CosmicCosmic DistancesDistances

1010 ly

107 ly

105 ly

102 ly

10-4 ly

Radar Ranging

ItIt is is based based on on the the measurement measurement ofof the the round-trip round-trip time time (“t”) (“t”) ofof a a powerful powerful radio radio signal signal (with(with speed speed “v”) “v”) that that is is reflected reflected onon the the atmosphere atmosphere of of Venus Venus

DD = = v v (t/2) (t/2) = = E-VE-V 6 == 42 42 x x 10 106km km (average) (average)

UsingUsing this this method method we we can can obtainobtain the the value value of of AstronomicalAstronomical Unit Unit

AstronomicalAstronomical Unit Unit is is the the averageaverage Earth-Sun Earth-Sun distance distance

SinceSince D D is is known, known, so so it's it's possible possible to to E-VE-V determinedetermine the the distance distance Earth Earth - - Sun Sun trigonometricallytrigonometrically

TheThe maximum maximum apparent apparent distance distance of of Venus Venus from from the the Sun Sun (as (as seen seen from from Earth) Earth) varies varies between between 45° 45° and and 48 48 °. °.

For For simplicity, simplicity, we we take take an an average average value value betweenbetween these these : : 46 46 ° °

D /D = sin 46° = 0,72 DS-V /DS-E = sin 46° = 0,72 D D = = 1 1 AU AU D D = = 0,72 0,72 AU AU D D = = 0,28 0,28 AU AU S-V S-E S-ES-E S-VS-V E-VE-V D = 0,72 D 88 DS-V = 0,72 DS-E 1 1 AU AU = = D D / /0,28 0,28 = = 1,5 1,5 x x 10 10 km km S-V S-E E-VE-V Parallax WhenWhen we we want want to to determine determine the the weight weight with with a a scale, scale, we we may may note note that that the the needleneedle varies varies position position each each time time we we move move our our head: head: if if we we move move it it toto the the right, right, we we will will project project the the needle needle to to the the left left

toto the the left, left, we we will will see see the the needle needle projectedprojected to to the the right. right.

The shift of the object is only apparent and it is This effect is called The shift of the object is only apparent and it is This effect is called causedcaused by by a a change change of of the the position position of of the the observer. observer. PARALLAX PARALLAX Another example

TheThe stars stars have have a a parallax parallax effect, effect, annual annual parallax, parallax, caused caused by by the the motion motion of of the the Earth Earth around around the the Sun. Sun.

TheThe Earth Earth revolves revolves around around the the Sun Sun drawing drawing an an ellipse ellipse whose whose major major axis axis is is about about 300 300 million million km km..

TheThe position, position, from from which which we we observe observe the the sky, sky, changes changes over over the the course course of of the the year. year.

LetLet us us fix fix the the position position of of a a star star and and let let repeat repeat the the observation observation from from the the same same place place on on Earth Earth after after six months when the Earth is in the opposite point in the orbit around the Sun, six months when the Earth is in the opposite point in the orbit around the Sun, wewe will will note note a a small small change change in in the the star's star's position position.. InIn the the course course of of a a year, year, a a star star describes describes a a small small ellipse ellipse in in the the sky. sky.

S S 2 1 TheThe parallax parallax method method is is a a method method similar similar toto the the triangulation. triangulation. In In fact, fact, if if we we join join thethe point point E E with with S S and and S S with with E E , , 11 11 22 22 wewe define define a a triangle, triangle, which which the the major major axis axis asas base base and and the the distances distances S-E S-E S-E S-E asas sides. sides. 11 22

S By By convention, convention, the the angle angle of of the the annual annual parallaxparallax (p) (p) is is equal equal to to half half the the apparent apparent angularangular shif shif of of a a star star in in 1 1 year, year, and and correspondscorresponds to to the the vertex vertex of of the the triangle triangle whichwhich is is based based on on the the semi-axis semi-axis ofof Earth's Earth's orbit orbit around around the the Sun Sun (R(R = = 150000000 150000000 km) km) R andand has has vertex vertex the the star. star.

E E 1 2 TheThe parallax parallax of of a a star star decreases decreases with with distance distance and and it it has has always always very very small small values. values.

TheThe nearest nearest stars stars to to Earth Earth have have a a value value of of the the parallax parallax a a little little less less than than 1 1 second second of of arc. arc.

