قانون هبل

قانون هبل Hubble's law أو قانون لومتر Lemaître's law، هو اسم نظرية في علم الكون الفيزيائي (تم إثباتها بالرصد)، وتنص على أن السرعة التي تبتعد بها مجرة من المجرات عنا تتناسب تناسبا طرديا مع المسافة بينها وبين الأرض. وقد استنبط الفيزيائي والقسيس في نفس الوقت جورج لومتر هذا القانون عن طريق حله ل النظرية النسبية العامة لأينشتاين عام 1927. ثم تبعه إدوين هابل عام 1929 وصاغ مثيلا لهذا القانون عن طريق القياس العملي لسرعة المجرات وسمي القانون باسمه "قانون هابل" حيث أنه يستند إلى قياسات عملية. وذلك بعد عدة سنوات من الرصد وتسجيل القياسات، وقد استنتجت سرعة ابتعاد المجرات عنا عن طريق قياس مقدار الانزياح الأحمر الذي نجده عند قياس أطياف تلك المجرات. وهي تعتبر أول مشاهدة تعتمد على المشاهدة العملية عن طريق التلسكوبات والتي تبين أن الكون يتمدد وهي أحد الإثباتات المعترف بها في وقتنا الحاضر لحدوث الانفجار العظيم منذ نحو 13.7 مليار سنة ونشأة الكون.

تلسكوب مرصد مونت ويلسون الذي استخدمه إدوين هابل لرصد المجرات، وقاده لصياغة القانون المعروف باسمه.

تطور نشأة الكون حتى الآن (توضيح بمقياس رسم اختياري لتمدد الكون ، الثانية 0 إلى اليسار).

تطورت نظرية الانفجار العظيم من ملاحظات واعتبارات نظرية. الملاحظات الأولى كانت واضحة منذ زمن وهي أن السدم اللولبية تبتعد عن الأرض، لكن من سجل هذه الملاحظات لم يذهب بعيدا في تحليل هذه النتائج. في عام 1927 قام الكاهن البلجيكي جورج لومتر باشتقاق معادلات فريدمان-ليمايتري-روبرتسون-ووكر انطلاقا من النظرية النسبية العامة لأينشتاين واستنتج بناء على ظاهرة استمرار السدم الحلزونية في الابتهاد عن مجرتنا، مجرة درب التبانة أن الكون لابد وأن يكون قد بدأ من انفجار ذرة بدئية، وهذا ما دعي لاحقا في الأوساط العلمية ب الانفجار العظيم.

وفي عام 1929، أثبت إدوين هابل نظرية لومتر بإعطاء دليل رصدي للنظرية. اكتشف هابل أن المجرات تبتعد بعيدا من الأرض في جميع الاتجاهات وبسرعة تتناسب طرديا مع بعدها عن الأرض. هذا ما عـُرف لاحقا باسم قانون هابل. حسب المبدأ الكوني فإن الكون لا يملك إتجاها مفضلا ولا مكانا مفضلا لذلك كان استنتاج هابل أن الكون يتمدد بشكل معاكس تماما لتصور أينشتاين الذي كان يعتقد في كون ساكن.

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 الاكتشاف

Three steps to the Hubble constant

A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of an expanding universe by using Einstein's field equations of general relativity. Applying the most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then-prevalent notion of a static universe.

 الجمع بين الانيزاح الأحمر وقياسات المسافة

Fit of redshift velocities to Hubble's law; patterned after William C. Keel (2007). The Road to Galaxy Formation. Berlin: Springer published in association with Praxis Pub., Chichester, UK. ISBN 3-540-72534-2.Various estimates for the Hubble constant exist. The HST Key H₀ Group fitted type Ia supernovae for redshifts between 0.01 and 0.1 to find that H₀ = 71 ± 2(statistical) ± 6 (systematic) km s⁻¹Mpc⁻¹, while Sandage et al. find H₀ = 62.3 ± 1.3 (statistical) ± 5 (systematic) km s⁻¹Mpc⁻¹.

