The formation of stars

Stars form from the immense low-density gas clouds that lie in the Universe between the existing stars. The photograph shows one such cloud - part of M42 – the Orion nebula. A star the size of our Sun might form from a cloud that was initially a few tens of light years across and with a mass of about 2x10³⁰ kg (that of our Sun) the density of these clouds is unimaginably small – about 5x10^{- 13} kgm^-3.

As these clouds condense under gravitational attraction the particles within it accelerate and collide with each other and so their random kinetic energy increases. This means an increase in their thermal energy.

The increase in thermal energy (E) of a particle whose kinetic energy increases by ΔE is given by the equation:

ΔE = 3kΔT/2

where k is the Boltzmann constant.

However from gravitational theory the gain in kinetic energy for a particle 'falling' from a radius R to a radius r is:

ΔE = 3kΔT/2 = GMm/r – GMm/R

but substituting values you will find that GMm/R is very much smaller than GMm/r and so we can ignore it. This means that the equation becomes:

3kΔT/2 = GMm/r and so DT/ = 2GMm/3kr

M is the mass of the whole cloud (assumed spherical) and m is the mass of a proton on the outer edge of the cloud.

Substituting the following values:
G = 6.67x10¹¹ Nm²kg-², M = 2x10³⁰ kg, m = 1.7x10^-27 kg, r = 7x10⁸ m, k = 1.38x10^-23 JK^-1 gives:

ΔT = 1.6x10⁷ – a sufficiently high temperature for the onset of nuclear fusion under the conditions of high pressure within the centre of the 'infant' star.