Newtonian Cosmology – FRIEDMANN EQUATIONS

Newtonian Cosmology – FRIEDMANN EQUATIONS

Cosmology, might be new subject to student who are new to the Astronomy or the people who start to read about astronomy from this article. My advice is you should start beginning. But if you didn’t get it the best thing is leave as it is and moving to quite fascinating subject such as Observation Astronomy. Unless you’ll think that the astronomy is the worst subject in the world. On the other hand you’ll find the articles about Cosmology is in English. Because there are several terms bit funny in Sinhala. So let’s start.

In this article series I try to give a brief idea about Newtonian cosmology, Friedmann equations, History and future of universe and Expansion of universe based on the Friedmann equations.
Cosmology can be divided in to two parts based on the theories that we used.

They are,
1. Newtonian Cosmology
2. Relativistic Cosmology

Now consider the spherical region of radius a, total mass M and constant density ρ. A galaxy of mass m is at edge of the region from the observer at a radius R.

Now using Energy conservation and the Newton’s second law of motion we can derive the first two Friedmann equations as mentioned below

Where k is constant which has values of ±1 or 0 (we will discuss about k in future articles.), p is pressure which come from the fluid equation.
By using equation 1 and 2 we can derive 3rd Friedmann equation,

In next articles we will go through the derivation of those equations, History and future of universe and Expansion of universe based on the Friedmann equations.

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