 التخلي عن الثابت الكوني

المقالة الرئيسية: الثابت الكوني

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of general relativity to allow them to produce a static solution, which he thought was the correct state of the universe. The Einstein equations in their simplest form model generally either an expanding or contracting universe, so Einstein's cosmological constant was artificially created to counter the expansion or contraction to get a perfect static and flat universe. After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "biggest mistake". On its own, general relativity could predict the expansion of the universe, which (through observations such as the bending of light by large masses, or the precession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

In 1931, Einstein made a trip to Mount Wilson Observatory to thank Hubble for providing the observational basis for modern cosmology.

The cosmological constant has regained attention in recent decades as a hypothesis for dark energy.

 التفسير

A variety of possible recessional velocity vs. redshift functions including the simple linear relation v = cz; a variety of possible shapes from theories related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts. See Davis and Lineweaver.

The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows:

$v=H_{0}\,D$

where

• $v$ is the recessional velocity, typically expressed in km/s.
• H₀ is Hubble's constant and corresponds to the value of $H$ (often termed the Hubble parameter which is a value that is time dependent and which can be expressed in terms of the scale factor) in the Friedmann equations taken at the time of observation denoted by the subscript 0. This value is the same throughout the universe for a given comoving time.
• $D$ is the proper distance (which can change over time, unlike the comoving distance, which is constant) from the galaxy to the observer, measured in mega parsecs (Mpc), in the 3-space defined by given cosmological time. (Recession velocity is just v = dD/dt).

Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts.

For distances D larger than the radius of the Hubble sphere r_HS , objects recede at a rate faster than the speed of light (See Uses of the proper distance for a discussion of the significance of this):

$r_{HS}={\frac {c}{H_{0}}}\ .$

Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today. Current evidence suggests that the expansion of the universe is accelerating (see Accelerating universe), meaning that for any given galaxy, the recession velocity dD/dt is increasing over time as the galaxy moves to greater and greater distances; however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at some fixed distance D and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones.

 سرعة الانزياح الأحمر والسرعة المتراجعة

 سرعة الانزياح الأحمر

$v_{rs}\equiv cz\ ,$

$z={\frac {\lambda _{o}}{\lambda _{e}}}-1={\sqrt {\frac {1+v/c}{1-v/c}}}-1\approx {\frac {v}{c}}\ .$

 السرعة المتراجعة

${\frac {D(t)}{D(t_{0})}}={\frac {R(t)}{R(t_{0})}}\ ,$

$z={\frac {R(t_{0})}{R(t_{e})}}-1\ .$

$v_{r}=d_{t}D={\frac {d_{t}R}{R}}D\ .$

We now define the Hubble constant as

$H\equiv {\frac {d_{t}R}{R}}\ ,$

واكتشاف قانون هبل:

$v_{r}=HD\ .$

$z={\frac {R(t_{0})}{R(t_{e})}}-1\approx {\frac {R(t_{0})}{R(t_{0})\left(1+(t_{e}-t_{0})H(t_{0})\right)}}-1\approx (t_{0}-t_{e})H(t_{0})\ ,$

$z\approx (t_{0}-t_{e})H(t_{0})\approx {\frac {D}{c}}H(t_{0})\ ,$ or $cz\approx DH(t_{0})=v_{r}\ .$

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 المصير النهائي وعمر الكون

The age and ultimate fate of the universe can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterized by values of density parameters (Ω_M for matter and Ω_Λ for dark energy). A "closed universe" with Ω_M > 1 and Ω_Λ = 0 comes to an end in a Big Crunch and is considerably younger than its Hubble age. An "open universe" with Ω_M ≤ 1 and Ω_Λ = 0 expands forever and has an age that is closer to its Hubble age. For the accelerating universe with nonzero Ω_Λ that we inhabit, the age of the universe is coincidentally very close to the Hubble age.

The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-called deceleration parameter $q$, which is defined by

$q=-\left(1+{\frac {\dot {H}}{H^{2}}}\right).$

In a universe with a deceleration parameter equal to zero, it follows that H = 1/t, where t is the time since the Big Bang. A non-zero, time-dependent value of $q$ simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.

It was long thought that q was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than 1/H (which is about 14 billion years). For instance, a value for q of 1/2 (once favoured by most theorists) would give the age of the universe as 2/(3H). The discovery in 1998 that q is apparently negative means that the universe could actually be older than 1/H. However, estimates of the age of the universe are very close to 1/H.

