Physics
Hubble's Law
Hubble's Law describes the relationship between the distance of galaxies from Earth and their recessional velocity. It states that the farther a galaxy is from us, the faster it appears to be moving away. This law is a key piece of evidence for the expansion of the universe and has significant implications for our understanding of cosmology.
Written by Perlego with AI-assistance
Related key terms
1 of 5
12 Key excerpts on "Hubble's Law"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
______________________________ WORLD TECHNOLOGIES ______________________________ Chapter- 5 Observational Evidence Hubble's Law Hubble's Law describes the observation in physical cosmology that the velocity at which various galaxies are receding from the Earth is proportional to their distance from us. The law was first derived from the General Relativity equations by Georges Lemaître in 1927. Edwin Hubble derived it empirically in 1929 after nearly a decade of observations. The recession velocity of the objects was inferred from their redshifts, many measured earlier by Vesto Slipher (1917) and related to velocity by him. It is considered the first observational basis for the expanding space paradigm and today serves as one of the pieces of evidence most often cited in support of the Big Bang model. The law is often expressed by the equation v = H 0 D , with H 0 the constant of proportionality (the Hubble constant ) between the proper distance D to a galaxy (which can change over time, unlike the comoving distance) and its velocity v (i.e. the derivative of proper distance with respect to cosmological time coordinate). The SI unit of H 0 is s -1 but it is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy one Megaparsec away. The reciprocal of H 0 is the Hubble time. The most recent observational determination of the proportionality constant obtained in 2010 based upon measurements of gravitational lensing by using the Hubble Space Telescope (HST) yielded a value of H 0 = 70.6 ± 3.1 (km/sec)/Mpc. In 2009 also using the Hubble Space Telescope the measure was 74.2 ± 3.6 (km/s)/Mpc. The results agree closely with an earlier measurement of H 0 = 72 ± 8 km/s/Mpc obtained in 2001 also by the HST. In August 2006, a less-precise figure was obtained independently using data from NASA's Chandra X-ray Observatory: H 0 = 77 (km/s)/Mpc or about 2.5×10 −18 s −1 with an uncertainty of ± 15%.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
______________________________ WORLD TECHNOLOGIES ______________________________ Chapter- 2 Hubble's Law and Comoving Distance Hubble's Law Hubble's Law describes the observation in physical cosmology that the velocity at which various galaxies are receding from the Earth is proportional to their distance from us. The law was first derived from the General Relativity equations by Georges Lemaître in 1927. Edwin Hubble derived it empirically in 1929 after nearly a decade of observations. The recession velocity of the objects was inferred from their redshifts, many measured earlier by Vesto Slipher (1917) and related to velocity by him. It is considered the first observational basis for the expanding space paradigm and today serves as one of the pieces of evidence most often cited in support of the Big Bang model. The law is often expressed by the equation v = H 0 D , with H 0 the constant of proportionality (the Hubble constant ) between the proper distance D to a galaxy (which can change over time, unlike the comoving distance) and its velocity v (i.e. the derivative of proper distance with respect to cosmological time coordinate). The SI unit of H 0 is s -1 but it is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy one Megaparsec away. The reciprocal of H 0 is the Hubble time. The most recent observational determination of the proportionality constant obtained in 2010 based upon measurements of gravitational lensing by using the Hubble Space Telescope (HST) yielded a value of H 0 = 70.6 ± 3.1 (km/sec)/Mpc. In 2009 also using the Hubble Space Telescope the measure was 74.2 ± 3.6 (km/s)/Mpc. The results agree closely with an earlier measurement of H 0 = 72 ± 8 km/s/Mpc obtained in 2001 also by the HST. In August 2006, a less-precise figure was obtained independently using data from NASA's Chandra X-ray Observatory: H 0 = 77 (km/s)/Mpc or about 2.5×10 −18 s −1 with an uncertainty of ± 15%.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 11 Observational Evidence Hubble's Law Hubble's Law describes the observation in physical cosmology that the velocity at which various galaxies are receding from the Earth is proportional to their distance from us. The law was first derived from the General Relativity equations by Georges Lemaître in 1927. Edwin Hubble derived it empirically in 1929 after nearly a decade of observations. The recession velocity of the objects was inferred from their redshifts, many measured earlier by Vesto Slipher (1917) and related to velocity by him. It is considered the first observational basis for the expanding space paradigm and today serves as one of the pieces of evidence most often cited in support of the Big Bang model. The law is often expressed by the equation v = H 0 D , with H 0 the constant of proportionality (the Hubble constant ) between the proper distance D to a galaxy (which can change over time, unlike the comoving distance) and its velocity v (i.e. the derivative of proper distance with respect to cosmological time coordinate). The SI unit of H 0 is s -1 but it is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy one Megaparsec away. The reciprocal of H 0 is the Hubble time. The most recent observational determination of the proportionality constant obtained in 2010 based upon measurements of gravitational lensing by using the Hubble Space Telescope (HST) yielded a value of H 0 = 70.6 ± 3.1 (km/sec)/Mpc. In 2009 also using the Hubble Space Telescope the measure was 74.2 ± 3.6 (km/s)/Mpc. The results agree closely with an earlier measurement of H 0 = 72 ± 8 km/s/Mpc obtained in 2001 also by the HST. In August 2006, a less-precise figure was obtained independently using data from NASA's Chandra X-ray Observatory: H 0 = 77 (km/s)/Mpc or about 2.5×10 −18 s −1 with an uncertainty of ± 15%.
