a spectrometer, will show a composite spectrum: the spectrum of each star will be added together. This composite spectrum becomes easier to detect when the stars are of similar luminosity and of different [[Stellar classification|spectral class]].<ref name=GrayCorbally />

[[Binary star#Spectroscopic binaries|Spectroscopic binaries]] can be also detected due to their [[radial velocity]]; as they orbit around each other one star may be moving towards the Earth whilst the other moves away, causing a Doppler shift in the composite spectrum. The [[Orbital plane (astronomy)|orbital plane]] of the system determines the magnitude of the observed shift: if the observer is looking perpendicular to the orbital plane there will be no observed radial velocity.<ref name=BinaryStars /><ref name=GrayCorbally /> For example, if you look at a [[carousel]] from the side, you will see the animals moving toward and away from you, whereas if you look from directly above they will only be moving in the horizontal plane.

== Planets, asteroids, and comets==
[[Planet]]s and [[asteroid]]s shine only by the reflected light of their parent star, while [[comets]] both absorb and emit light at various wavelengths.

===Planets===
The reflected light of a planet contains absorption bands due to [[mineral]]s in the rocks present for rocky bodies, or due to the elements and molecules present in the atmospheres of [[gas giants]]. To date almost 1000 [[exoplanets]] have been discovered. These include so-called [[Hot Jupiter]]s, as well as Earth-like planets. Using spectroscopy, compounds such as alkali metals, water vapor, carbon monoxide, carbon dioxide, and methane have all been discovered.<ref name=Tessenyi />

===Asteroids===
Asteroids can be classified into three major types according to their spectra. The original categories were created by Clark R. Chapman, David Morrison, and Ben Zellner in 1975, and further expanded by [[David J. Tholen]] in 1984. In what is now known as the [[Asteroid spectral types#Tholen classification|Tholen classification]], the [[C-type asteroid|C-types]] are made of carbonaceous material, [[S-type asteroid|S-types]] consist mainly of [[silicates]], and [[X-type asteroid|X-types]] are 'metallic'. There are other classifications for unusual asteroids. C- and S-type asteroids are the most common asteroids. In 2002 the Tholen classification was further "evolved" into the [[Asteroid spectral types#SMASS classification|SMASS classification]], expanding the number of categories from 14 to 26 to account for more precise spectroscopic analysis of the asteroids.<ref name=Bus /><ref name=Chapman />

===Comets===
[[File:Spectrum of Comet Hyakutake.gif|thumb|300px|right|Optical spectrum of [[Comet Hyakutake]].]]
The spectra of comets consist of a reflected solar spectrum from the dusty clouds surrounding the comet, as well as emission lines from gaseous atoms and molecules excited to [[fluorescence]] by sunlight and/or chemical reactions. For example, the chemical composition of [[C/2012 S1|Comet ISON]] was determined by spectroscopy due to the prominent emission lines of cyanogen (CN), as well as two- and three-carbon atoms (C2 and C3).<ref name=CIOC /> Nearby comets can even be seen in X-ray as solar wind ions flying to the [[Coma (cometary)|coma]] are neutralized. The cometary X-ray spectra therefore reflect the state of the solar wind rather than that of the comet.<ref name=Lisse />

== See also ==
* [[Atomic and molecular astrophysics]]
* [[Emission spectrum]]
* [[Gunn-Peterson trough]]
* [[Lyman-alpha forest]]
* [[Photometry (astronomy)]]
* [[Prism]]
* [[Spectrometer]]

==References==
{{reflist|2|refs=
<ref name=Acetone>
{{cite journal|last=Johansson|first=LE|coauthors=Andersson, C; Ellder, J; Friberg, P; Hjalmarson, A; Hoglund, B; Irvine, WM; Olofsson, H; Rydbeck, G|title=Spectral scan of Orion A and IRC+10216 from 72 to 91 GHz|journal=Astronomy and astrophysics|year=1984|volume=130|pages=227–56|pmid=11541988|bibcode=1984A&A...130..227J}}</ref>

