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Line 1: − + + − The Greeks devised a rough and ready brightness scale for stars. The brightest stars were designated 'stars of the first magnitude', less bright stars were designated 'stars of the second magnitude', etc., down to stars of the sixth magnitude, which were barely visible to the naked eye. The magnitude scale is still in use, but modern telescopes and photometers have made it very much more exact and rigorous. A star of magnitude 1.0 is now 2.51188643 times as bright as a magnitude 2.0 star, which is 2.51188643 times as bright as a magnitude 3.0 star, and so on. This number has been chosen so that a magnitude 1.0 star is exactly 100 times as bright as a magnitude 6.0 star, i.e. 2.51188643 = 10<sup>0.4</sup>.+ − The brightness of a star as seen from Earth depends on two things, how luminous it really is, and how far away it is. Stars vary greatly in their luminosity and their distance from Earth. The apparent brightness of a star varies according to the [[inverse-square law]]. Consider two stars that are equal in actual brightness, but one is at a distance of 100 [[light year]]s and the other is at a distance of 200 light-years. The farther star is twice as far away, but it will not appear to be half as bright, it will be only one quarter as bright. More generally, if one star is ''x'' times further away than the other it will appear to be ''x''<sup>2</sup> times less bright.+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Additional information
'''Stars''' are extremely large, luminous bodies of gas. They are the most obvious features found in the [[universe]]. They are principally composed of [[hydrogen]] that is undergoing nuclear [[fusion]] to become [[helium]]. Our Sun is the nearest star to Earth, at a distance averaging 93 million miles. The Earth orbits the Sun in a period of approximately 365.25 days, and this defines the [[year]]. The diameter of the Sun, which is a typical star, is about 870,000 miles and its power output is about 10<sup>26</sup> watts. The temperature inside the Sun is estimated to be in excess of ten million degrees, and this is hot enough for [[nuclear reactions]] to occur.
'''Stars''' are extremely large, luminous bodies of gas. They are the most obvious features found in the [[universe]]. They are principally composed of [[hydrogen]] that is undergoing nuclear [[fusion]] to become [[helium]]. Our Sun is the nearest star to Earth, at a distance averaging 93 million miles. The Earth orbits the Sun in a period of approximately 365.25 days, and this defines the [[year]]. The diameter of the Sun, which is a typical star, is about 870,000 miles and its power output is about 10<sup>26</sup> watts. The temperature inside the Sun is estimated to be in excess of ten million degrees, and this is hot enough for [[nuclear reactions]] to occur.
==The Magnitude scale of brightness==
== Measuring stellar distances ==
The oldest method of measuring the distance from our solar system to a distant star is the parallax method. To use this method, astronomers measure the right ascension on the sky of the star at two times of the year, half a year apart. The two measurements will differ by a small angle with respect to the most distant stars in that region of the sky. Exactly half this angle is the ''parallax angle'', having symbol ''p''. This is the angle that the star makes with the [[sun]] and the position of the [[earth]] at a right angle with that star.<ref name=Britannica3>"[http://www.britannica.com/eb/article-52809/star Star: Determinig stellar distances]." ''Encyclopædia Britannica''. 2008. Encyclopædia Britannica Online. Accessed 21 Apr. 2008</ref> The distance s of the star, in astronomical units (AU), is:
<math>\,\!s = \cot p</math>
In the range of the very small angles typically encountered, the cotangent of the angle measure (in radians) is very nearly equal to the reciprocal, and thus:
<math>\,\!s \approx \frac {180 \times 3600}{p \times \pi}</math>
where p is measured in seconds of arc.
The cotangent of one second (1/3600 of a degree) of arc is approximately 206,264.81. No parallax angle for any star will be larger than one second. Therefore astronomers initially defined a unit of stellar distance, the ''parsec'' (symbol pc), from this relationship. One parsec is the distance corresponding to a parallax angle of one second of arc. Hence:
<math>1 pc \approx 206,264.81 AU</math>
However, the error of measurement of parallax angle is 0.005 arc seconds, and beyond a distance of 100 parsecs, this error becomes significant. 700 stars are near enough to measure their distances directly by using parallax.<ref name=Britannica3/> To measure distances further out than this, astronomers typically use absolute and relative magnitudes, or they apply Hubble's Law to the star's estimated [[redshift]].
