### October 28: Hubble’s Law

Meaning of Equation

Farther a galaxy from us in deep space, faster it is moving away from us.

As the ‘*Month of Equations*‘ series is coming to an end, I thought of including an equation of cosmology in this series. Before I begin with today’s equation, I want to tell you something very interesting. Astronomy is a subject that mankind has studied for more than 2000 years but there are three major discoveries/inventions that really lifted the game of astronomy. First was the invention of the telescope by Hans Lippershey. After this discovery, Galileo was the first person to turn them skywards and what followed is history. Second was the Laws of Planetary Motion by Kepler. The reason why this was important is because it was one of the first formal amalgamation of classical mechanics and astronomy. These laws are the pillars of the branch of astronomy, called celestial mechanics. Third was none other than the Hubble’s law. Let us learn about this third discovery!

Hubble’s law is basically an observation that tells the behaviour of deep space objects. By the word deep space, I mean objects that are at a distance of more than 10 mega parsecs. 1 mega parsec is 3,260,000 light years and 1 light year is 6 trillion miles. Surprised? Welcome to the universe! So deep sky objects are really really far away. This law tells us that farther an object is from us, faster it is moving away (receding) from us. This is exactly what the above equation tells us. The velocity of recession is directly proportional to the distance of the object from us.

Also Read: What Does Chandrasekhar Limit in Astrophysics Really Mean?

Hubble actually calculated the distance of the object in deep space and found a rough relationship between the wavelength of a known hydrogen transition in galaxy and that in a stationary reference frame. So he just plotted a straight line graph between the object’s recession velocity and its distance. He presented his findings in a conference and did not comment on what it actually meant. So it was basically an empirical observation.

Later it was found that Hubble actually provided the proof of expanding universe. Prior to him, the law was theoretically derived by Alexander Friedmann in 1922, using general relativity. Then in 1927, two years before Hubble published his own article, Georges Lemaitre proposed the expansion of the universe and suggested an estimated value of the rate of expansion. This was corrected by Hubble and hence, it is now known as the Hubble’s law.

The word Hubble’s constant is a misnomer. It is a constant only in space and not in time. The value of this constant is changing as the universe is evolving. The term H with the subscript 0 actually defines its value for present day. In an accelerating expanding universe, the age of the universe is linked with the reciprocal of the Hubble’s constant. Our calculations show that the value of 1/H is indeed very close to the age of the universe.

There is one final piece of information that I will add. Many people ask the question: **“If galaxies are moving away from us, then why is Andromeda galaxy moving towards us? Why is it showing a blueshift?”**

Well, the answer lies in the Hubble’s law itself. Read the law once again carefully. It has a word “deep space” in it. Remember, Hubble’s law is good for objects only in deep space i.e. at a distance of about 10 million parsecs. The gravitational attraction between our galaxy and those galaxies in deep space is negligible (almost zero). However, Andromeda is a distance of only 778 kilo parsecs. At such a distance, the gravitational attraction of the local group of galaxies plays a crucial role and hence Andromeda is showing a blueshift, i.e, moving towards the Milky Way galaxy. It is moving towards us a a rate of 140 Km/s and will ultimately collide with us after about 5 billion years.

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