Hubble and Doppler Shift

30 01 2013

Edwin Hubble, after whom the Hubble Space Telescope is named, was an astronomer in the early twentieth century. At that time, modern cosmology was still in its infancy and there were many assumptions and false conclusions about the universe.

Probably the most noteworthy assumption of that time was the presence of “island universes.” For years, astronomers had observed strange, rounded clouds in the distant sky. They had assumed that these were other universes, isolated by nothingness. Today, we now know that these are galaxies, collections of billions or even trillions of individual stars, gravitationally bound to each other.

Another assumption was that the universe was static. This is called the “steady-state” model. In this model, all stars and other large objects were fixed in place and the energy and mass densities of the Universe could not change. In this case the energy density is the amount of energy contained within a certain amount of a space, a cubic meter, for example. The same goes for mass density. The Universe’s size was fixed and all matter and energy had to be conserved. Therefore, the density of the Universe remained constant.

Doppler shift

Another basic subject that should be covered here is that of Doppler shift. Doppler shift is a phenomenon that can be observed in every day life. A common example is that of an ambulance driving by with its siren on. As it approaches the listener, the siren’s pitch sounds slightly higher than normal. As it leaves the listener, the siren’s pitch sounds lower. This is because the sound waves are being accelerated by the motion of the ambulance. This causes the crests of the sound waves to become compressed as the approach the listener and expand as the wave source moves away.

In astronomy, the is typically known as “redshift” for receding wave sources and “blueshift” for approaching wave sources. This phenomenon became critical to Hubble’s research in 1929.

Discovery of galaxies

Hubble’s first discovery in 1919 radically altered our understanding of the universe. By identifying several characteristic of certain nebulae, including Andromeda (M31), he realized that these were not the island universes that everyone had assumed them to be. They were, in fact, other galaxies like our own and were much more distant than previously thought. Naturally, there were those in the scientific community who resisted the notion at first, but they were eventually compelled by the evidence.

Redshift of the galaxies

This discovery paved the way for another, equally important, realization that came ten years later. Hubble observed that nearly all the other galaxies were receding from our own. Working from the assumption that the galaxies most similar to ours should have similar types of stars in similar proportions, Hubble observed that most of these galaxies were redshifted, indicating that they were moving away from us with extreme velocity.

Expansion of the Universe

Furthermore, the farther the galaxies were, the greater the redshift. This means that the farther a galaxy is from us, the greater its speed away from us is. This can be represented by the following equation, called Hubble’s Law.

v = H0D

v is the speed with which a galaxy is moving away from us.
D is our distance from that galaxy.
H00 is the Hubble constant, which describes the relationship between the two variables.

The Hubble constant has been changed and updated as new cosmological observations and measurements have been made over the past 90 years. As of research performed with the Chandra X-Ray Observatory in 2006, one current estimate places the current Hubble constant at 77 kilometers per second per megaparsec (77 [km•s-1]•Mpsc-1). That is, that, in one dimension, 77 kilometers of space is being added to each linear megaparsec of space every second. This gives us a rate of expansion of the universe.

Space is expanding at every point in the universe but the expansion is only observable at distances where it can overcome the four basic forces, including gravity.

Hubble sphere

Since Hubble’s law states that recessional velocity will increase with relative distance, this would mean that, eventually, the recessional velocity would equal the speed of light. We could then rearrange the law to find what distance is required for this to happen.

If v = c = H0D,
then D = c/H0.

In this case D could be represented by RHS, the radius of the Hubble sphere, or Hubble volume. The Hubble sphere is a spherical region around an observer that defines the boundary of the observable universe. At this point, the light from distant galaxies becomes so redshifted that we can no longer observe it because they are receding at a rate of speed faster than the light they emit.

We have no way of observing anything beyond the Hubble sphere because the distances are so vast that light is not fast enough to overcome the expansion of the Universe to reach us. There is likely more universe beyond this sphere, but we simply cannot see it.

When we run the numbers, we find RHS to be approximately 13.9 billion lightyears. Since the universe is roughly 13.7 billion years old, any light we see at the edge of the Hubble sphere has been traveling toward us almost as long as the Universe has allowed light to travel.

The difference between the age of the Universe and the size of the Hubble radius can be explained by taking into account the acceleration of the Universe’s expansion. The Hubble constant is actually variable and is increasing slowly.


All of this forms the backbone of modern cosmology. Without Hubble or the work he and his collaborators did, it is likely that cosmology would not be where it is today.

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