AsAs the the distance distance increases, increases, the the measurement measurement of of the the parallax parallax angle angle becomes becomes more more difficult, difficult, as as thethe annual annual change change in in position position decreases decreases significantly. significantly. For For this this reason reason the the more more distant distant stars stars maintainmaintain a a fixed fixed position position and and do do not not exhibit exhibit apparent apparent shifts. shifts.

ToTo derive derive the the distance distance to to a a star star directly directly from from the the value value of of the the parallax, parallax, itit is is convenient convenient to to adopt adopt a a particular particular unit unit of of measurement: measurement: parsec parsec (pc). (pc).

11 parsec parsec is is the the distance distance at at which which a a body body subtend subtend a a parallactic parallactic angle angle of of 1” 1” of of arc. arc.

IfIf we we express express the the distance distance in in parsecs parsecs and and assign assign the the value value 1 1 to to the the distance distance Sun-Earth Sun-Earth = = “R”, “R”, “d” “d” is is d=1/p d=1/p

To obtain it we use trigometric p ratios : d = R / sin p = 1/ sin p

d Since the angles with which we deal are very small, we use the approximation sin p ~ p

dd (pc) (pc) = = 1/p 1/p R

By studying the annual shifts in the positions of the stars, we are able to measure parallaxes corresponding to a maximum distance of 50 pc.

TheThe measurement measurement of of parallax parallax seems seems very very easy, easy, but but in in reality reality it it is is necessary necessary to to use use tools tools that that reach reach accuraciesaccuracies much much greater greater than than those those of of a a "normal" "normal" telescope, telescope, that that does does not not reach reach the the required required accuracy. accuracy.

WithWith the the Spacecraft Spacecraft Hypparcos Hypparcos we we can can measure measure parallaxes parallaxes up up to to 300 300 pc. pc.

300 pc

ByBy the the end end of of 2013 2013 the the Spacecraft Spacecraft Gaia Gaia will will be be launched launched and and it it will will be be able able to to measuremeasure parallaxes parallaxes up up to to 10000 10000 parsec parsec

ExercisesExercises Proxima Centauri

Proxima Proxima Centauri Centauri is the nearest star to the SolarSystem. It has a parallax of 0,775"; so its distance is 1 /0,775 = 1,295 pc

Sirius Sirius

SiriusSirius is is the the brightest brightest starstar in in the the night night sky. sky. ItIt has has a a parallax parallax of of 0,380”;0,380”; so so its its distance distance is is

1/0,3801/0,380 = = 2,632 2,632 parsec parsec UnitUnit ofof MeasuramentMeasurament

ConversionConversion FactorsFactors

AstronomicalAstronomical Unit Unit ( (auau):): average average 1 au ≈ 4.85×10-6 pc ≈ 15.81×10-6 ly Earth-SunEarth-Sun distance distance (149 (149 600 600 000 000 km) km)

ParsecParsec (pc): (pc): the the distance distance from from the the Sun Sun toto an an astronomical astronomical object object which which 1 light-year ≈ 63,24x103 au ≈ 0,31 pc hashas a a parallax parallax angle angle of of oneone arcsecond arcsecond (1/3,600 (1/3,600 of of a a degree). degree).

LightLight Year Year (l.y.): (l.y.): the the distance distance that that 4 lightlight travels travels in in a a vacuum vacuum in in one one year year 1 parsec ≈ 20,62x10 au ≈ 3,26 ly withwith a a speed speed of of ~ ~ 300 300 000 000 km/s km/s

CAUTION! LIGHT YEAR is NOT a unit of measurament of time. It is correct to say that the image of celestial body, which is far a certain number of light years, shows us that celestial body as it was the same number of years ago, and not at this time.

The distance Earth - Andromeda is 2 million ly, so if an observer could see the Earth from Andromeda, he would see the Earth today as it

was 2 million years ago. MainMain –– SequenceSequence FittingFitting

BothBoth the the temperature temperature and and the the brightnessbrightness of of a a star star can can be be derived derived fromfrom the the analysis analysis of of its its spectrum. spectrum.

TheThe knowledge knowledge of of these these parametersparameters allows allows us us to to locate locate a a starstar in in the the HR HR diagram diagram and and then then to to derivederive the the absolute absolute magnitude magnitude ( (MM).).

