vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Speed of light
Another method is to use the aberration of light , discovered and explained by James Bradley in the 18th century . This effect results from the vector addition of the velocity of light arriving from a distant source ( such as a star ) and the velocity of its observer ( see diagram on the right ) . A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position . Since the direction of the Earth 's velocity changes continuously as the Earth orbits the Sun , this effect causes the apparent position of stars to move around . From the angular difference in the position of stars ( maximally 20.5 arcseconds ) it is possible to express the speed of light in terms of the Earth 's velocity around the Sun , which with the known length of a year can be converted to the time needed to travel from the Sun to the Earth . In 1729 , Bradley used this method to derive that light travelled 10,210 times faster than the Earth in its orbit ( the modern figure is 10,066 times faster ) or , equivalently , that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth . Astronomical
Observable universe
27.6 billion light - years This is a diameter obtained from the ( incorrect ) radius of 13.8 billion light - years .
Speed of light
The setup as used by Fizeau consists of a beam of light directed at a mirror 8 kilometres ( 5 mi ) away . On the way from the source to the mirror , the beam passes through a rotating cogwheel . At a certain rate of rotation , the beam passes through one gap on the way out and another on the way back , but at slightly higher or lower rates , the beam strikes a tooth and does not pass through the wheel . Knowing the distance between the wheel and the mirror , the number of teeth on the wheel , and the rate of rotation , the speed of light can be calculated .
International System of Units
The 1960 definition of the standard metre in terms of wavelengths of a specific emission of the krypton 86 atom was replaced with the distance that light travels in a vacuum in exactly 1 / 7008299792458000000 ♠ 299 792 458 second , so that the speed of light is now an exactly specified constant of nature .
South Africa
< 1 / km 1 -- 3 / km 3 -- 10 / km 10 -- 30 / km 30 -- 100 / km 100 -- 300 / km 300 -- 1000 / km 1000 -- 3000 / km > 3000 / km
Observable universe
The figures quoted above are distances now ( in cosmological time ) , not distances at the time the light was emitted . For example , the cosmic microwave background radiation that we see right now was emitted at the time of photon decoupling , estimated to have occurred about 7005380000000000000 ♠ 380,000 years after the Big Bang , which occurred around 13.8 billion years ago . This radiation was emitted by matter that has , in the intervening time , mostly condensed into galaxies , and those galaxies are now calculated to be about 46 billion light - years from us . To estimate the distance to that matter at the time the light was emitted , we may first note that according to the Friedmann -- Lemaître -- Robertson -- Walker metric , which is used to model the expanding universe , if at the present time we receive light with a redshift of z , then the scale factor at the time the light was originally emitted is given by
Speed of light
History of measurements of c ( in km / s ) < 1638 Galileo , covered lanterns inconclusive < 1667 Accademia del Cimento , covered lanterns inconclusive 1675 Rømer and Huygens , moons of Jupiter 7005220000000000000 ♠ 220 000 1729 James Bradley , aberration of light 7005301000000000000 ♠ 301 000 1849 Hippolyte Fizeau , toothed wheel 7005315000000000000 ♠ 315 000 1862 Léon Foucault , rotating mirror 7005298000000000000 ♠ 298 000 ± 500 1907 Rosa and Dorsey , EM constants 7005299710000000000 ♠ 299 710 ± 30 1926 Albert A. Michelson , rotating mirror 7005299796000000000 ♠ 299 796 ± 4 1950 Essen and Gordon - Smith , cavity resonator 7005299792500000000 ♠ 299 792. 5 ± 3.0 1958 K.D. Froome , radio interferometry 7005299792500000000 ♠ 299 792. 50 ± 0.10 1972 Evenson et al. , laser interferometry 7005299792456200000 ♠ 299 792. 4562 ± 0.0011 17th CGPM , definition of the metre 7005299792458000000 ♠ 299 792. 458 ( exact )
Observable universe
156 billion light - years This figure was obtained by doubling 78 billion light - years on the assumption that it is a radius . Because 78 billion light - years is already a diameter ( the original paper by Cornish et al. says , `` By extending the search to all possible orientations , we will be able to exclude the possibility that we live in a universe smaller than 24 Gpc in diameter , '' and 24 Gpc is 78 billion light - years ) , the doubled figure is incorrect . This figure was very widely reported . A press release from Montana State University -- Bozeman , where Cornish works as an astrophysicist , noted the error when discussing a story that had appeared in Discover magazine , saying `` Discover mistakenly reported that the universe was 156 billion light - years wide , thinking that 78 billion was the radius of the universe instead of its diameter . '' As noted above , 78 billion was also incorrect .