== Stellar positions and movements ==
The most common system for describing the position of a star in the sky is the equatorial system. This system uses two coordinates:
# Right ascension on the sky, or the number of hours required for the earth to rotate before an observer can see the star at its highest point in the sky. The zero for right ascension is midnight on the day of the vernal equinox.<ref name=WeissteinRA>Weisstein, Eric W. "[http://scienceworld.wolfram.com/astronomy/RightAscension.html Right Ascension]." ''Eric Weisstein's World of Astronomy'', 2007. Accessed April 21, 2008.</ref>
# Declination, or the north-south angle between the star and the celestial equator.<ref name=WeissteinD>Weisstein, Eric W. "[http://scienceworld.wolfram.com/astronomy/Declination.html Declination]." ''Eric Weisstein's World of Astronomy'', 2007. Accessed April 21, 2008.</ref>
All stars move, but the most distant stars are considered "fixed" because their motion would be undetectable. The ''proper motion'' (symbol m) of any star is the angular velocity of its position across the sky. This describes the motion at right angles to the line of sight of the observer. To convert this to actual ''tangential velocity'', multiply the tangent of this angular velocity by the star's distance.
The motion ''in'' line of sight, or ''radial velocity'', is currently determined from spectral shift.
== Measuring stellar magnitudes ==
The visual magnitude system is defined as follows: a star of any given magnitude is about 2.512 times as bright as is a star of the next magnitude. [[Hipparchus]] devised the magnitude system, and [[Ptolemy]] refined it further. By convention, an arbitrary sample of the twenty brightest stars that they could observe were assigned to the first magnitude, and the stars that they could barely observe were assigned to the sixth. Sixth-magnitude stars are actually 100 times less bright than first-magnitude stars. Magnitude levels between these extremes are assigned on a logarithmic scale. Thus, given two stars of brightness l<sub>1</sub> and l<sub>2</sub>, their magnitude difference (V<sub>2</sub> - V<sub>1</sub>) relates to their respective brightnesses in this way:<ref name=Haworth>Haworth, David. "[http://www.stargazing.net/david/constel/magnitude.html Star Magnitudes]." ''[http://www.stargazing.net/david/index.html Observational Astronomy]'', 2003. Accessed April 21, 2008.</ref>
<math>\,\!V_2 - V_1 = 2.5 \times \operatorname{log} \frac{l_1}{l_2}</math>
The ''absolute'' magnitude of any star is the visual magnitude that it would have if it were ten parsecs distant. To convert apparent magnitude V to actual magnitude M, use this formula:
<math>\,\!M = V + 5 \times \operatorname{log} \frac{s_0}{s}</math>
where s<sub>0</sub> is the standard distance. This distance is ten parsecs, or about 2,062,650 AU.
Brightness declines with the square of distance, and squares correpond to doubling of logarithms. One must then multiply that result by 2.5 to stay within the magnitude scale.
== Stellar colors and spectra ==
The ''color'' of a star is objectively quantifiable. To determine color, astronomers view the star through a variety of colored filters and compute ''color indices'' as the differences in apparent magnitudes through the various filters. Stellar colors vary, in order from the coolest to the hottest, from red to yellow to white to blue-white to blue or violet. This is the same gamut of colors that a black body shows as its temperature rises.
In addition, each star has a unique ''spectrum'', which depends on the gases and other elements that it contains, and their distribution. A spectrum can serve two purposes:
# It can serve as a unique signature for the star, to distinguish it from other stars.
# It can provide information on the star's radial velocity vis-à-vis the earth.
To accomplish the latter, astronomers note the placement of various lines in the spectrum and then determine the star's likely constituent elements from the spacing of those lines. Lines that are out of ''place'' are shifted, either toward the blue or toward the red. Nearly all stellar spectrum are shifted toward the red; this [[redshift]] indicates a recession, either of the star or of the part of space where the star resides.<ref>Some [[cosmology|cosmological]] models call for an expansion of space itself, not merely the matter in it. According to these models, a redshifted star is in a part of space that was still expanding as the incident light was generated.</ref>
=== Spectral types ===
[[Image:Hertzsprung-Russell.jpg|thumb|300px|right|Hertzsprung-Russell Diagram]]
In the late nineteenth century, astronomers at the [[Harvard University]] observatory developed the first classification scheme for stellar spectra that would become known as the '''Harvard spectral classification'''. In 1924, Annie Jump Cannon<ref name=Cannon>"[http://imagine.gsfc.nasa.gov/docs/teachers/lifecycles/LC_main_p8.html Life Cycles of Stars]." ''Goddard Space Flight Center'', November 21, 2002. Accessed April 22, 2008.</ref> refined the classification from the original A-Q gamut to the familiar "OBAFGKM" gamut. Astronomers have since added classes to this range at the high end and the low.<ref name=Swinburne>"[http://astronomy.swin.edu.au/cosmos/H/Harvard+Spectral+Classification Harvard Spectral Classification]." ''Study Astronomy Online at Swinburne University''. Accessed April 22, 2008.</ref><ref name=Seattle>Irizarry, David. "[http://www.seattleastro.org/webfoot/feb00/pg2.htm The Secrets of the Harvard Classification Revealed]." ''The Webfooted Astronomer'', Seattle Astronomical Society, February 2000. Accessed April 22, 2008.</ref>
The classic Harvard spectral classes are O, B, A, F, G, K, and M. Each of these has ten subclasses, varying from 0 to 9 in order of decreasing stellar temperature. Thus, for example, the next class after an F9 star is a G0 star. Recently astronomers recognized one class of stars hotter than the O stars (the very hot Wolf-Rayet stars) and three classes of stars (the N, R, and S stars) cooler than the M stars. (Some astronomers include the N and R stars in one class, the C stars, for the carbon compounds that their spectra exhibit.)
In addition to the spectral type, astronomers today add a ''luminosity class'', which varies from I to VI in order of decreasing brightness. The [[sun]]'s spectral type is G2 and its luminosity class is V (five).
{| class="wikitable"
|-
! Class
! Temperature
! Color
! Elements
! Notes
|-
| W
| 106,000 K
| Violet
| Ionized [[helium]], [[carbon]], [[oxygen]], [[nitrogen]]
| Wolf-Rayet stars. Additional subclasses include WC (overabundant carbon and oxygen) and WN (overabundant nitrogen)
|-
| O
| 30,000 K
| Blue
| Ionized [[Helium]], [[nitrogen]], [[oxygen]]
| Weak Balmer lines ([[hydrogen]] at higher subclasses.
|-
| B
| 13,000 K to 20,000 K
| Blue
| Neutral helium; ionized [[silicon]], oxygen and [[magnesium]].
| [[Hydrogen]] (Balmer lines) appear in strength
|-
| A
| 75,00 to 10,000 K
| Blue-white
| [[Hydrogen]], [[calcium]], [[helium]]
| Balmer lines dominant. K lines (calcium) now appearing.
|-
| F
| 7,000K to 9,000K
| White-yellow
| [[Hydrogen]], [[calcium]], [[iron]], [[manganese]], [[sodium]]
| Balmer lines weakening. K lines stronger.
|-
| G
| 5,200 to 6,000K
| Yellow
| [[Calcium]], [[hydrogen]], other [[metal]]s
| Balmer lines weaker still. K lines dominant. Metals now appearing.
|-
| K
| 4000K to 5100K
| Orange
| [[Calcium]], neutral metals, [[titanium oxide]]
|
|-
| M
| 3000K
| Red
| [[Titanium oxide]], [[iron iodide]]
| Strong molecular bands
|-
| N,R
| 2300K to 2600K
| Red
| [[Carbon]] compounds
|
|-
| S
| 2300K to 2600K
| Red
| [[Hydrogen]], [[zirconium oxide]]
|
|}
In the early twentieth century, astronomers Ejnar Hertzsprung and Henry Norris Russell prepared the first plot of stellar temperature as a function of luminosity, or brightness. Other astronomers have since prepared versions of the diagram showing absolute magnitude as a function of color. This diagram shows a "main sequence" of stars for which brightness declines as temperature increases, but also shows a "white dwarf" population of very hot but dim stars, and the population of giants and supergiants that are far brighter than their temperatures would indicate.<ref name=HR>"[http://astronomy.swin.edu.au/cosmos/H/Hertzsprung-Russell+Diagram Hertzsprung-Russell Diagram]." ''Study Astronomy Online at Swinburne University''. Accessed April 22, 2008.</ref>
==Variable stars==
==Variable stars==