<ref name=Australia>
{{cite web|title=Luminosity of Stars|publisher=[[Australia Telescope National Facility]]|url=http://outreach.atnf.csiro.au/education/senior/astrophysics/photometry_luminosity.html|date=12 July 2004|accessdate=2 July 2012}}</ref>

<ref name=Ball>
{{cite book|last=Ball|first=David W.|title=Basics of Spectroscopy|year=2001|publisher=Society of Photo-Optical Instumentation Engineers|location=Bellingham, Washington|isbn=0-8194-4104-X|pages=24, 28}}</ref>

<ref name=BinaryStars>
{{cite web|title=Types of Binary Stars|url=http://outreach.atnf.csiro.au/education/senior/astrophysics/binary_types.html|work=Australia Telescope Outreach and Education|publisher=Australia Telescope National Facility|accessdate=26 November 2013}}</ref>

<ref name=Bowen>
{{cite journal|last=Bowen|first=I. S.|title=The Origin of the Nebulium Spectrum|journal=Nature|date=1 October 1927|volume=120|issue=3022|pages=473–473|doi=10.1038/120473a0}}</ref>

<ref name=Buckyball>{{cite journal|last=Cami|first=J.|coauthors=Bernard-Salas, J.; Peeters, E.; Malek, S. E.|title=Detection of C60 and C70 in a Young Planetary Nebula|journal=Science|date=22 July 2010|volume=329|issue=5996|pages=1180–1182|doi=10.1126/science.1192035|pmid=20651118}}</ref>

<ref name=Bus>
{{cite journal|last=Bus|first=S|title=Phase II of the Small Main-Belt Asteroid Spectroscopic Survey A Feature-Based Taxonomy|journal=Icarus|date=July 2002|volume=158|issue=1|pages=146–177|doi=10.1006/icar.2002.6856}}</ref>

<ref name=Chapman>
{{cite journal|last=Chapman|first=Clark R.|coauthors=Morrison, David; Zellner, Ben|title=Surface properties of asteroids: A synthesis of polarimetry, radiometry, and spectrophotometry|journal=Icarus|date=May 1975|volume=25|issue=1|pages=104–130|doi=10.1016/0019-1035(75)90191-8}}</ref>

<ref name=Chiu>
{{cite journal|last=Chiu|first=Hong-Yee|title=GRAVITATIONAL COLLAPSE|journal=Physics Today|year=1964|volume=17|issue=5|pages=21|doi=10.1063/1.3051610}}</ref>

<ref name=CIOC>
{{cite web|last=Knight|first=Matthew|title=Why does ISON look green?|url=http://www.isoncampaign.org/why-does-ison-look-green|publisher=Comet ISON Observing Campaign|accessdate=26 November 2013}}</ref>

<ref name=DustChemistry>
{{cite book|last=Millar|first=TJ|title=Dust and chemistry in astronomy|year=1993|publisher=Inst. of Physics|location=Bristol [u.a.]|isbn=0-7503-0271-2|page=116|coauthors=DA Williams}}</ref>

<ref name=Efremov>
{{cite journal|last=Efremov|first=Yu. N.|title=On the spiral structure of the Milky Way Galaxy|journal=Astronomy Reports|date=22 February 2011|volume=55|issue=2|pages=108–122|doi=10.1134/S1063772911020016}}</ref>

<ref name=Ellis>
{{cite journal|last=Ellis|first=Richard S.|coauthors=McLure, Ross J.; Dunlop, James S.; Robertson, Brant E.; Ono, Yoshiaki; Schenker, Matthew A.; Koekemoer, Anton; Bowler, Rebecca A. A.; Ouchi, Masami; Rogers, Alexander B.; Curtis-Lake, Emma; Schneider, Evan; Charlot, Stephane; Stark, Daniel P.; Furlanetto, Steven R.; Cirasuolo, Michele|title=THE ABUNDANCE OF STAR-FORMING GALAXIES IN THE REDSHIFT RANGE 8.5-12: NEW RESULTS FROM THE 2012 HUBBLE ULTRA DEEP FIELD CAMPAIGN|journal=The Astrophysical Journal|date=20 January 2013|volume=763|issue=1|pages=L7|doi=10.1088/2041-8205/763/1/L7}}</ref>