KnowingKnowing M M and and the the apparent apparent magnitudemagnitude ( (mm)) we we can can obtain obtain thethe value value of of the the distance distance d d : : MM – – m m = = 5 5 – – 5 5 log log d d

ThisThis method method is is called called

spectroscopicspectroscopic parallax parallax.. TheThe determination determination of of spectroscopic spectroscopic parallaxes parallaxes is is particularly particularly useful useful to to determinedetermine the the distance distance of of the the stars stars that that belong belong to to a a cluster. cluster.

TheThe star star clusters clusters are are generally generally far far away, away, so so the the direct direct determination determination ofof the the distance distance of of their their individual individual stars stars is is very very uncertain. uncertain.

AlmostAlmost all all clusters clusters have have a a small small angularangular diameter; diameter; therefore therefore theythey are are aggregates aggregates of of stars stars of of modest size compared to the great modest size compared to the great distancedistance that that separates separates them them from from us. us. UsingUsing the the apparent apparent magnitudes magnitudes instead instead ofof absolute absolute ones, ones, we we can can build build the the HR HR diagramdiagram of of the the stars stars in in the the cluster cluster

M67

FromFrom the the traslation traslation thatthat must must be be NGC188 introducedintroduced in in orderorder to to obtain obtain the the overlapoverlap of of the the two two sequences,sequences, wewe can can determine determine thethe value value of of the the averageaverage distance distance of the stars of the of the stars of the clustercluster from from Earth. Earth. StandardStandard CandleCandle

It'sIt's an an object, object, such such as as a a star, star, that that lies lies within within a a galaxy galaxy and and for for which which we we know know the the luminosity. luminosity. ComparingComparing the the known known luminosity luminosity with with the the observed observed luminosity luminosity (apparent (apparent magnitude), magnitude), wewe can can calculate calculate the the distance distance ( (dd):): M M – – m m = = 5 5 – – 5 5 log log d d

ToTo be be useful, useful, standard standard candles candles should should have have the the following following properties: properties:

They should be luminous, They should be luminous, TheyThey should should be be so we can see them out TheyThey should should be be so we can see them out WeWe should should be be fairly fairly certain certain relativelyrelatively common, common, to great distances. easilyeasily identifiable. identifiable. to great distances. aboutabout their their luminosities. luminosities. soso we we can can use use them them to to determine determine the the distancesdistances to to many many differentdifferent galaxies galaxies TypeType of of Standard Standard Candles: Candles: CepheidsCepheids TypeType Ia Ia Supernovae Supernovae

Spiral Galaxy M-100 Supernovae 2006X

CepheidsCepheids

CepheidsCepheids are are variable variable stars; stars; stars stars showing showing variations variations ofof luminosity luminosity in in the the course course of of their their existence. existence.

TheThe period period of of pulsation pulsation ( (PP)) is is related related to to the the luminosityluminosity of of the the star. star. The The longer longer is is the the period, period, thethe higher higher is is the the luminosity. luminosity.

AA Cepheid Cepheid with with a a three-day three-day period period has has a a brightnessbrightness equal equal to to 800 800 times times that that of of the the Sun; Sun; aa Cepheid Cepheid with with a a period period of of thirty thirty daysdays is is 10000 10000 times times more more luminous luminous than than the the Sun Sun

IfIf you you analyze analyze the the spectrum spectrum of of a a star, star, youyou can can determine determine its its temperature temperature and and its its color. color. Cepheid Variable Stars in Spiral Galaxy NGC3021 (Hubble Space Telescope) FromFrom these these parameters parameters we we derive derive the the luminosity. luminosity. ThroughThrough the the period period – – luminosity luminosity relation relation one one can can determine determine the the absolute absolute magnitude magnitude of of a a Cepheid: Cepheid: ( (MM = = -1,43 -1,43 – – 2,81 2,81 log log P P))

ComparingComparing M M with with the the apparent apparent magnitude magnitude m m, ,we we can can determine determine the the distance distance d d:: M M – – m m = = 5 5 – – 5log 5log d d

OwingOwing to to the the great great accuracy accuracy of of the the measurementmeasurement of of the the pulsation pulsation and and of of thethe period-luminosity period-luminosity relation, relation, CepheidsCepheids can can then then be be used used as as standard standard candlescandles to to determine determine the the distance distance ofof globular globular clusters clusters and and the the galaxies galaxies inin which which they they are are contained. contained.