 مفارقة أولبرز

المقالة الرئيسية: مفارقة أولبرز

The expansion of space summarized by the Big Bang interpretation of Hubble's law is relevant to the old conundrum known as Olbers' paradox: If the universe were infinite in size, static, and filled with a uniform distribution of stars, then every line of sight in the sky would end on a star, and the sky would be as bright as the surface of a star. However, the night sky is largely dark.

Since the 17th century, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part on the Big Bang theory, and in part on the Hubble expansion: In a universe that exists for a finite amount of time, only the light of a finite number of stars has had enough time to reach us, and the paradox is resolved. Additionally, in an expanding universe, distant objects recede from us, which causes the light emanated from them to be redshifted and diminished in brightness by the time we see it.

 ثابت هبل عديم الأبعاد

Instead of working with Hubble's constant, a common practice is to introduce the dimensionless Hubble constant, usually denoted by h, and to write Hubble's constant H₀ as h × 100 km s⁻¹ Mpc⁻¹, all the relative uncertainty of the true value of H₀ being then relegated to h. The dimensionless Hubble constant is often used when giving distances that are calculated from redshift z using the formula d ≈ c/H₀ × z. Since H₀ is not precisely known, the distance is expressed as:

$cz/H_{0}\approx (2998\times z){\text{ Mpc }}h^{-1}$

In other words, one calculates 2998×z and one gives the units as ${\text{Mpc }}h^{-1}$ or $h^{-1}{\text{ Mpc}}.$

Occasionally a reference value other than 100 may be chosen, in which case a subscript is presented after h to avoid confusion; e.g. h₇₀ denotes $H_{0}=70\,h_{70}$ km s⁻¹ Mpc⁻¹, which implies $h_{70}=h/0.7$.

This should not be confused with the dimensionless value of Hubble's constant, usually expressed in terms of Planck units, obtained by multiplying H₀ by 1.75 × 10⁻⁶³ (from definitions of parsec and t_P), for example for H₀=70, a Planck unit version of 1.2 × 10⁻⁶¹ is obtained.

 تحديد ثابت هبل

Value of the Hubble Constant including measurement uncertainty above measurement method

تقدر أحدث القياسات (مارس 2010) ثابت هابل التي حصل عليها تلسكوب هابل الفضائي بواسطة مسبار ويلكينسون لقياس اختلاف الموجات الراديوية (تقدير ديسمبر 2012 (http://arxiv.org/pdf/1212.5225.pdf) ) بـ 3و69 (km/s)/(Mpc ), أي نحو 3و69 كيلومتر في الثانية لكل مليون فرسخ فلكي. (الفرسخ الفلكي = 3,26 سنة ضوئية).

• أي أنه إذا كانت مجرة تبعد عن مجرتنا 3و3 مليون سنة ضوئية مثلا فتكون المجرة تبتعد عنا بسرعة 3و69 كيلومتر/ثانية ، أو
• لو كانت المجرة تبعد عنا 33 مليون سنة ضوئية فهي تبتعد عنا بسرعة 693 كيلومتر في الثانية.

إلا أنه توجد أيضا بعض القياسات الأخرى:

يهتم العلماء منذ سنين طويلة بالحصول على ثابت هابل بدقة. وهم لذلك يستخدمون أجهزة مختلفة لقياسه، منها تلسكوب هابل الفضائي، ومسبار ويلكينسون لقياس اختلاف الموجات الراديوية WMAP وأيضا قياسات تلسكوب شاندرا الفضائي للأشعة السينية.

يستغل تلسكوب هابل قياس ضوء المتغيرات القيفاوية (هي نجوم نباضة وتتميز بتناسب بين دورة ضوئها (الدورية) وقدر سطوعها)، كما تستغل المستعرات العظمى من نوع a1 كي تشكل "شمعات عيارية".