<ref name=EllisRef>
{{cite web|title=Hubble census finds galaxies at redshifts 9 to 12|url=http://www.spacetelescope.org/news/heic1219/|publisher=NASA/ESA|accessdate=26 November 2013}}</ref>

<ref name=Foukal>
{{cite book|last=Foukal|first=Peter V.|title=Solar Astrophysics|year=2004|publisher=Wiley VCH|location=Weinheim|isbn=3-527-40374-4|page=69}}</ref>

<ref name=Fraunhofer>
{{cite journal|last=Fraunhofer|first=Joseph|title=Bestimmung des Brechungs- und des Farben-Zerstreuungs - Vermögens verschiedener Glasarten, in Bezug auf die Vervollkommnung achromatischer Fernröhre|journal=Annalen der Physik|year=1817|volume=56|pages=282–287|url=http://books.google.com/?id=2-AAAAAAYAAJ&pg=PA203#v=onepage&q&f=false|doi=10.1002/andp.18170560706|issue=7}}</ref>

<ref name=GrayCorbally>
{{cite book|last=Gray|first=Richard O.|title=Stellar spectral classification|year=2009|publisher=Princeton University Press|location=Princeton, N.J.|isbn=978-0-691-12510-7|pages=507–513|coauthors=Christopher J. Corbally}}</ref>

<ref name=GoddardISM>{{cite web|last=Hudson|first=Reggie L.|title=The Interstellar Medium|url=http://wind.gsfc.nasa.gov/mfi/lepedu/terms/ism.htm|publisher=Goddard Space Flight Center Astrochemistry Laboratry|accessdate=19 November 2013}}</ref>

<ref name=Hearnshaw>
{{cite book|last=Hearnshaw|first=J.B.|title=The analysis of starlight|year=1986|publisher=Cambridge University Press|location=Cambridge|isbn=0-521-39916-5}}</ref>

<ref name=Hirsh>
{{cite journal|last=Hirsh|first=Richard F|title=The Riddle of the Gaseous Nebulae|journal=Isis|date=June 1979|volume=70|pages=162–212|jstor=230787|bibcode=1979Isis...70..197H|doi=10.1086/352195|issue=2}}</ref>

<ref name=Hubble>
{{cite news|title=Hubble Pinpoints Furthest Protocluster of Galaxies Ever Seen|url=http://www.spacetelescope.org/news/heic1201/|accessdate=13 January 2012|newspaper=ESA/Hubble Press Release}}</ref>

<ref name=HubbleLaw>
{{cite web|last=Haynes|first=Martha|title=Hubble's Law|url=http://www.astro.cornell.edu/academics/courses/astro201/hubbles_law.htm|publisher=Cornell University|accessdate=26 November 2013}}</ref>

<ref name=Huggins>
{{cite book|last=Huggins|first=Sir William|title=The Scientific Papers of Sir William Huggins|year=1899|publisher=William Wesley and Son|location=London|pages=114–115}}</ref>

<ref name=Jenkins>
{{cite book|last=Jenkins|first=Francis A.|title=Fundamentals of Optics|year=1957|publisher=McGraw-Hill|location=New York|isbn=0-07-085346-0|pages=430–437|edition=4th|coauthors=Harvey E. White}}</ref>

<ref name=Kirchhoff>
{{cite journal |url=http://books.google.com/books?id=RVYEAAAAYAAJ&pg=PA1&lpg=PA1 |journal=The London, Edinburgh and Dublin philosophical magazine and journal of science |publisher=Taylor & Francis |year=1860|title=On the relation between the radiating and absorbing powers of different bodies for light and heat |author=G. Kirchhoff |volume=20 |issue=130 |date=July 1860}}
</ref>