CepheidsCepheids in in particular particular are are very very importantimportant because, because, duedue to to their their high high luminosity, luminosity, theythey can can be be easly easly observed observed inin nearby nearby galaxies. galaxies. InIn 1912, 1912, Henrietta Henrietta Leavitt Leavitt discovered discovered that that the the periods periods of of Cepheides Cepheides variable variable starsstars in in the the Small Small Magellanic Magellanic Cloud Cloud are are related related to to their their luminosity. luminosity.

More More recently, recently, the the Hubble Hubble Space Space Telescope Telescope was was able able to to identify identify somesome Cepheid Cepheid variables variables in in the the Virgo Virgo cluster, cluster, at at a a distance distance of of ~ ~ 20 20 Mpc Mpc..

WithWith Cepheid Cepheid variables variables we we can can estimate estimate the the distance distance of of the the nearest nearest galaxies galaxies up up to to 30 30 Mpc. Mpc.

Therefore,Therefore, they they are are the the main main step step connecting connecting galactic galactic and and extragalactic extragalactic distances. distances. EuroVoEuroVo

ToTo experience experience the the emotion emotion of of the the scientific scientific research research and and of of the the astronomy, astronomy, wewe can can use use a a free free tool tool available available on on the the Internet: Internet:

EuroVoEuroVo → → a a project project developed developed within within the the European European Virtual Virtual Observatory Observatory which which has has asas goal goal the the diffusion diffusion of of data data and and software software EuroVo EuroVo to to the the public. public.

ThisThis project project provides provides examples, examples, teaching teaching modules modules and and semplified semplified professional professional software. software.

ToTo download download it: it: http://wwwas.oats.inaf.it/aidawp5/eng_download.html?fsize=medium http://wwwas.oats.inaf.it/aidawp5/eng_download.html?fsize=medium WorthWorth of of mention mention is is Aladin Aladin that that has has several several built-in built-in functions functions thatthat allow allow the the image image handling handling and and a a quick quick analysis. analysis.

WeWe can can see see two two possible possible applications applications of of Aladin Aladin on on cosmic cosmic distances distances

DistanceDistance of of Barnard Barnard Star Star

StarStar Aladin Aladin

Click here

The distance of the Barnard star from Earth is : d = 1 / 0,54831 ~ ~ 1,82 pc

548,31 mas (milliarcsecond) = 0,54831 as DistanceDistance of of Andromeda Andromeda Galaxy Galaxy

InIn 1924 1924 Edwin Edwin Hubble Hubble identified identified some some Cepheids Cepheids in in the the Andromeda Andromeda Galaxy; Galaxy; hehe concluded concluded that that it it was was located located far far away away from from our our Galaxy. Galaxy.

StartStart Aladin Aladin

After restart

WeWe choose choose the the most most recent recent catalog catalog

It means the period of the stars, It means the period of the stars, butbut not not all all have have it it shown. shown. ToTo see see only only the the stars stars of of which which the the period period is is indicated, indicated, we we create create a a filter. filter.

ToTo calculate calculate absolute absolute magnitude magnitude

ToTo calculate calculate the the distances distances

It'sIt's the the distance distance of of all all Cepheids Cepheids

6 ByBy averaging, averaging, we we find find the the approximate approximate distance distance to to the the Andromeda Andromeda Galaxy: Galaxy: (2,52 (2,52 ± ± 0,14) 0,14) 10 10 6ly ly

TypeType IaIa SupernovaeSupernovae

ToTo extend extend the the distance distance scale scale even even further, further, we we need need brighter brighter objects objects butbut just just as as reliable reliable as as standard standard candles, candles, and and the the best best candidates candidates are are the the Type Type Ia Ia Supernovae. Supernovae.

These These are are used used beyond beyond 30 30 Mpc Mpc and and occur occur when when a a white white dwarf dwarf in in a a close close binary binary system system accretes accretes enough enough matter matter from from its its companion companion to to blow blow itself itself apart apart in in a a thermonuclear thermonuclear explosion. explosion.

IfIf a a Type Type Ia Ia supernova supernova is is seen seen in in a a distantdistant galaxy galaxy and and its its maximum maximum apparentapparent brightness brightness measured, measured, we can find the galaxy’s distance. we can find the galaxy’s distance. The inset shows one of the 10 most distant and ancient Type Ia supernovae NotNot all all Type Type Ia Ia supernovae supernovae are are equally equally luminous, luminous, but but a a simple simple relation relation holds: holds: thethe slower slower the the brightness brightness decreases, decreases, the the more more luminous luminous the the supernova. supernova.