eBook - PDF- Harry Chi-sing Lam, Narendra Kumar, Ho-kim Quang(Authors)
- 1991(Publication Date)
- World Scientific(Publisher)
CHAPTER VII COSMOLOGY 408 VII. COSMOLOGY C O N T E N T S 1. Hubble's Law 1.1 Astronomical distances 1.2 Velocity measurements 2. The Big Bang 3. The Fate of the Universe 3.1 Open, critical, and closed universes 3.2 Gravitational physics 4. Cosmic Background Radiation 5. The Thermal Evolution of the Universe 5.1 A brief history of the universe 5.2 Quantitative estimates 6. Primordial Nucleosynthesis 7. Cosmology and Particle Physics 7.1 Cosmological constant 7.2 Topological objects 7.3 The asymmetry between nucleons and antinucleons 7.4 Superstring theory 8. Inflationary Universe 1. Hubble's Law 409 1. Hubble's Law Modern cosmology is founded on the 1929 discovery of Edwin Hubble that all galaxies are flying away from us. This Hubble's Law states that a galaxy at a distance 5 from us recedes with a velocity v = Hs. The proportionality constant H is called Hubble's constant. Its value, H = ho x 100 km/s per Mpc, is not very well measured, with ho known only within the range 0.4 < h 0 < 1. Nevertheless, for the sake of illustration, we shall set ho = 0.7 when we need to quote a number that depends on ho. The unit 'Mpc' stands for megaparsec; it is a distance unit which we will discuss below. Hubble's Law means that a galaxy 5 = 1 Mpc away recedes from us with a velocity v = 70 km/s, and a galaxy 5 = 2 Mpc away recedes from us with a vecolcity v = 140 km/s, etc. The more distant the galaxy, the faster it runs away. Since this is the most important discovery in modern astronomy, it is worthwhile to spend some time finding out how this law was arrived at. To establish the law, both the distance to a galaxy and its recession velocity have to be measured. We shall discuss separately how these are done. 1.1 Astronomical Distances Distances between cities are measured in kilometers (km), but this is too small a unit for astronomy.
eBook - PDFThe Cosmos
Astronomy in the New Millennium
- Jay M. Pasachoff, Alex Filippenko(Authors)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
(Interestingly, Humason had first come to Mt. Wilson as a mule-team driver, helping to bring telescope parts up the mountain. He worked his way up within the organization.) This behavior is similar to that produced by an explosion: bits of shrapnel are given a wide range of speeds, and those that are moving fastest travel the largest distance in a given amount of time. The implication of Hubble’s law is that the Universe is expanding! (Interestingly, Edwin Hubble himself resisted this idea and never quite signed on to the expanding Universe whose con- cept he had fostered.) As we shall see in Chapter 18, however, there is no unique center to the expansion, so in this way it is not like an explosion. Moreover, the expansion of the Universe marks the creation of space itself, unlike the explosion of a bomb in a preex- isting space. Library research in 2011 dealt with a historical matter long pon- dered: did the Belgian abbé Georges Lemaître deserve credit for what we call Hubble’s law? Indeed, he put together Slipher’s velocities and some of Hubble’s distances in 1927, two years before Hubble did, and published it in French in an obscure Belgian journal. After Hubble’s 1929 widely read paper, the editor of a major British jour- nal asked Lemaître to translate his paper. In the translation, key paragraphs about the velocity–distance relation disappeared. A few conspiracy-prone astronomers speculated that the journal editor left them out on purpose, or even that Hubble had exerted influ- ence to omit this discovery, which preceded his own. But the original ■ Figure 16–34 (a) The speed–distance relation, in Hubble’s original diagram from 1929. Note that the units of velocity (speed) on the vertical axis should be km/s, not km; Hubble, or the artist who labeled the graph, made a mistake in the units. One million parsecs equals 3.26 million light-years. Dots are individual galaxies; open circles represent groups of galaxies.