<ref name=Kitchin>
{{cite book|last=Kitchin|first=C.R.|title=Optical Astronomical Spectroscopy|year=1995|publisher=Institute of Physics Publishing|location=Bristol|isbn=0-7503-0346-8|pages=127, 143}}</ref>

<ref name=KitchinGas>
{{cite book|last=Kitchin|first=C.R.|title=Stars, nebulae, and the interstellar medium : observational physics and astrophysics|year=1987|publisher=A. Hilger|location=Bristol|pages=265–277|isbn=0-85274-580-X}}</ref>

<ref name=Kudritzki>
{{cite journal|last=Kudritzki|first=R.-P.|title=Dissecting galaxies with quantitative spectroscopy of the brightest stars in the Universe|journal=Astronomische Nachrichten|date=May 2010|volume=331|issue=5|pages=459–473|doi=10.1002/asna.200911342}}</ref>

<ref name=Lisse>
{{cite journal|last=Lisse|first=C. M.|coauthors=Dennerl, K.; Englhauser, J.; Harden, M.; Marshall, F. E.; Mumma, M. J.; Petre, R.; Pye, J. P.; Ricketts, M. J.; Schmitt, J.; Trumper, J.; West, R. G.|title=Discovery of X-ray and Extreme Ultraviolet Emission from Comet C/Hyakutake 1996 B2|journal=Science|date=11 October 1996|volume=274|issue=5285|pages=205–209|doi=10.1126/science.274.5285.205}}</ref>

<ref name=Massoud>
{{cite book |url=http://books.google.com/books?id=9KIp_fmC9A0C&pg=PA568 |page=568 |author=Mahmoud Massoud |title=Engineering thermofluids: thermodynamics, fluid mechanics, and heat transfer |chapter=§2.1 Blackbody radiation |isbn=3-540-22292-8 |publisher=Springer |year=2005}}
</ref>

<ref name=Matthews>
{{cite journal|last=Matthews|first=Thomas A.|coauthors=Sandage, Allan R.|title=Optical Identification of 3c 48, 3c 196, and 3c 286 with Stellar Objects|journal=The Astrophysical Journal|date=July 1963|volume=138|pages=30|doi=10.1086/147615}}</ref>

<ref name=Morison>
{{cite book|last=Morison|first=Ian|title=Introduction to Astronomy and Cosmology|year=2008|publisher=Wiley-Blackwell|isbn=0-470-03333-9|page=61|url=http://astro.ustc.edu.cn/ycb/doc/Introduction_to_Astronomy_and_Cosmology.pdf}}</ref>

<ref name=Opticks>
{{cite book|last=Newton|first=Isaac|title=Oticks: Or, A Treatise of the Reflections, Refractions, Inflections and Colours of Light|year=1705|publisher=Royal Society|location=London|pages=13–19|url=http://gallica.bnf.fr/ark:/12148/bpt6k3362k}}</ref>

<ref name=PeculiarMotion>
{{cite web|title=Peculiar Velocity|url=http://astronomy.swin.edu.au/cosmos/P/Peculiar+Velocity|publisher=Swinburne University of Technology|accessdate=26 November 2013}}</ref>

<ref name=PlanckHubble>
{{cite web|date=21 March 2013|title=Planck reveals an almost perfect universe|url=http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe|publisher=[[European Space Agency|ESA]]|accessdate=26 November 2013}}</ref>

<ref name=Pradhan>
{{cite book|last=Nahar|first=Anil K. Pradhan, Sultana N.|title=Atomic astrophysics and spectroscopy|year=2010|publisher=Cambridge University Press|location=Cambridge|isbn=978-0-521-82536-8|pages=7,221}}</ref>

<ref name=redshift>
{{cite web|last=Huchra|first=John|title=Extragalactic Redshifts|url=http://ned.ipac.caltech.edu/help/zdef.html|publisher=California Institute of Technology|accessdate=26 November 2013}}</ref>