Speed of light
For many practical purposes , light and other electromagnetic waves will appear to propagate instantaneously , but for long distances and very sensitive measurements , their finite speed has noticeable effects . In communicating with distant space probes , it can take minutes to hours for a message to get from Earth to the spacecraft , or vice versa . The light seen from stars left them many years ago , allowing the study of the history of the universe by looking at distant objects . The finite speed of light also limits the theoretical maximum speed of computers , since information must be sent within the computer from chip to chip . The speed of light can be used with time of flight measurements to measure large distances to high precision .
Speed of light
In his 1704 book Opticks , Isaac Newton reported Rømer 's calculations of the finite speed of light and gave a value of `` seven or eight minutes '' for the time taken for light to travel from the Sun to the Earth ( the modern value is 8 minutes 19 seconds ) . Newton queried whether Rømer 's eclipse shadows were coloured ; hearing that they were not , he concluded the different colours travelled at the same speed . In 1729 , James Bradley discovered stellar aberration . From this effect he determined that light must travel 10,210 times faster than the Earth in its orbit ( the modern figure is 10,066 times faster ) or , equivalently , that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth .
Global Positioning System
d i = ( x − x i ) 2 + ( y − y i ) 2 + ( z − z i ) 2 ( \ displaystyle d_ ( i ) = ( \ sqrt ( ( x-x_ ( i ) ) ^ ( 2 ) + ( y - y_ ( i ) ) ^ ( 2 ) + ( z - z_ ( i ) ) ^ ( 2 ) ) ) )
Event horizon
d p = ∫ 0 t 0 c a ( t ) d t . ( \ displaystyle d_ ( p ) = \ int _ ( 0 ) ^ ( t_ ( 0 ) ) ( \ frac ( c ) ( a ( t ) ) ) dt \ . )
Binary star
In a simple binary case , r , the distance from the center of the first star to the center of mass or barycenter , is given by :
History of the center of the Universe
In 1920 , the Great Debate between Harlow Shapley and Curtis took place , concerning the nature of the Milky Way , spiral nebulae , and the dimensions of the Universe . To support his claim that the Great Andromeda Nebula ( M31 ) was an external galaxy , Curtis also noted the appearance of dark lanes resembling the dust clouds in our own Galaxy , as well as the significant Doppler shift . In 1922 Ernst Öpik presented a very elegant and simple astrophysical method to estimate the distance of M31 . His result put the Andromeda Nebula far outside our Galaxy at a distance of about 450,000 parsec , which is about 1,500,000 ly . Edwin Hubble settled the debate about whether other galaxies exist in 1925 when he identified extragalactic Cepheid variable stars for the first time on astronomical photos of M31 . These were made using the 2.5 metre ( 100 in ) Hooker telescope , and they enabled the distance of Great Andromeda Nebula to be determined . His measurement demonstrated conclusively that this feature was not a cluster of stars and gas within our Galaxy , but an entirely separate galaxy located a significant distance from our own . This proved the existence of other galaxies .
Observable universe
The observable universe is a spherical region of the Universe comprising all matter that can be observed from Earth at the present time , because electromagnetic radiation from these objects has had time to reach Earth since the beginning of the cosmological expansion . There are at least 2 trillion galaxies in the observable universe . Assuming the Universe is isotropic , the distance to the edge of the observable universe is roughly the same in every direction . That is , the observable universe has a spherical volume ( a ball ) centered on the observer . Every location in the Universe has its own observable universe , which may or may not overlap with the one centered on Earth .
Speed of light
The speed of light in vacuum , commonly denoted c , is a universal physical constant important in many areas of physics . Its exact value is 7008299792458000000 ♠ 299,792,458 metres per second ( approximately 300,000 km / s ( 186,000 mi / s ) ) . It is exact because by international agreement a metre is defined to be the length of the path travelled by light in vacuum during a time interval of 1 / 299792458 second . According to special relativity , c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel . Though this speed is most commonly associated with light , it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum ( including electromagnetic radiation and gravitational waves ) . Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer . In the special and general theories of relativity , c interrelates space and time , and also appears in the famous equation of mass -- energy equivalence E = mc .
Base pair
The centimorgan is also often used to imply distance along a chromosome , but the number of base pairs it corresponds to varies widely . In the Human genome , the centimorgan is about 1 million base pairs .
