The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

Show that the critical density of the universe is

\[\frac{{3{H^2}}}{{8\pi G}}\]

where H is the Hubble parameter and G is the gravitational constant.

interstellar gas/dust «from earlier supernova»

gravitational attraction between particles

if the mass is greater than the Jean’s mass/M_j the interstellar gas coalesces

as gas collapses temperature increases leading to nuclear fusion

MP3 can be expressed in terms of potential and kinetic energy

fluctuations in CMB due to differences in temperature/mass/density

during the inflationary period/epoch/early universe

leading to the formation of galaxies/stars/structures

gravitational interaction between galaxies can lead to collision

[Max 3 Marks]

ALTERNATIVE 1

kinetic energy of galaxy \(\frac{1}{2}\)mv² = \(\frac{1}{2}\)mH²r² «uses Hubble’s law»

potential energy = \(\frac{{GMm}}{r}\) = G\(\frac{4}{3}\)\(\pi \)r³\(\rho \frac{m}{r}\) «introduces density»

KE=PE to get expression for critical \(\rho \)

ALTERNATIVE 2

escape velocity of distant galaxy v = \(\sqrt {\frac{{2GM}}{r}} \)

where H₀r = \(\sqrt {\frac{{2GM}}{r}} \)

substitutes M =  \(\frac{4}{3}\)\(\pi \)r³\(\rho \) to get result