<ref name=Romanowsky>
{{cite journal|last=Romanowsky|first=A. J.|title=A Dearth of Dark Matter in Ordinary Elliptical Galaxies|journal=Science|date=19 September 2003|volume=301|issue=5640|pages=1696–1698|doi=10.1126/science.1087441|pmid=12947033|first2=NG|first3=M|first4=K|first5=MR|first6=NR|first7=M|first8=KC}}</ref>

<ref name=Rubin>
{{cite journal|last=Rubin|first=Vera C.|coauthors=Graham, J. A.; Kenney, Jeffrey D. P.|title=Cospatial counterrotating stellar disks in the Virgo E7/S0 galaxy NGC 4550|journal=The Astrophysical Journal|date=July 1992|volume=394|pages=L9|doi=10.1086/186460}}</ref>

<ref name=Shu>
{{cite book|last=Shu|first=Frank H.|title=The physical universe : an introduction to astronomy|year=1982|publisher=Univ. Science Books|location=Sausalito, Calif.|isbn=0-935702-05-9|pages=232–234|edition=12. [Dr.].}}</ref>

<ref name=Tennyson>
{{cite book|last=Tennyson|first=Jonathan|title=Astronomical spectroscopy : an introduction to the atomic and molecular physics of astronomical spectra|year=2005|publisher=Imperial College Press|location=London|isbn=1-86094-513-9|pages=46–47, 99–100|edition=[Online-Ausg.].}}</ref>

<ref name=Tessenyi>
{{cite journal|last=Tessenyi|first=M.|coauthors=Tinetti, G.; Savini, G.; Pascale, E.|title=Molecular detectability in exoplanetary emission spectra|journal=Icarus|date=November 2013|volume=226|issue=2|pages=1654–1672|doi=10.1016/j.icarus.2013.08.022}}</ref>

<ref name=VirgoCluster>
{{cite journal|last=Yasuda|first=Naoki|coauthors=Fukugita, Masataka; Okamura, Sadanori|title=Study of the Virgo Cluster Using the B‐Band Tully‐Fisher Relation|journal=The Astrophysical Journal Supplement Series|date=February 1997|volume=108|issue=2|pages=417–448|doi=10.1086/312960}}</ref>

<ref name=Wallace>
{{cite book|last=Wallace|first=P.R.|title=Physics : imagination and reality|year=1991|publisher=World Scientific|location=Singapore|isbn=997150930X|pages=235–246}}</ref>

<ref name=Zwicky>
{{cite journal|last=Zwicky|first=F.|title=On the Masses of Nebulae and of Clusters of Nebulae|journal=The Astrophysical Journal|date=October 1937|volume=86|pages=217|doi=10.1086/143864}}</ref>
}}

{{Commons category}}

{{BranchesofSpectroscopy}}

[[Category:Spectroscopy]]
[[Category:Astronomical spectroscopy| ]]
[[Category:Observational astronomy]]

{{Link FA|hu}}

Duration gap

2013-11-24T03:39:54Z

184.175.26.203:

{{No footnotes|article|date=April 2009}}A '''numerical model of the [[Solar System]]''' is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time. Attempts to create such a model established the more general field of [[celestial mechanics]]. The results of this simulation can be compared with past measurements to check for accuracy and then be used to predict future positions. Its main use therefore is in preparation of almanacs.

==Older efforts==
The simulations can be done in either [[Cartesian coordinate system|Cartesian]] or in [[Spherical coordinate system|spherical]] coordinates. The former are easier, but extremely calculation intensive, and only practical on an electronic computer. As such only the latter was used in former times. Strictly speaking not much less calculation intensive, but it was possible to start with some simple approximations and then to add [[Perturbation (astronomy)|perturbations]], as much as needed to reach the wanted accuracy.

In essence this mathematical simulation of the Solar System is a form of the ''[[N-body problem]]''. The symbol '''''N''''' represents the number of bodies, which can grow quite large if one includes 1 sun, 8 planets, dozens of moons and countless planetoids, comets and so forth. However the influence of the sun on any other body is so large, and the influence of all the other bodies on each other so small that the problem can be reduced to the analytically solvable 2-body problem. The result for each planet is an orbit, a simple description of its position as function of time. Once this is solved the influences moons and planets have on each other are added as small corrections. (Small compared to a full planetary orbit, some corrections might be still several degrees large, while measurements can be made to an accuracy of better than 1″).