International System of Units
A second is 1 / 60 of a minute , which is 1 / 60 of an hour , which is 1 / 24 of a day , so a second is 1 / 86400 of a day ; a second is the time it takes a dense object to freely fall 4.9 metres from rest . The metre is close to the length of a pendulum that has a period of 2 seconds ; most dining tabletops are about 0.75 metre high ; a very tall human ( basketball forward ) is about 2 metres tall . The kilogram is the mass of a litre of cold water ; a cubic centimetre or millilitre of water has a mass of one gram ; a 1 - euro coin , 7.5 g ; a Sacagawea US 1 - dollar coin , 8.1 g ; a UK 50 - pence coin , 8.0 g . A candela is about the luminous intensity of a moderately bright candle , or 1 candle power ; a 60 W tungsten - filament incandescent light bulb has a luminous intensity of about 64 candela . A mole of a substance has a mass that is its molecular mass expressed in units of grams ; the mass of a mole of table salt is 58.4 g . A temperature difference of one kelvin is the same as one degree Celsius : 1 / 100 of the temperature differential between the freezing and boiling points of water at sea level ; the absolute temperature in kelvins is the temperature in degrees Celsius plus about 273 ; human body temperature is about 37 ° C or 310 K . A 60 W incandescent light bulb consumes 0.5 amperes at 120 V ( US mains voltage ) and about 0.26 amperes at 230 V ( European mains voltage ) .
Speed of light
The speed of light is of relevance to communications : the one - way and round - trip delay time are greater than zero . This applies from small to astronomical scales . On the other hand , some techniques depend on the finite speed of light , for example in distance measurements .
Observable universe
78 billion light - years In 2003 , Cornish et al. found this lower bound for the diameter of the whole universe ( not just the observable part ) , postulating that the universe is finite in size due to its having a nontrivial topology , with this lower bound based on the estimated current distance between points that we can see on opposite sides of the cosmic microwave background radiation ( CMBR ) . If the whole universe is smaller than this sphere , then light has had time to circumnavigate it since the Big Bang , producing multiple images of distant points in the CMBR , which would show up as patterns of repeating circles . Cornish et al. looked for such an effect at scales of up to 24 gigaparsecs ( 78 Gly or 7.4 × 10 m ) and failed to find it , and suggested that if they could extend their search to all possible orientations , they would then `` be able to exclude the possibility that we live in a universe smaller than 24 Gpc in diameter '' . The authors also estimated that with `` lower noise and higher resolution CMB maps ( from WMAP 's extended mission and from Planck ) , we will be able to search for smaller circles and extend the limit to ~ 28 Gpc . '' This estimate of the maximum lower bound that can be established by future observations corresponds to a radius of 14 gigaparsecs , or around 46 billion light - years , about the same as the figure for the radius of the visible universe ( whose radius is defined by the CMBR sphere ) given in the opening section . A 2012 preprint by most of the same authors as the Cornish et al. paper has extended the current lower bound to a diameter of 98.5 % the diameter of the CMBR sphere , or about 26 Gpc .
Space Race
The first step was witnessed by at least one - fifth of the population of Earth , or about 723 million people . His first words when he stepped off the LM 's landing footpad were , `` That 's one small step for ( a ) man , one giant leap for mankind . '' Aldrin joined him on the surface almost 20 minutes later . Altogether , they spent just under two and one - quarter hours outside their craft . The next day , they performed the first launch from another celestial body , and rendezvoused back with Columbia .
Polygon
where Q i , j ( \ displaystyle Q_ ( i , j ) ) is the squared distance between ( x i , y i ) ( \ displaystyle ( x_ ( i ) , y_ ( i ) ) ) and ( x j , y j ) ; ( \ displaystyle ( x_ ( j ) , y_ ( j ) ) ; ) and
Speed of light
NASA must wait several hours for information from a probe orbiting Jupiter , and if it needs to correct a navigation error , the fix will not arrive at the spacecraft for an equal amount of time , creating a risk of the correction not arriving in time .