eBook - PDFPrecision Cosmology
The First Half Million Years
- Bernard J. T. Jones(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
So we would certainly be justified in calling the Hubble velocity–distance relationship the ‘Hubble–Lemaître–Robertson Law’. A few years after the publication of Hubble’s paper, Hubble collaborated with Richard Tolman on writing an important 35 page paper, Hubble and Tolman (1935). In that paper, they discussed the relationship between observations of galaxies and the issues in inter- preting the Hubble diagram in the light of relativistic cosmological models. The numerous issues involved in making quantitative photometric observations of galaxies that are limited by the wavelength sensitivity of the photographic emulsions are discussed at length, and all set within the framework provided by the metric of Friedmann, Lemaître and Robertson. 15 Arguably, the paper of Hubble and Tolman marked the start of observational relativistic cosmology. By 1956, Humason et al. (1956) were able to publish a catalogue of almost 1000 galaxy redshifts confirming not only the Hubble law, but allowing the first determination of the parameters of the cosmic expansion: the rate of expansion and the acceleration of the expansion. With that came the determination of the age of the Universe. This was not, however, without problems. Although the apparent brightness of galaxies was known from measurements, the intrinsic brightness was not known. Hence the distance to the galaxies could not be established, and the scale and age of the Universe were therefore uncertain. The uncertainty was considerable: it took many decades to sort this out. 16 1.3.2 The Physics of the Big Bang – George Gamow Not everyone, and notably Hubble himself, were happy with the expanding Universe inter- pretation of the redshift–distance relation and there were important alternative theories.
eBook - PDFThe Sciences
An Integrated Approach
- James Trefil, Robert M. Hazen(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
Comparing two galaxies—one twice as far away from Earth as the other—the farther galaxy moves away from us twice as fast. his statement, which has been amply con- irmed by measurements in the subsequent half-century, is now called Hubble’s law. Hubble’s law states: In words: he farther away a galaxy is, the faster it recedes. In equation form: galaxy’s velocity = (Hubble’s constant) × (galaxy’s distance) FIGURE 15-6 In the upper view, Earth and a distant galaxy are stationary with respect to each other; therefore, the characteristic lines in the spectrum from that galaxy are not shifted. In the middle example, the galaxy is moving away from us, so the characteristic spectral lines are shifted toward the red end of the spectrum. In the lower view, the galaxy is moving toward us, so we observe a blue shift of the spectral lines. Edwin Hubble discovered that virtually all galaxies have redshifts, and the farther away a galaxy is from us, the faster it is moving way. David Parker/Photo Researchers, Inc. 333 15.2 THE REDSHIFT AND HUBBLE’S LAW THE DISTANCE TO A RECEDING GALAXY Astronomers discover a new galaxy and determine from its redshift that it is moving away from us at approximately 100,000 kilometers per second (about one-third the speed of light). Approximately how far away is this galaxy? Reasoning: According to Hubble’s law, a galaxy’s distance equals its velocity divided by the Hubble constant. Solution: Distance (in Mpc) = velocity (in km/s) [Hubble’s constant (in km/s/Mpc)] = (100,000 km/s) (70 km/s/Mpc) = 100,000 70 Mpc = 1,429 Mpc Remember, a megaparsec equals about 3.3 million light-years, so this galaxy is almost 5 billion light-years away. he light that we observe from such a distant galaxy began its trip about the time that our solar system was born. EXAMPLE 15-1 FIGURE 15-7 Illustration of Hubble expansion. The more distant a galaxy is from Earth, the faster it moves away from us.