كما توجد طريقة جديدة لرصد المجرات وهي ظاهرة عدسة الجاذبية، وهي طريقة تمكن من قياس تغيرات سطوع المجرات عند عبرور ضوئها أحد عدسات الجاذبية. فعند عبور ضوء مجرة تقع خلف مجرة بالنسبة للمشاهد فإن مسارات ضوء المجرة الخلفية تتأثر بمجال الجاذبية للمجرة الوسطية بحيث تظهر للمشاهد كما لو كانت عدة مجرات وليست مجرة واحدة. فعند تغير سطوع المجرة المصدرة للضوء فإن هذا يغير أيضا من الصور التي يحصل عليها المشاهد. ومن معرفة هذا التغير في درجة السطوع يمكن حساب المافة بيننا وبين المجرة المصدرة للضوء. وبمعرفة بعدها وكذلك مقدار الانزياح الأحمر والذي يعطي سرعة اتعاد المجرة عنا يمكن تعيين معدل تمدد الكون.

أما الطريقة الثالثة وهي قياسات مسبار ويلكينسون لقياس اختلاف الموجات الراديوية فهي تختص بقياس توزيع الحرارة للموجات الكهرومغناطيسية في نطاق الميكروويف. ويمثل إشعاع الخلفية الميكروني الكوني جزءا تلك الأشعة الكهرومغناطيسية، وما إشعاع الخلفية هذا إلا بواقي التوزيع الحراري بعد الانفجار العظيم مباشرة. فمسبار ويلكينسون يقيس ذلك الاختلاف الضعيف في درجة الحرارة في صفحة السماء، وهي تمثل تشتت الإشعاع الأولي بوساطة المجرات وقت نشأتها وعطينا في وقتنا الحالي صورة لما كان في الماضي.

• وتعطي نتائج تلسكوب هابل الفضائي حاليا أدق قيمة لثابت هابل $H_{0}$ المقدار:

$H_{0}\approx (74,2\pm 3,6)\ {\frac {\rm {km}}{\rm {s\cdot Mpc}}}$

• ومن نتائج قياسات أجراها مسبار ويلكينسون لمدة 5 سنوات نصل إلى القيمة::

$H_{0}\approx (70,5\pm 1,3)\ {\frac {\rm {km}}{\rm {s\cdot Mpc}}}$

• ومن تحليل صور تلسكوب هابل التي أجراها باستخدام طريقة عدسات الجاذبية فهي تعطي قيمة لثابت هابل $H_{0}$ تبلغ:

:

$H_{0}\approx (69,7\pm 4,9)\ {\frac {\rm {km}}{\rm {s\cdot Mpc}}}$

حيث : Mpc تساوي مليون parsec أي لكل مليون فرسخ فلكي. (مع العلم بأن الفرسخ الفلكي يعادل مسافة 3.3 سنة ضوئية)

 تسارع الاتساع

المقالة الرئيسية: الكون المتسارع

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 اشتقاقات من متغير هبل

$H^{2}\equiv \left({\frac {\dot {a}}{a}}\right)^{2}={\frac {8\pi G}{3}}\rho -{\frac {kc^{2}}{a^{2}}}+{\frac {\Lambda c^{2}}{3}},$

 الكون المهمين عليه المادة (والثابت الكوني)

$\rho =\rho _{m}(a)={\frac {\rho _{m_{0}}}{a^{3}}},$

$\rho _{c}={\frac {3H^{2}}{8\pi G}};$

$\Omega _{m}\equiv {\frac {\rho _{m_{0}}}{\rho _{c}}}={\frac {8\pi G}{3H_{0}^{2}}}\rho _{m_{0}};$

so $\rho =\rho _{c}\Omega _{m}/a^{3}.$ Also, by definition,

$\Omega _{k}\equiv {\frac {-kc^{2}}{(a_{0}H_{0})^{2}}}$

and

$\Omega _{\Lambda }\equiv {\frac {\Lambda c^{2}}{3H_{0}^{2}}},$

$H^{2}(z)=H_{0}^{2}\left(\Omega _{M}(1+z)^{3}+\Omega _{k}(1+z)^{2}+\Omega _{\Lambda }\right).$

 الكون المهمين عليه المادة والطاقة المظلمة

$\rho =\rho _{m}(a)+\rho _{de}(a),$

${\dot {\rho }}+3{\frac {\dot {a}}{a}}\left(\rho +{\frac {P}{c^{2}}}\right)=0;$

${\frac {d\rho }{\rho }}=-3{\frac {da}{a}}\left(1+w\right).$

لوكان كان الثابت w،

$\ln {\rho }=-3\left(1+w\right)\ln {a};$

$\rho =a^{-3\left(1+w\right)}.$

$H^{2}(z)=H_{0}^{2}\left(\Omega _{M}(1+z)^{3}+\Omega _{de}(1+z)^{3\left(1+w\right)}\right).$