Earth's location in the Universe
Milky Way subgroup 840,500 pc The Milky Way and those satellite dwarf galaxies gravitationally bound to it . Examples include the Sagittarius Dwarf , the Ursa Minor Dwarf and the Canis Major Dwarf . Cited distance is the orbital diameter of the Leo T Dwarf galaxy , the most distant galaxy in the Milky Way subgroup . Local Group 3 Mpc Group of at least 47 galaxies of which the Milky Way is a part . Dominated by Andromeda ( the largest ) , the Milky Way and Triangulum ; the remainder are dwarf galaxies . Local Sheet 7 Mpc Group of galaxies including the Local Group moving at the same relative velocity towards the Virgo Cluster and away from the Local Void . Virgo Supercluster 30 Mpc The supercluster of which the Local Group is a part . It comprises roughly 100 galaxy groups and clusters , centred on the Virgo Cluster . The Local Group is located on the outer edge of the Virgo Supercluster . Laniakea 160 Mpc A group connected with the superclusters of which the Local Group is a part . Comprises roughly 300 to 500 galaxy groups and clusters , centred on the Great Attractor in the Hydra - Centaurus Supercluster . Observable universe 28,000 Mpc More than 100 billion galaxies , arranged in millions of superclusters , galactic filaments , and voids , creating a foam - like superstructure . Universe Minimum 28,000 Mpc Beyond the observable universe lie the unobservable regions from which no light has reached the Earth yet . No information is available , as light is the fastest travelling medium of information . However , uniformitarianism argues that the Universe is likely to contain more galaxies in the same foam - like superstructure .
Time dilation
Δ t ′ = 2 D c . ( \ displaystyle \ Delta t ' = ( \ frac ( 2D ) ( c ) ) . )
2004 Indian Ocean earthquake and tsunami
The largest run - up measured was at 12.5 m ( 41 ft ) with inundation distance of 390 m to 1.5 km ( 0.242 miles - 0.932 miles ) in Yala . In Hambantota , tsunami run - ups are measured at 11 m ( 36.1 ft ) with the greatest inundation distance of 2 km ( 1.24 miles ) , and tsunami run - up measurements along the Sri Lankan coasts are at 2.4 -- 11 m ( 7.87 ft -- 36.1 ft ) . Tsunami waves measured on the east coast ranged from 4.5 m - 9 m ( 14.8 ft -- 29.5 ft ) at Pottuvill to around Batticaloa , 2.6 m - 5 m ( 8.53 ft -- 16.4 ft ) in the northeast around Trincomalee and 4 m - 5 m ( 13.1 ft -- 16.4 ft ) in the west coast from Moratuwa to Ambalangoda . Fishermen
2004 Indian Ocean earthquake and tsunami
Consequently , tsunami runup heights vary from 5 m ( 16.4 ft ) to 9 m ( 29.5 ft ) with inundation distances varying from 44 m ( 0.027 miles ) to 704 m ( 0.44 miles ) . The maximum runup height of almost 9 m ( 29.5 ft ) was recorded in Bandarbeyla . An even higher runup point was measured on a cliff near the town of Eyl , solely on an eyewitness account .
Observable universe
where G is the gravitational constant and H is the present value of the Hubble constant . The current value for H , due to the European Space Agency 's Planck Telescope , is H = 67.15 kilometers per second per mega parsec . This gives a critical density of 6973850000000000000 ♠ 0.85 × 10 kg / m ( commonly quoted as about 5 hydrogen atoms per cubic meter ) . This density includes four significant types of energy / mass : ordinary matter ( 4.8 % ) , neutrinos ( 0.1 % ) , cold dark matter ( 26.8 % ) , and dark energy ( 68.3 % ) . Note that although neutrinos are Standard Model particles , they are listed separately because they are difficult to detect and so different from ordinary matter . The density of ordinary matter , as measured by Planck , is 4.8 % of the total critical density or 6972408000000000000 ♠ 4.08 × 10 kg / m . To convert this density to mass we must multiply by volume , a value based on the radius of the `` observable universe '' . Since the universe has been expanding for 13.8 billion years , the comoving distance ( radius ) is now about 46.6 billion light - years . Thus , volume ( 4 / 3πr ) equals 7080358000000000000 ♠ 3.58 × 10 m and the mass of ordinary matter equals density ( 6972408000000000000 ♠ 4.08 × 10 kg / m ) times volume ( 7080358000000000000 ♠ 3.58 × 10 m ) or 7053146000000000000 ♠ 1.46 × 10 kg .
Speed of light
In 2011 , the CGPM stated its intention to redefine all seven SI base units using what it calls `` the explicit - constant formulation '' , where each `` unit is defined indirectly by specifying explicitly an exact value for a well - recognized fundamental constant '' , as was done for the speed of light . It proposed a new , but completely equivalent , wording of the metre 's definition : `` The metre , symbol m , is the unit of length ; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 7008299792458000000 ♠ 299 792 458 when it is expressed in the SI unit ms . '' This is one of the proposed changes to be incorporated in the next revision of the SI also termed the New SI .
