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# Hubble’s Law Definition, Formula, Example, Redshift

Sep 5, 2022

Edwin Hubble’s 1929 PNAS article, one of the most well-known iconic papers in the history of science, observed the relationship between the distance and speed (velocity) of galaxies. Hubble’s Law revealed the concept of a never-ending universe and fundamentally altered our concepts of the cosmos. It initiated the study of observational cosmology, which has shown an astonishingly large universe that has been growing and changing for 14 billion years and is made up of many galaxies, dark matter, and cosmic waves.

## Hubble Law and the Expanding Universe

It is impossible to comprehend that we were clueless about the existence of the majority of the world around us just 90 years ago. From our current point of view, the existence of an immense expanding universe, made up of billions of galaxies that are moving away from one another as cosmic space expands from an initial “Big Bang” several billion years ago, seems so evident that we assume it must have been known for ages. Not so. Our knowledge of the universe witnessed a massive change due to Edwin Hubble’s ground-breaking 1929 PNAS paper, “A correlation between distance and angular velocity among extra-galactic nebulae.”

Hubble’s law and the expanding universe were one of science’s greatest discoveries, and Hubble provided observational proof. As demonstrated by Hubble, galaxies are drifting away from us with a speed (velocity) that is directly related to their distance from us. Thus, more distant galaxies are moving further away from Earth at a faster rate than nearby galaxies.

Hubble’s iconic graph of the estimated velocity vs distance for neighboring galaxies has become a scientific benchmark in astronomy textbooks. A linear relationship between galactic velocity (v) and distance (d) is shown in the graph below.

## Hubble’s Law Formula

#### The Hubble’s Law Formula of cosmic expansion can be stated as follows:

v = Ho × d

Where,

Ho = Hubble constant (calculated in km/s/Mpc)

v = galaxy’s velocity (calculated in km/s)

d = galaxy’s distance (calculated in Mpc)

## Hubble’s Law Formula examples

Example: Determine the velocity of the NGC 55 galaxy if it is two megaparsecs away from Earth.

First, we must calculate the distance, which requires converting from parsecs to kilometers. A parsec is a distance traveled by light in 3.26 light years. If the distance traveled by light in a vacuum in one second is 300,000,000m, we must multiply the distance by the number of seconds in a year, which is 31,556,926 seconds, and then multiply by 3.26.

light’s annual distance traveled = 31,556,926 (3 x 108) = 9.4671 x 1015m

Parsec distance = 3.086 x 1016m

Because the NGC 55 galaxy is two megaparsecs away, we must multiply the parsec distance per parsec to NGC 55.

NGC 55 (distance) = 2 x 106(3.086 x 1016) = 6.17 x 1022m

We can now plug this data into Hubble’s law equation to calculate the galaxy’s velocity. However, the Hubble constant must first be converted to meters per second per meter.

And now we apply Hubble’s law:

V = 1.476 x 1011 m/s

Example: The velocity of some clusters is measured as v = 103 km/s. How far is the distance?   Assume Ho = 60km/s/Mpc.

Solution:

We know that v = 103 km/s.

60 km/s/Mpc = Ho

The formula is as follows:

d = v/Ho

= (103 km/s/60 km/s/Mpc)

= 16.7 Mpc

### Outline of the Hubble Constant

The Hubble constant is the measurement unit that describes how fast the cosmos is expanding. 160 km/s is the Hubble constant H for a million light-years.

The above formula best explains the concept of Hubble’s law. It suggests that the universe is always expanding and that galaxies move away from one another at a consistent speed per unit distance, like the dates in an expanding date cake that inflate in size. As a result, distant objects move more quickly than close ones.

 Hubble’s law observation can be expressed as follows: Hubble law simplified: The galaxy’s velocity, commonly referred to as the redshift, is directly related to its distance. Physical cosmology studies Hubble’s law is sometimes referred to as Hubble-Lemaitre law. Hubble’s law is the only mechanism that enables the cosmos to grow and realize the cosmological principle.

### Origin of Hubble’s Law Theory

Hubble’s exceptional observational relation was discovered using 24 neighboring galaxies for which both the measured velocities and distances were accessible. Most of the velocities came from ground-breaking spectroscopic Doppler-shift studies by the renowned astronomer Vesto Melvin Slipher.

Hubble determined the distances to these galaxies with much greater accuracy than previously possible, which had previously only been estimated inaccurately, based on the visible brightness of their stars and, for the four most distant galaxies in the survey, which are all located in the Virgo cluster and have recession velocities of about 1,000 km/s each, based on their celestial brightness.

This technique compares the known intrinsic luminosity of the stars (or galaxies)—known from comparable, well-calibrated surrounding objects with the observed visible brightness to determine the distance to each entity. The thing appears dimmer when positioned at a distance. Hubble distance estimates were accurate enough to distinguish between close and far away galaxies, allowing researchers to find this startling linear relationship.