eBook - PDF- Matthew Malcolm Colless(Author)
- 2005(Publication Date)
- World Scientific(Publisher)
Finally, in 1929, Hubble presented data in support of an expanding universe, with a clear plot of galaxy distance versus r e d ~ h i f t ~ ~ . It is for this paper that Hubble is given credit for discovering the expanding universe. Within two years, Hubble and Humason had extended the Hubble law out to 20000 km/s using the brightest galaxies, and the field of measuring extragalactic distance, from a 21st century perspective, made little substantive progress for the next 30 and some might argue even 60 years. 2. The Cosmological Paradigm Astronomers use a standard model for understanding the Universe and its evolution. The assumptions of this standard model, that general relativity is correct, and the Universe is isotropic and homogenous on large scales, are not proven beyond a reasonable doubt - but they are well tested, and they do form the basis of our current understanding of the Universe. If these pillars of our standard model are wrong, then any inferences using this model about the Universe around us may be severely flawed, or irrelevant. The standard model for describing the global evolution of the Universe is based on two equations that make some simple, and hopefully valid, assumptions. If the universe is isotropic and homogenous on large scales, the Robertson-Walker metric, ds2 = dt2 - a(t) [g dr2 + r2d02] . gives the line element distance (s) between two objects with coordinates r,8 and time separation, t. The Universe is assumed to have a simple topology such that if it has negative, zero, or positive curvature, k takes the value -l , O , 1, respectively. These universes are said to be open, flat, or closed, respectively. The dynamic evolution of the Universe needs to be input into the Robertson-Walker metric by the specification of the scale factor a(t), which gives the radius of curvature of the Universe over time - or more simply, provides the relative size of a piece of space at any time.
eBook - PDF- Donald H. Perkins(Author)
- 2000(Publication Date)
- Cambridge University Press(Publisher)
10 Particle physics and cosmology In this chapter, we discuss the connection between particle physics and the physics of the cosmos. This is not a text on cosmology or astrophysics, and all that we shall do here is reproduce a few of the essential features of the ‘Standard Model’ of the early universe, insofar as they affect and are affected by particle physics. The presently accepted cosmological model rests on four main pieces of experi-mental evidence: (i) Hubble’s law; (ii) the cosmic microwave background radiation; (iii) the cosmic abundances of the light elements; (iv) anisotropies in the background radiation, of the right magnitude to seed the formation of large-scale structure (galaxies, clusters, superclusters etc.). 10.1 Hubble’s law and the expanding universe As described in Section 1.9, Hubble in 1929 observed that spectral lines from distant galaxies appeared to be redshifted and interpreted this as a result of the Doppler effect associated with their velocity of recession v = β c , according to the formula λ = λ ( 1 + β)/( 1 − β) = λ( 1 + z ) (10.1) where λ is the wavelength in the rest frame of the source, and z = λ/λ is the redshift parameter, which has currently been measured up to values of z 5. Hubble deduced that for a particular galaxy, the velocity v is proportional to the distance r from Earth, v = Hr (10.2) where H is the so-called Hubble constant. Figure 1.11 shows the evidence supporting Hubble’s law. Although, for z 1 (10.1) can indeed be interpreted as a 303 304 10 Particle physics and cosmology Doppler shift, the factor 1 + z more generally describes an overall homogeneous and isotropic expansion of the universe (analogous to the stretching of a rubber sheet in the two-dimensional case), which expands all lengths – be they wavelengths or distances between galaxies – by a time-dependent universal factor R ( t ) .
eBook - PDF- Keiji Kikkawa, H Kunitomo, Hisao Ohtsubo(Authors)
- 1997(Publication Date)
- World Scientific(Publisher)
The recession velocity is computed by where c is the velocity of light. In the nearby universe where z « 1, we have v ~ cz. (3) What Hubble found in 1929 is that the ressession velocity is proportional to the distance of galaxies (Hubble 1929; 1936). This is called the Hubble's Law. The standard model to describe the expanding Universe is the Friedmann models (Friedmann 1924). According to the Friedmann models, structure and V -(l+*)» ' (i + z y -i + 1' (2) 156 time evolution of the Universe are characterized by two parameters, the Hub-ble constant H 0 and the dimension-less density parameter f2 0 . The Hubble constant represents the present expansion rate of the Universe. The density parameter represents the present mean density of the Universe in units of the critical density fi 0 ,c = 3H$/8nG, which is the mean density of a universe where the expansion energy is equal to the gravitational potential energy. Figure 1 shows the behavior of the scale factor of Friedmann models as a function of time for different values of f2 0 . The scale factor a(t) is a convention to express the cosmological expansion. The coordinate of a point v(t) in the expanding Universe is written as r(t)=a(t) x £ using the time independent proper coordinate £. If 0 < fl 0 < 1, the Universe continues to expand forever. On the other hand, if fi„ > 1, the Universe will stop the expansion some time in the future and start contracting. The Hubble constant is the delivative of the lines in Fig. 1 at the present epoch, i.e., t = T 0 , and it determines the order of the age of the Universe. The actual age of the Universe is modulated Fig. 1 Behavior of the scale factor a(t) of Friedmann models with different values of fto- 157 by fi 0 as r 0 = fl 0 -1 /(o), (4) as shown in Fig. 2, where /(&o) = 1 for fi 0 = 0 and /(flo) = 2 / 3 for H 0 = 1. There could be another parameter, the cosmological constant A, in the Friedmann models.