Speed of light
In 1983 the 17th CGPM found that wavelengths from frequency measurements and a given value for the speed of light are more reproducible than the previous standard . They kept the 1967 definition of second , so the caesium hyperfine frequency would now determine both the second and the metre . To do this , they redefined the metre as : `` The metre is the length of the path travelled by light in vacuum during a time interval of 1 / 7008299792458000000 ♠ 299 792 458 of a second . '' As a result of this definition , the value of the speed of light in vacuum is exactly 7008299792458000000 ♠ 299 792 458 m / s and has become a defined constant in the SI system of units . Improved experimental techniques that prior to 1983 would have measured the speed of light , no longer affect the known value of the speed of light in SI units , but instead allow a more precise realization of the metre by more accurately measuring the wavelength of Krypton - 86 and other light sources .
Time dilation
Δ t = 2 L c . ( \ displaystyle \ Delta t = ( \ frac ( 2L ) ( c ) ) . )
2004 Indian Ocean earthquake and tsunami
In Meulaboh based on survivor testimonies , tsunami arrived after the sea receded about 500 m ( 0.31 miles ) , followed by an advancing small tsunami . The second and third destructive waves arrived later , which exceeded the height of the coconut trees . The inundation distance is about 5 km ( 3.1 miles ) .
Degrees of freedom (physics and chemistry)
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 ( \ displaystyle d = ( \ sqrt ( ( x_ ( 2 ) - x_ ( 1 ) ) ^ ( 2 ) + ( y_ ( 2 ) - y_ ( 1 ) ) ^ ( 2 ) + ( z_ ( 2 ) - z_ ( 1 ) ) ^ ( 2 ) ) ) )
Speed of light
In 1629 , Isaac Beeckman proposed an experiment in which a person observes the flash of a cannon reflecting off a mirror about one mile ( 1.6 km ) away . In 1638 , Galileo Galilei proposed an experiment , with an apparent claim to having performed it some years earlier , to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away . He was unable to distinguish whether light travel was instantaneous or not , but concluded that if it were not , it must nevertheless be extraordinarily rapid . In 1667 , the Accademia del Cimento of Florence reported that it had performed Galileo 's experiment , with the lanterns separated by about one mile , but no delay was observed . The actual delay in this experiment would have been about 11 microseconds . Rømer
Speed of light
A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back . This is the working principle behind the Fizeau -- Foucault apparatus developed by Hippolyte Fizeau and Léon Foucault .
Global Positioning System
Δ r ( Δ s ( φ 1 , 1 , 1 ) ) = Δ r ( φ 1 , 2 , 1 − φ 1 , 1 , 1 ) = Δ r ( φ 1 , 2 , 1 ) − Δ r ( φ 1 , 1 , 1 ) = ( φ 2 , 2 , 1 − φ 1 , 2 , 1 ) − ( φ 2 , 1 , 1 − φ 1 , 1 , 1 ) ( \ displaystyle ( \ begin ( aligned ) \ Delta ^ ( r ) ( \ Delta ^ ( s ) ( \ phi _ ( 1 , 1 , 1 ) ) ) \ , & = \ , \ Delta ^ ( r ) ( \ phi _ ( 1 , 2 , 1 ) - \ phi _ ( 1 , 1 , 1 ) ) & = \ , \ Delta ^ ( r ) ( \ phi _ ( 1 , 2 , 1 ) ) - \ Delta ^ ( r ) ( \ phi _ ( 1 , 1 , 1 ) ) & = \ , ( \ phi _ ( 2 , 2 , 1 ) - \ phi _ ( 1 , 2 , 1 ) ) - ( \ phi _ ( 2 , 1 , 1 ) - \ phi _ ( 1 , 1 , 1 ) ) \ end ( aligned ) ) )
Global Positioning System
d i = ( t ~ i − b − s i ) c , i = 1 , 2 , ... , n ( \ displaystyle d_ ( i ) = \ left ( ( \ tilde ( t ) ) _ ( i ) - b - s_ ( i ) \ right ) c , \ ; i = 1 , 2 , \ dots , n )
Earth's orbit
Mathematicians and astronomers ( such as Laplace , Lagrange , Gauss , Poincaré , Kolmogorov , Vladimir Arnold , and Jürgen Moser ) have searched for evidence for the stability of the planetary motions , and this quest led to many mathematical developments and several successive `` proofs '' of stability for the Solar System . By most predictions , Earth 's orbit will be relatively stable over long periods .