Using Using this this relationship, relationship, we we have have measured measured distances distances to to supernovae supernovae more more than than 1000 1000 Mpc Mpc from from Earth. Earth.

ThisThis technique technique can can be be used used only only for for galaxies galaxies in in which which we we happen happen to to observe observe a a Type Type Ia Ia supernova. supernova. NowNow we we are are able able to to identify identify many many dozens dozens of of these these supernovae supernovae every every year, year, so so the the number number of of galaxies galaxies whosewhose distances distances can can be be measured measured in in this this way way is is continually continually increasing. increasing. TheThe distancedistance scalescale

TheThe figure figure shows shows the the ranges ranges of of application application of of several several important important methods methods for for the the determination determination of of astronomicalastronomical distances. distances. Because Because these these ranges ranges overlap, overlap, one one technique technique can can be be used used to to calibrate calibrate another. another.

For For this this reason, reason, we we go go to to great great lengths lengths to to check check the the accuracy accuracy and and reliability reliability of of our our standard standard candles. candles.

AA change change in in distance-measuring distance-measuring techniques techniques used used for for nearby nearby objects objects can can also also

havehave substantial substantial effects effects on on the the distances distances to to remote remote galaxies. galaxies. AsAs an an example, example, the the distance distance to to the the galaxy galaxy M100 M100 shown shown in in the the figure figure is is determined determined using using Cepheids. Cepheids. AA Type Type Ia Ia supernova supernova has has been been seen seen in in M100, M100, as as the the figure figure shows, shows, and and its its luminosity luminosity is is determined determined usingusing the the Cepheid-derived Cepheid-derived distance distance to to M100. M100. Any Any change change in in the the calculated calculated distance distance to to M100 M100 would would changechange the the calculated calculated luminosity luminosity of of the the Type Type Ia Ia supernova, supernova, and and so so would would have have an an effect effect on on all all distances distances derivedderived from from this. this.

BecauseBecause one one measuring measuring technique technique leadsleads us us to to the the next next one one like like rungs rungs on on a a ladder,ladder, the the techniques techniques shown shown in in the the figurefigure of of the the previous previous slide, slide, are are referred referred toto collectively collectively as as the the distance distance ladder. ladder.

HubbleHubble LawLaw

DuringDuring the the 1920s, 1920s, Edwin Edwin Hubble, Hubble, b byy observing observing thethe luminosity luminosity and and pulsation pulsation periods periods ofof Cepheid Cepheid variables variables in in many many galaxies, galaxies, waswas able able to to measure measure the the distance distance to to each each galaxy. galaxy.

ManyMany spectral spectral lines lines emitted emitted by by chemical chemical elements elements similarsimilar to to those those present present in in the the Sun Sun areare found found in in the the light light emitted emitted by by distant distant stars. stars.

AnalyzingAnalyzing the the spectra spectra we we can can notice notice that that the the lines lines producedproduced by by the the distant distant stars stars correspond correspond to to thosethose emitted emitted by by known known elements elements only only with with a a systematicsystematic shift shift towards towards longer longer wavelengths. wavelengths.

HubbleHubble found found that that most most galaxies galaxies show show a a shift shift toward toward the the red red portion portion of of the the spectrum. spectrum. TheThe redshift redshift ( (zz)) is is found found from from the the ratio: ratio: z z = = ( (λ λ – – λₒ) λₒ) / /λₒ λₒ

λλ is is the the wavelength wavelength of of the the line line ofof the the spectrum spectrum emitted emitted by by a a starstar in in motion motion and and the the correspondingcorresponding wavelength wavelength λₒ λₒ ofof the the same same line line of of a a reference reference spectrum,spectrum, usually usually the the solar solar one. one.

HubbleHubble found found a a correlation correlation between between the the distance distance to to a a galaxy galaxy and and its its redshift: redshift: nearby nearby galaxies galaxies are are movingmoving away away from from us us slowly, slowly, while while more more distant distant galaxies galaxies are are rushing rushing away away from from us us much much more more rapidly. rapidly. CAUTION!

The redshift is similar to a Doppler effect, but in reality its physical nature is different.

It is the basis of the most shocking cosmological theory: the expansion of the Universe. It creates new space between source and observer, "stretching" the wavelength.