eBook - PDF- Helen R. Quinn, Yossi Nir(Authors)
- 2010(Publication Date)
- Princeton University Press(Publisher)
How we know the distance to a given star or galaxy is another interesting and complex story, particularly for the most distant objects, but one that we will not discuss in detail here. The basic idea is this: The brightness you observe for a light of any standard type of source decreases as you increase the distance between yourself and it. Anyone who has driven a car at night knows this. So, if we can observe standard types of stars, that is, stars for which we know their characteristic intrinsic brightness, we can tell how far away they are by how bright they appear to be. It turns out that there are indeed certain types of stars that provide such standard brightness sources. This is sufficient to establish a rough law that red-shift grows more or less linearly with distance. The only reasonable source of such a law is an expanding Universe. Hubble’s first example of a standard star was a type of star called a Cepheid variable; more recent observations use a particular type of supernova, which, with modern methods, can be detected over much greater distances. The fact that the universe is expanding was first proposed by Hubble in 1928 based on his observations of red-shifts. Recent evidence from observations of distant supernovae dramatically confirms this basic picture, p h y s i c s i n a n e v o l v i n g u n i v e r s e 17 but extends it to tell us also that the rate of expansion is changing in a quite unexpected way. The picture of an expanding Universe predicts a number of other effects, as we will explain below. Its most important predictions have been confirmed in some detail by very precise measure- ments made in the past few years. The new discovery, on the way the rate is changing, opens new questions at a next level of detail, but does not change these overall features. Ideas about cosmology that originally seemed to be untestable specula- tions have recently been remarkably well tested.
eBook - PDFNew Trends In Mathematical Physics: In Honour Of The Salvatore Rionero 70th Birthday - Proceedings Of The International Meeting
In Honour of the Salvatore Rionero 70th Birthday
- Paolo Fergola, Florinda Capone, Maurizio Gentile(Authors)
- 2005(Publication Date)
- World Scientific(Publisher)
It is obvious that R(tJ = 1 . Introducing the Hubble parameter defined by6 . for all three cases from (4.1) Hubble’s law immediately follows: d ( t ) = h(t)d(t) . (4.3) At this point we can observe that: in case E ’, equations (4.1’) [and therefore (4.1)) and (4.3) remain unchanged both if we interpret the fluid Zt (i.e. the Universe) to be expanding in E ’, and i j in analogy to cases S ’ and PS ’, we consider E ’ to be expanding, with the particles of Zi? at rest in it and therefore dragged by E ’ in its expansion process. While the first interpretation does not place any limit on the velocity of the particles of Zt in E ’, the second leaves the particles of 2 at rest with respect to E ’ and transfers result (4.3) to the points of E ’. Therefore, in this second interpretation, result (4.3) must be regarded as the expression for the veloicity of recession of the points of E ’, in analogy with what happens with (4.3) for the points of S ’ and PS ’. More precisely, with reference to the Universe, both in case E ’ and in cases S ’ and PS ’ , it is clusters (or even clusters of clusters) of galaxies that are to be understood as being dragged in the expansion process. Due to their intense gravitational field, space is not expanding inside them. In this paper, in case E ’, we will always and only resort to the second of the interpretations we have just seen. In case E ’, even though R(r) is indeterminate, h(r) is determinate. And indeed in all three cases we can easily obtain: p(f)R ’(I) =cost., from which follows both for case E and for cases S and PS ’ 59 5 On the Metrics of Zt in Cases E 3, S and PS In case E ’, once we have introduced into the frame of reference ;Po and at the fixed instant ti a system of polar coordinates x, 19, p , with x the radial coordinate (previously introduced while writing (4.1’) in scalar form), from (4.1’) it follows that the metric for E in such coordinates is expressed by’ do2 = R2(t) ( d x 2 + X2(dtY2 + sin2tY dq2)).
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