Although this method is no longer used for simulations, it is still useful to find an approximate ephemeris as one can take the relatively simple main solution, perhaps add a few of the largest perturbations, and arrive without too much effort at the wanted planetary position. The disadvantage is that perturbation theory is very advanced mathematics.

==Modern method==
The modern method consists of numerical integration in 3-dimensional space. One starts with a high accuracy value for the position (''x'', ''y'', ''z'') and the velocity (''vx'', ''vy'', ''vz'') for each of the bodies involved. When also the mass of each body is known, the acceleration (''ax'', ''ay'', ''az'') can be calculated from [[Newton's Law of Gravitation]]. Each body attracts each other body, the total acceleration being the sum of all these attractions. Next one chooses a small time-step Δ''t'' and applies [[Newton's Second Law of Motion]]. The acceleration multiplied with Δ''t'' gives a correction to the velocity. The velocity multiplied with Δ''t'' gives a correction to the position. This procedure is repeated for all other bodies.

The result is a new value for position and velocity for all bodies. Then, using these new values one starts over the whole calculation for the next time-step Δ''t''. Repeating this procedure often enough, and one ends up with a description of the positions of all bodies over time.

The advantage of this method is that for a computer it is a very easy job to do, and it yields highly accurate results for all bodies at the same time, doing away with the complex and difficult procedures for determining perturbations. The disadvantage is that one must start with highly accurate figures in the first place, or the results will drift away from the reality in time; that one gets ''x'', ''y'', ''z'' positions which are often first to be transformed into more practical ecliptical or equatorial coordinates before they can be used; and that it is an all or nothing approach. If one wants to know the position of one planet on one particular time, then all other planets and all intermediate time-steps are to be calculated too.

==Integration==
In the previous section it was assumed that acceleration remains constant over a small timestep Δt so that the calculation reduces to simply the addition of V × Δt to R and so forth. In reality this is not the case, except when one takes Δt so small that the number of steps to be taken would be prohibitively high. Because while at any time the position is changed by the acceleration, the value of the acceleration is determined by the instantaneous position. Evidently a full integration is needed.

Several methods are available. First notice the needed equations:

<math>\vec{a}_j = \sum_{i \neq j}^n G \frac{M_i}{|\vec{r}_i - \vec{r}_j|^3} (\vec{r}_i - \vec{r}_j)</math>

This equation describes the acceleration all bodies '''i''' running from 1 to N exercise on a particular body '''j'''. It is a vector equation, so it is to be split in 3 equations for each of the X, Y, Z components, yielding:

<math>(a_j)_x = \sum_{i \neq j}^n G \frac{M_i}{( (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 )^{3/2}} (x_i - x_j)</math>

with the additional relationships

<math>a_{x} = \frac{dv_{x}}{dt}</math>, <math>v_{x} = \frac{dx}{dt}</math>

likewise for Y and Z.

The former equation (gravitation) may look foreboding, but its calculation is no problem. The latter equations (motion laws) seems simpler, but yet it cannot be calculated. Computers cannot integrate, they cannot work with infinitesimal values, so instead of dt we use Δt and bringing the resulting variable to the left:

<math>\Delta v_x = a_{x} \Delta t </math>, and: <math>\Delta x = v_{x} \Delta t </math>

Remember that '''a''' is still a function of time. The simplest way to solve these is just the [[Euler]] algorithm, which in essence is the linear addition described above. Limiting ourselves to 1 dimension only in some general computer language:
a.old = gravitationfunction(x.old)
x.new = x.old + v.old * dt
v.new = v.old + a.old * dt

As in essence the acceleration used for the whole duration of the timestep, is the one as it was in the beginning of the timestep, this simple method has no high accuracy. Much better results are achieved by taking a mean acceleration, the average between the beginning value and the expected (unperturbed) end value:

a.old = gravitationfunction(x.old)
x.expect = x.old + v.old * dt
a.expect = gravitationfunction(x.expect)
v.new = v.old + (a.old + a.expect) * 0.5 * dt
x.new = x.old + (v.new + v.old) * 0.5 * dt

Of course still better results can be expected by taking intermediate values. This is what happens when using the [[Runge-Kutta]] method, especially the one of grade 4 or 5 are most useful.