TheThe movement movement away away from from our our of of the the other other galaxies galaxies is is called called reccession reccession motion. motion. The The relation relation between between

thethe recession recession velocity velocity v v and and distance distance d d of of a a galaxy galaxy from from Earth Earth is is expressed expressed by by the the Hubble Hubble law: law: v v = = d d H H00

HH00 is is the the Hubble Hubble constant constant and and its its value value is is constantly constantly revised. revised. It It is is costant costant because because if if at at this this time time we we repeat repeat its its measure,measure, again, again, in in any any other other point point in in the the universe, universe, we we would would get get the the same same value value of of H H00 ; ;but but it it varies varies over over time. time.

TheThe evolution evolution of of H H00 is is due due to to the the effects effects of of the the gravitational gravitational force force of of the the matter matter in in the the Universe Universe thatthat tends tends to to slow slow the the expansion, expansion, and and the the so-called so-called dark dark energy, energy, which which instead instead tends tends to to speed speed it it up. up. Hubble Hubble Space Telescope Space Infrared Planck Spacecraft Telescope Spitzer

Measured by

H0 500 73,8 ± 2,4 74,3 ± 2,1 67,15 ± 1,2 (km/s/Mpc)

FromFrom these these measurements measurements continuously continuously updated, updated, we we can can conclude conclude that that the the sequence sequence ofof measurements measurements of of the the Hubble Hubble constant constant is is converging converging to to a a value value more more accurately. accurately. CAUTION! The use of the Hubble law has some limitations. We can not use it when:

the distances are less than a few million light years, because the gravitational effect would occur due to the proximity.

the distances are very large, in excess of several billion light years, for two reasons: on one hand the uncertainties increase with distance; on the other hand, the proportionality speed - distance requires knowledge of the developmental characteristics of the galaxy, to as the Hubble parameter that has characterized the expansion of the universe in the distant past (cosmological parameters were measured using the Type Ia Supernovae as standard candles).

Finally, it should be noted that this law expresses a situation existing at a given moment and not as the velocity of an object changes when it moves away. GivenGiven the the value value of of H H00 , ,we we can can use use the the Hubble Hubble law law to to find find the the distance distance d d to to the the galaxy galaxy ifif we we know know how how to to determine determine the the recession recession velocity velocity v v from from the the laws laws of of the the Doppler Doppler effect effect..

IfIf the the redshift redshift and and recession recession velocity velocity are are not not too too great, great, we we can can use use the the following following equation: equation: vv = = c c z z , ,where where c c is is the the speed speed of of light. light.

Not all galaxies are moving away from us! Some of the nearest galaxies, including Not all galaxies are moving away from us! Some of the nearest galaxies, including AndromedaAndromeda Galaxy, Galaxy, are are actually actually approaching approaching us us and and have have blueshifts blueshifts rather rather than than redshifts redshifts.. Let's take an example, for us closer, to understand the orders of magnitude with which we deal in the distance scales: if the Sun was an orange, the Earth would be the head of a needle turning 15 meters away around the orange, Jupiter was a cherry, turning around 77 meters, Pluto a grain of sand at 580 meters and Proxima Centauri another orange at 4000 km!

Sun Earth Jupiter Pluto Proxima Centauri

15 m 77 m 580 m 4000000 m AppendixAppendix A:A: KnowledgeKnowledge RequiredRequired

TrigonometricTrigonometric RatiosRatios

b = a sin b C c = b tg g δ b = a cos g a c = b cotg b b c = a sin g b = c tg b β c = a cos b b = c cotg g A c B

BrightnessBrightness andand LuminosityLuminosity

Brightness is the amount of light received by an object. Luminosity is the amount of light emitted from the star in the unit of time. Its unit of measurement is “candela”. MagnitudeMagnitude The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere. The absolute magnitude (M) is the measure of a celestial object's intrinsic brightness. M – m = 5 – 5log d The difference (M – m) is called distance modulus HRHR diagramdiagram

The HR diagram collects key information on stars. Each star is identified by two coordinates: in the x-axis is the spectral type, in the y-axis the absolute brightness. The spectral types indicate the surface temperature of the star, they are arranged in the upper x-axis in order of decreasing temperature. The central area of the​​ diagram, that extends diagonally from top left to bottom right, is called the main sequence. It collects the highest number of stars in the diagram . DopplerDoppler EffectEffect It is a physical phenomenon which consists in the apparent change in frequency or wavelength of a wave perceived by an observer who is in motion or at rest relative to the source of the waves, also in motion or at rest Example

If the car with siren is approaching us, we hear an higher sound than the same one issued by the source when it is stationary; when it goes away it appears lower.