If dark energy does not have a constant equation-of-state w, then

$\rho _{de}(a)=\rho _{de0}e^{-3\int {\frac {da}{a}}\left(1+w(a)\right)},$

and to solve this we must parametrize $w(a)$, for example if $w(a)=w_{0}+w_{a}(1-a)$, giving

$H^{2}(z)=H_{0}^{2}\left(\Omega _{M}a^{-3}+\Omega _{de}a^{-3\left(1+w_{0}+w_{a}\right)}e^{-3w_{a}(1-a)}\right).$

 وحدات مشتقة من ثابت هبل

 حجم هبل

المقالة الرئيسية: حجم هبل

 قيم مرصودة لثابت هبل

Multiple methods have been used to determine the Hubble constant. "Late universe" measurements using calibrated distance ladder techniques have converged on a value of approximately 73 km/s/Mpc. Since 2000, "early universe" techniques based on measurements of the cosmic microwave background have become available, and these agree on a value near 67.7 km/s/Mpc. (This is accounting for the change in the expansion rate since the early universe, so is comparable to the first number.) As techniques have improved, the estimated measurement uncertainties have shrunk, but the range of measured values has not, to the point that the disagreement is now statistically significant. This discrepancy is called the Hubble tension.

اعتبارا من 2020, the cause of the discrepancy is not understood. In April 2019, astronomers reported further substantial discrepancies across different measurement methods in Hubble constant values, possibly suggesting the existence of a new realm of physics not currently well understood. By November 2019, this tension had grown so far that some physicists like Joseph Silk had come to refer to it as a "possible crisis for cosmology", as the observed properties of the universe appear to be mutually inconsistent. In February 2020, the Megamaser Cosmology Project published independent results that confirmed the distance ladder results and differed from the early-universe results at a statistical significance level of 95%. In July 2020, measurements of the cosmic background radiation by the Atacama Cosmology Telescope predict that the Universe should be expanding more slowly than is currently observed.

Estimated values of the Hubble constant, 2001–2020. Estimates in black represent calibrated distance ladder measurements which tend to cluster around 73 km/s/Mpc; red represents early universe CMB/BAO measurements with ΛCDM parameters which show good agreement on a figure near 67 km/s/Mpc, while blue are other techniques, whose uncertainties are not yet small enough to decide between the two.