A completely different method is the use of [[Taylor series]]. In that case we write: <math>r = r_0 + r'_0 t + r''_0 \frac{t^2}{2!} + (etc) </math>

but rather than developing up to some higher derivative in r only, one can develop in r and v (that is r') by writing <math>r = f r_0 + g r'_0</math>and then write out the factors ''f'' and ''g'' in a series.

All these more advanced methods easily allow for Solar System calculations with a stepsize Δt of 10 days and yet yield satisfactory results{{Citation needed|date=January 2010}}.

==Approximations==
To calculate the accelerations the gravitational attraction of each body on each other body is to be taken into account. As a consequence the amount of calculation in the simulation goes up with the square of the number of bodies: Doubling the number of bodies increases the work with a factor four. To increase the accuracy of the simulation not only more decimals are to be taken but also smaller timesteps, again quickly increasing the amount of work. Evidently tricks are to be applied to reduce the amount of work. Some of these tricks are given here.

By far the most important trick is the use of a proper integration method, as already outlined above.

The choice of units is important. Rather than to work in [[SI units]], which would make some values extremely small and some extremely large, all units are to be scaled such that they are in the neighbourhood of 1. For example for distances in the Solar System the [[astronomical unit]] is most straightforward. If this is not done one is almost certain to see a simulation aborted in the middle of a calculation on a [[floating point]] [[arithmetic overflow|overflow]] or [[arithmetic underflow|underflow]], and if not that bad, still accuracy is likely to get lost due to [[truncation]] errors.

If N is large (not so much in Solar System simulations, but more in galaxy simulations) it is customary to create dynamic groups of bodies. All bodies in a particular direction and on large distance from the reference body, which is being calculated at that moment, are taken together and their gravitational attraction is averaged over the whole group.

The total amount of [[energy]] and [[angular momentum]] of a closed system are conserved quantities. By calculating these amounts after every time step the simulation can be programmed to increase the stepsize Δt if they do not change significantly, and to reduce it if they start to do so. Combining the bodies in groups as in the previous and apply larger and thus less timesteps on the faraway bodies than on the closer ones, is also possible.

To allow for an excessively rapid change of the acceleration when a particular body is close to the reference body, it is customary to introduce a small softness parameter ''e'' so that
<math>a = \frac{G M}{r^2 + e}</math>

==Complications==
If the highest possible accuracy is needed, things become much more complex. In the case of comets, nongravitational forces (radiation pressure and gas drag) must be taken into account. In the case of Mercury, relativistic effects cannot be ignored. Then also the total energy is no longer a constant (because the four vector energy with linear momentum is). The finite speed of light also makes it important to allow for light-time effects, both classical and relativistic. Planets can no longer be considered as particles, but their shape and density must also be considered. For example, the flattening of the Earth causes precession, which causes the axial tilt to change, which affects the long-term movements of all planets.

==See also==
*[[Ephemeris]]
*[[Astronomical algorithm]]
*[[VSOP (planets)]]

==References==
*{{Cite book|first=Dan L. |last=Boulet |title=Methods of orbit determination for the microcomputer |publisher=Willmann-Bell, Inc |location=[[Richmond, Virginia]] |year=1991 |pages= |isbn=0-943396-34-4 |oclc=23287041}}{{Page needed|date=September 2010}}

{{DEFAULTSORT:Numerical Model Of Solar System}}
[[Category:Numerical analysis]]
[[Category:Dynamical systems]]
[[Category:Dynamics of the Solar System]]