In addition to showing each of the 24 galaxies individually in the chart, Hubble also divided them into nine groups depending on how close they were to one another in distance and direction. It was an effective technique to reduce the significant scatter.

Hubble also used 22 more galaxies with known velocities (from Slipher measurements) but no individually determined distances. Hubble used the velocities of the 22 galaxies to calculate their average distance from their average observed brightness. This average number is well comparable to the rest of the information.

 Interesting Facts: Before Hubble’s discoveries, many scientists and mathematicians had developed a consistent explanation of the link between space and time by applying Einstein’s field equation of relativity theory. When Hubble’s discoveries were made public, Albert Einstein gave up on the cosmological constant he had developed to enable a static solution to his computations. Because his belief in a static cosmos prevented him from foreseeing the expanding world, he later referred to his work as the “biggest mistake.” In 1931, Einstein made a well-known pilgrimage to Mount Wilson to express his gratitude to Hubble for laying the empirical foundation for contemporary cosmology.

### What is Hubble’s Law Redshift?

Redshift and Hubble’s law are important topics for astronomers. The phrase means that; when the light’s wavelength is extended, the light is perceived as having “shifted” toward the red portion of the spectrum.

Since light has wave-like properties, it will shift comparable to Doppler if the source moves concerning us. We have known that most other galaxies are revolving away from us since 1929 when Edwin Hubble observed that the universe was expanding. The light from all these galaxies is “red-shifted,” or shifted to extended (and thus redder) wavelengths.

We don’t see this redshift in our everyday life since light moves quickly compared to other things (a million times faster than sound).

The Hubble’s law redshift of the object can be quickly determined by contrasting the spectra of distant galaxies or celestial objects with a standard laboratory spectrum. Atomic discharge and absorption lines can be observed at well-known wavelengths. Astronomers can calculate the redshift of receding sources by monitoring the positions of these lines in astronomical spectra.

The redshifts seen in far-off objects are caused less by the Doppler effect and more by the universe’s expansion.

### Importance of Hubble’s Law

Here are some quick introductions to the wide-ranging uses of Hubble’s discovery.

The importance of Hubble’s law lies in the fact that it has enabled ground-breaking investigation into several topics, including the evolution and characteristics of galaxies and celestial objects, the expansion of the universe as a whole, and the nature of the universe. Additionally, scientists can use Hubble’s Law to carry out the essential task of determining Hubble distances to galaxies and celestial objects.

Hubble distances can be derived from Hubble’s law by utilizing the estimated velocity of the object or galaxy. These distances also include a modest special motion component and are typical of the actual cosmic distance. These distances, therefore, make it possible to use the observed redshift velocities of many celestial objects and galaxies obtained from extensive redshift surveys of galaxies to determine the 3D location and distribution of those objects.

These studies discovered striking connectivity between the vast network of galaxies, voids, and filaments. Additionally, astronomers regularly employ Hubble distances to calculate galaxies’ distances from their (relatively) simple spectroscopic redshift measurements.

The determination of these distances is responsible for tracing the expansion of galaxies and celestial objects from the early universe. The precise measurement of the Hubble constant also makes it possible to calculate the universe’s age accurately. This age corresponds well to the oldest stars (celestial objects).

### Limitations of Hubble’s Law

After measuring the recession velocity, specialists can use Hubble’s equation to calculate the distance of the galaxies from Earth when the detected light shifts into the redshift region of the spectrum. The following are some of Hubble’s law restrictions that create a range of problems:

• The observed velocity is affected because of the galaxies’ inherent motion.
• Due to gravitational movements, the galaxy is in orbit.

### Conclusion

Hubble law is the exploration in big bang cosmology that the speed at which galaxies travel away from the Earth is directly related to their distance. Thus, if a galaxy is at a distance from Earth, it would travel at a faster speed away from us. Additionally, the redshift of the galaxies—a shift of the light reflected toward the red end of the spectrum—is used to calculate their velocities.

### 1. What does the Hubble constant mean?

Ans. According to experts, the Hubble constant is the measuring unit used to describe the expansion of the cosmos. Additionally, the Hubble constant H is 160 km/s per million light-years.

### 2. Describe the principle of Hubble law redshift.

Ans. Hubble law redshift is a phrase used to describe the phenomenon whereby electromagnetic radiation causes the wavelength of an object to increase. Blueshift is also the opposite of redshift when energy levels rise due to shorter wavelengths and is referred to as negative redshift. The following are the primary causes of Hubble’s law redshift:

• The Doppler effect is the motion of objects in space, either towards or apart from one another.
• The powerful gravitational field present in the universe is responsible for gravitational redshift.
• Cosmological redshift is an increase in space that causes objects to separate from one another without changing their positions.

### 3. Describe Hubble law.

Ans. A cosmological principle says the speed at which celestial objects travel apart in the universe is proportional to their distance from one another.

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