تاريخ النشر	ثابت هبل (كم/ث)/Mpc	الراصد	المصدر	تعليقات / منهاج
2020-12-16	72.1±2.0	Hubble Space Telescope and Gaia EDR3		Combining earlier work on red giant stars, using the tip of the red-giant branch (TRGB) distance indicator, with parallax measurements of Omega Centauri from Gaia EDR3.
2020-12-15	73.2±1.3	Hubble Space Telescope and Gaia EDR3		Combination of HST photometry and Gaia EDR3 parallaxes for Milky Way Cepheids, reducing the uncertainty in calibration of Cepheid luminosities to 1.0%. Overall uncertainty in the value for $H_{0}$ is 1.8%, which is expected to be reduced to 1.3% with a larger sample of type Ia supernovae in galaxies that are known Cepheid hosts. Continuation of a collaboration known as Supernovae, $H_{0}$, for the Equation of State of Dark Energy (SHoES).
2020-12-04	73.5±5.3	E. J. Baxter, B. D. Sherwin		Gravitational lensing in the CMB is used to estimate $H_{0}$ without referring to the sound horizon scale, providing an alternative method to analyze the Planck data.
2020-11-25	71.8+3.9 −3.3	P. Denzel et al.		Eight quadruply lensed galaxy systems are used to determine $H_{0}$ to a precision of 5%, in agreement with both "early" and "late" universe estimates. Independent of distance ladders and the cosmic microwave background.
2020-09-29	67.6+4.3 −4.2	S. Mukherjee et al.		Gravitational waves, assuming that the transient ZTF19abanrh found by the Zwicky Transient Facility is the optical counterpart to GW190521. Independent of distance ladders and the cosmic microwave background.
2020-02-26	73.9±3.0	Megamaser Cosmology Project		Geometric distance measurements to megamaser-hosting galaxies. Independent of distance ladders and the cosmic microwave background.
2019-10-14	74.2+2.7 −3.0	STRIDES		Modelling the mass distribution & time delay of the lensed quasar DES J0408-5354.
2019-09-12	76.8±2.6	SHARP/H0LiCOW		Modelling three galactically lensed objects and their lenses using ground-based adaptive optics and the Hubble Space Telescope.
2019-08-20	70.3+1.36 −1.35	K. Dutta et al.		This $H_{0}$ is obtained analysing low-redshift cosmological data within ΛCDM model. The datasets used are type-Ia supernovae, baryon acoustic oscillations, time-delay measurements using strong-lensing, $H(z)$ measurements using cosmic chronometers and growth measurements from large scale structure observations.
2019-08-15	73.5±1.4	M. J. Reid, D. W. Pesce, A. G. Riess		Measuring the distance to Messier 106 using its supermassive black hole, combined with measurements of eclipsing binaries in the Large Magellanic Cloud.
2019-07-16	69.8±1.9	Hubble Space Telescope		Distances to red giant stars are calculated using the tip of the red-giant branch (TRGB) distance indicator.
2019-07-10	73.3+1.7 −1.8	H0LiCOW collaboration		Updated observations of multiply imaged quasars, now using six quasars, independent of the cosmic distance ladder and independent of the cosmic microwave background measurements.
2019-07-08	70.3+5.3 −5.0	LIGO and Virgo detectors		Uses radio counterpart of GW170817, combined with earlier gravitational wave (GW) and electromagnetic (EM) data.
2019-03-28	68.0+4.2 −4.1	Fermi-LAT		Gamma ray attenuation due to extragalactic light. Independent of the cosmic distance ladder and the cosmic microwave background.
2019-03-18	74.03±1.42	Hubble Space Telescope		Precision HST photometry of Cepheids in the Large Magellanic Cloud (LMC) reduce the uncertainty in the distance to the LMC from 2.5% to 1.3%. The revision increases the tension with CMB measurements to the 4.4σ level (P=99.999% for Gaussian errors), raising the discrepancy beyond a plausible level of chance. Continuation of a collaboration known as Supernovae, $H_{0}$, for the Equation of State of Dark Energy (SHoES).
2019-02-08	67.78+0.91 −0.87	Joseph Ryan et al.		Quasar angular size and baryon acoustic oscillations, assuming a flat LambdaCDM model. Alternative models result in different (generally lower) values for the Hubble constant.
2018-11-06	67.77±1.30	Dark Energy Survey		Supernova measurements using the inverse distance ladder method based on baryon acoustic oscillations.
2018-09-05	72.5+2.1 −2.3	H0LiCOW collaboration		Observations of multiply imaged quasars, independent of the cosmic distance ladder and independent of the cosmic microwave background measurements.
2018-07-18	67.66±0.42	Planck Mission		Final Planck 2018 results.
2018-04-27	73.52±1.62	Hubble Space Telescope and Gaia		Additional HST photometry of galactic Cepheids with early Gaia parallax measurements. The revised value increases tension with CMB measurements at the 3.8σ level. Continuation of the SHoES collaboration.
2018-02-22	73.45±1.66	Hubble Space Telescope		Parallax measurements of galactic Cepheids for enhanced calibration of the distance ladder; the value suggests a discrepancy with CMB measurements at the 3.7σ level. The uncertainty is expected to be reduced to below 1% with the final release of the Gaia catalog. SHoES collaboration.
