Editing Gravitational wave (section)

==Effects of passing==
[[File:GravitationalWave PlusPolarization.gif|thumb|150px|The effect of a plus-polarized gravitational wave on a ring of particles]]
[[File:GravitationalWave CrossPolarization.gif|thumb|150px|The effect of a cross-polarized gravitational wave on a ring of particles]]

Gravitational waves are constantly passing [[Earth]]; however, even the strongest have a minuscule effect since their sources are generally at a great distance. For example, the waves given off by the cataclysmic final merger of [[GW150914]] reached Earth after travelling over a billion [[light-year]]s, as a ripple in [[spacetime]] that changed the length of a 4&nbsp;km LIGO arm by a thousandth of the width of a [[proton]], proportionally equivalent to changing the distance to the [[Alpha Centauri|nearest star]] outside the Solar System by one hair's width.<ref>LIGO press conference 11 February 2016</ref> This tiny effect from even extreme gravitational waves makes them observable on Earth only with the most sophisticated detectors.

The effects of a passing gravitational wave, in an extremely exaggerated form, can be visualized by imagining a perfectly flat region of [[spacetime]] with a group of motionless test particles lying in a plane, e.g., the surface of a computer screen. As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles, i.e., following the observer's line of vision into the screen, the particles will follow the distortion in spacetime, oscillating in a "[[cruciform]]" manner, as shown in the animations. The area enclosed by the test particles does not change and there is no motion along the direction of propagation.{{citation needed|date=March 2016}}

The oscillations depicted in the animation are exaggerated for the purpose of discussion{{snd}} in reality a gravitational wave has a very small [[amplitude]] (as formulated in [[linearized gravity]]). However, they help illustrate the kind of oscillations associated with gravitational waves as produced by a pair of masses in a [[circular orbit]]. In this case the amplitude of the gravitational wave is constant, but its plane of [[Polarization (waves)|polarization]] changes or rotates at twice the orbital rate, so the time-varying gravitational wave size, or 'periodic spacetime strain', exhibits a variation as shown in the animation.<ref name="LL75">{{cite book |last1=Landau |first1=L. D. |last2=Lifshitz |first2=E.M. |title=The Classical Theory of Fields |edition=4thRevised English |publisher=Pergamon Press |year=1975 |isbn=978-0-08-025072-4 |pages=356–57 |url=https://books.google.com/books?id=X18PF4oKyrUC&pg=PA356 }}</ref> If the orbit of the masses is elliptical then the gravitational wave's amplitude also varies with time according to Einstein's [[quadrupole formula]].<ref name="Gravitationswellen" />

As with other [[wave]]s, there are a number of characteristics used to describe a gravitational wave:
* Amplitude: Usually denoted ''h'', this is the size of the wave{{snd}} the fraction of stretching or squeezing in the animation. The amplitude shown here is roughly ''h''&nbsp;=&nbsp;0.5 (or 50%). Gravitational waves passing through the Earth are many [[sextillion]] times weaker than this{{snd}} ''h''&nbsp;≈&nbsp;10<sup>−20</sup>.
* [[Frequency]]: Usually denoted ''f'', this is the frequency with which the wave oscillates (1 divided by the amount of time between two successive maximum stretches or squeezes)
* [[Wavelength]]: Usually denoted ''λ'', this is the distance along the wave between points of maximum stretch or squeeze.
* [[Speed]]: This is the speed at which a point on the wave (for example, a point of maximum stretch or squeeze) travels. For gravitational waves with small amplitudes, this [[speed of gravity|wave speed]] is equal to the [[speed of light]] (''c'').

The speed, wavelength, and frequency of a gravitational wave are related by the equation {{nowrap|1=''c'' = ''λf''}}, just like the equation for a [[Electromagnetic radiation#Wave model|light wave]]. For example, the animations shown here oscillate roughly once every two seconds. This would correspond to a frequency of 0.5&nbsp;Hz, and a wavelength of about 600&nbsp;000&nbsp;km, or 47 times the diameter of the Earth.

In the above example, it is assumed that the wave is [[linear polarization|linearly polarized]] with a "plus" polarization, written ''h''<sub>+</sub>. Polarization of a gravitational wave is just like polarization of a light wave except that the polarizations of a gravitational wave are 45&nbsp;degrees apart, as opposed to 90&nbsp;degrees.<ref>{{citation|title=The Science and Detection of Gravitational Waves |page=Introduction |url=https://labcit.ligo.caltech.edu/~BCBAct/talks00/Alberta/LakeLouisepaper.PDF |access-date=8 October 2022}}</ref> In particular, in a "cross"-polarized gravitational wave, ''h''<sub>×</sub>, the effect on the test particles would be basically the same, but rotated by 45 degrees, as shown in the second animation. Just as with light polarization, the polarizations of gravitational waves may also be expressed in terms of [[circular polarization|circularly polarized]] waves. Gravitational waves are polarized because of the nature of their source.