2017-10-16	70.0+12.0 −8.0	The LIGO Scientific Collaboration and The Virgo Collaboration		Standard siren measurement independent of normal "standard candle" techniques; the gravitational wave analysis of a binary neutron star (BNS) merger GW170817 directly estimated the luminosity distance out to cosmological scales. An estimate of fifty similar detections in the next decade may arbitrate tension of other methodologies. Detection and analysis of a neutron star-black hole merger (NSBH) may provide greater precision than BNS could allow.
2016-11-22	71.9+2.4 −3.0	Hubble Space Telescope		Uses time delays between multiple images of distant variable sources produced by strong gravitational lensing. Collaboration known as $H_{0}$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW).
2016-08-04	76.2+3.4 −2.7	Cosmicflows-3		Comparing redshift to other distance methods, including Tully–Fisher, Cepheid variable, and Type Ia supernovae. A restrictive estimate from the data implies a more precise value of 75±2.
2016-07-13	67.6+0.7 −0.6	SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS)		Baryon acoustic oscillations. An extended survey (eBOSS) began in 2014 and is expected to run through 2020. The extended survey is designed to explore the time when the universe was transitioning away from the deceleration effects of gravity from 3 to 8 billion years after the Big Bang.
2016-05-17	73.24±1.74	Hubble Space Telescope		Type Ia supernova, the uncertainty is expected to go down by a factor of more than two with upcoming Gaia measurements and other improvements. SHoES collaboration.
2015-02	67.74±0.46	Planck Mission		Results from an analysis of Planck's full mission were made public on 1 December 2014 at a conference in Ferrara, Italy. A full set of papers detailing the mission results were released in February 2015.
2013-10-01	74.4±3.0	Cosmicflows-2		Comparing redshift to other distance methods, including Tully–Fisher, Cepheid variable, and Type Ia supernovae.
2013-03-21	67.80±0.77	Planck Mission		The ESA Planck Surveyor was launched in May 2009. Over a four-year period, it performed a significantly more detailed investigation of cosmic microwave radiation than earlier investigations using HEMT radiometers and bolometer technology to measure the CMB at a smaller scale than WMAP. On 21 March 2013, the European-led research team behind the Planck cosmology probe released the mission's data including a new CMB all-sky map and their determination of the Hubble constant.
2012-12-20	69.32±0.80	WMAP (9 years), combined with other measurements.
2010	70.4+1.3 −1.4	WMAP (7 years), combined with other measurements.		These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the ΛCDM model. If the data are fit with more general versions, H0 tends to be smaller and more uncertain: typically around 67±4 (km/s)/Mpc although some models allow values near 63 (km/s)/Mpc.
2010	71.0±2.5	WMAP only (7 years).
2009-02	70.5±1.3	WMAP (5 years), combined with other measurements.
2009-02	71.9+2.6 −2.7	WMAP only (5 years)
2007	70.4+1.5 −1.6	WMAP (3 years), combined with other measurements.
2006-08	76.9+10.7 −8.7	Chandra X-ray Observatory		Combined Sunyaev–Zel'dovich effect and Chandra X-ray observations of galaxy clusters. Adjusted uncertainty in table from Planck Collaboration 2013.
2001-05	72±8	Hubble Space Telescope Key Project		This project established the most precise optical determination, consistent with a measurement of H0 based upon Sunyaev–Zel'dovich effect observations of many galaxy clusters having a similar accuracy.
before 1996	50–90 (est.)
early 1970s	≈ 55 (est.)	Allan Sandage and Gustav Tammann
1958	75 (est.)	Allan Sandage		This was the first good estimate of H0, but it would be decades before a consensus was achieved.
1956	180	Humason, Mayall and Sandage
1929	500	Edwin Hubble, Hooker telescope
1927	625	Georges Lemaître		First measurement and interpretation as a sign of the expansion of the universe

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 المصادر

• Eng, A. E. (1985). "A New Approach to Starlight Runs". Oswego. {{cite journal}}: Cite journal requires |journal= (help); Invalid |ref=harv (help)
• Hubble, E. P. (1937). The Observational Approach to Cosmology. Oxford: Clarendon Press 
• Kutner, Marc (2003). Astronomy: A Physical Perspective. New York: Cambridge University Press. ISBN 0-521-52927-1. {{cite book}}: Invalid |ref=harv (help)
• Liddle, Andrew R. (2003). An Introduction to Modern Cosmology (2nd ed.). Chichester: Wiley. ISBN 0-470-84835-9. {{cite book}}: Invalid |ref=harv (help)

 قراءات إضافية

• DOI:10.1146/annurev-astro-082708-101829
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 وصلات خارجية

• The Hubble Key Project
• The Hubble Diagram Project
• Merrifield, Michael (2009). "Hubble Constant". Sixty Symbols. Brady Haran for the University of Nottingham.
• Hubble's quantum law.